## Abstracts

Poster Abstracts | Talk Abstracts

### Quantum supremacy

**Presenting Author**: Scott Aaronson, Texas, Austin**Contributing Author(s)**: Lijie Chen

In the near future, there will likely be special-purpose quantum computers with 40-50 high-quality qubits. In this talk, I'll discuss general theoretical foundations for how to use such devices to demonstrate "quantum supremacy": that is, a clear quantum speedup for *some* task, motivated by the goal of overturning the Extended Church-Turing Thesis (which says that all physical systems can be efficiently simulated by classical computers) as confidently as possible.

Read this article online: https://arxiv.org/abs/1612.05903

(Session 10 : Saturday from 8:30am - 9:15am)

### Towards quantum information transport through a classical conductor

**Presenting Author**: Da An, University of California, Berkeley**Contributing Author(s)**: Dylan Gorman, Erik Urban, Maya Lewin-Berlin and Hartmut Haeffner

Establishing quantum links between separately trapped ions is a significant step towards scalable trapped ion quantum computation. Here, we present our design, simulation, and ongoing implementation of a novel surface ion trap for studying quantum correlations between separate trapping sights through an ordinary conducting wire. This is a challenging task since the thermal noise in the wire is much greater than the motional ion energy, but as long as the decoherence sources are minimized, we can achieve quantum coupling through the wire. We also include intermediate steps towards this goal, such as characterizing the stability of our novel trap, which has variable trapping height, and establishing a classical link through the wire. This technology may lead to quantum computation with mixed ion species, sympathetic cooling of ion species that cannot be co-trapped, and hybrid quantum devices that couple ion based qubits with superconducting qubits.

### Techniques for scaling trapped-ion QIP

**Presenting Author**: Christopher Ballance, Oxford

Demonstration experiments on small numbers of qubits are approaching the fidelity needed for large scale computation. However scaling these systems to the size needed to build a useful quantum computer presents significant challenges. We are mounting a two-pronged attack on these challenges for trapped-ion systems: using microwave control fields instead of lasers to simplify the control requirements, and pursing a networked modular scheme based on many simple nodes with complexity close to the current state of the art. Here we present the realization of high-fidelity single- and two-qubit gates (99.9999% and 99.7% respectively) driven with microwaves generated by electrodes embedded in the ion-trap chip, and discuss the potential for scaling this design. Furthermore, we present initial results on a modular architecture, involving mapping information from a memory qubit to an interface qubit, and from an interface qubit to a photon.

(Session 11 : Saturday from 10:15am - 11:00am)

### Experimentally generated random numbers certified by the impossibility of superluminal signaling

**Presenting Author**: Peter Bierhorst, NIST Boulder**Contributing Author(s)**: Lynden K. Shalm, Alan Mink, Stephen Jordan, Yi-Kai Liu, Andrea Rommal, Scott Glancy, Bradley Christensen, Sae Woo Nam, and Emanuel Knill

Random numbers are an important resource for applications such as numerical simulation and secure communication. However, it is difficult to certify whether a physical random number generator is truly unpredictable. Here, we exploit the phenomenon of quantum entanglement in a loophole-free photonic Bell test experiment to obtain data containing randomness that cannot be predicted within any non-superdeterministic physical theory that does not also allow the sending of signals faster than the speed of light. To certify and quantify the randomness, we develop a new protocol that performs well in an experimental regime characterized by low violation of Bell inequalities. Applying an extractor function to our data, we obtain 256 new random bits, uniform to within 10^{-3}.

### Quantum simulation and sensitive force detection using hundreds of ions in a Penning trap

**Presenting Author**: Justin Bohnet, National Institute of Standards and Technology**Contributing Author(s)**: K. Gilmore, B. C. Sawyer, J. W. Britton, M. L. Wall, M. Gaerttner, A. Safavinaini, M. Foss-Feig, A. M. Rey and J. J. Bollinger

Systems of trapped ions have made substantial progress as simulators of quantum magnetic models. But increasing a simulator’s complexity by controlling more than 30 ions is an outstanding challenge. Here we perform quantum simulations of long range Ising spin models far from equilibrium using hundreds of beryillium ions in a Penning trap. We benchmark the fidelity of the quantum simulator by producing entangled states in planar arrays of ions, directly observing spin- squeezed states with up to 6.0 dB of spectroscopic enhancement. We show how the ability to time-reverse the spin dynamics allows for tracking the spread of quantum information through the system by measuring out-of-time-order correlation functions. To study the stability of the center-of-mass mode of the ions, one of the limitations to our simulations, we use the spin-motion coupling of the ions to sense small electric fields, which we present in terms of detection of sub-yoctoNewton forces. In the future, we will apply these techniques to simulations of non-trivial spin models, such as the XY model and the transverse field Ising model with variable range interactions.

### Necessary adiabatic run times in quantum optimization

**Presenting Author**: Lucas Brady, UC Santa Barbara**Contributing Author(s)**: Wim van Dam

Quantum annealing is guaranteed to find the ground state of optimization problems in the adiabatic limit. Recent work [Phys. Rev. X 6, 031010 (2016)] has found that for some barrier tunneling problems, quantum annealing can be run much faster than is adiabatically required. Specifically, an n-qubit optimization problem was presented for which a non-adiabatic, or diabatic, annealing algorithm requires only constant runtime, while an adiabatic annealing algorithm requires a runtime polynomial in n. Here we show that this non-adiabatic speed-up is a direct result of a specific symmetry in the studied problems. In the more general case, no such non-adiabatic speed-up occurs. We furthermore show why the special case achieves this speed-up compared to the general case. We conclude with the observation that the adiabatic annealing algorithm has a necessary and sufficient runtime that is quadratically better than the standard quantum adiabatic condition suggests.

Read this article online: https://arxiv.org/abs/1611.02585

(Session 9c : Friday from 4:45pm - 5:15pm)

### Quantum Gibbs sampling

**Presenting Author**: Fernando Brandao, IQIM, Caltech

Quantum thermal states, aka Gibbs states, are fundamental objects in physics. I will discuss recent results on the role of Gibbs states on quantum information theory. First I will show how we can use them to give quantum speed-ups for semidefinite programming. Then I will discuss how to prepare Gibbs states efficiently on a quantum computer.

### Practical quantum simulators for quantum field theory

**Presenting Author**: Gavin Brennen, Macquarie University**Contributing Author(s)**: G. Pupillo, E. Rico, T. M. Stace, S. Singh and D. Vodola

An exciting prospect for quantum simulators is to probe physics that is difficult to compute using analytical methods or classical numerical simulations. An especially compelling direction is to simulate quantum field theory. I will discuss two new approaches in this regard. The first is an analogue quantum simulation of 2+1 dimensional U(1) lattice gauge theory using superconducting fluxonium arrays which allows for non destructive measurements of non local order parameters including space like Wilson loops and 'tHooft strings. The second is a digital quantum simulation of the holographic principle for a critical 1+1 dimensional conformal field theory. The method uses an encoding based on Daubechies wavelets and can be realized as a multimode entangled Gaussian state of continuous variable systems using e.g. trapped ions or frequency modes in photonic networks. Extensions to interacting field theory are described.

Read this article online: https://arxiv.org/abs/1512.06565, https://arxiv.org/abs/1606.05068

### Randomized benchmarking with restricted gate sets

**Presenting Author**: Winton Brown, Northrop Grumman Corporation**Contributing Author(s)**: Bryan Eastin

Standard randomized benchmarking protocols require sampling from a unitary 2-design, which is not always practical. In this talk I examine randomized benchmarking protocols based on subgroups of the Clifford group that are not unitary 2-designs. I show in a variety of cases that one can benchmark the error probability to within a small factor that rapidly approaches unity as the number of qubits in the benchmarking experiment grows.

### Classical simulation of quantum circuits by dynamical localization: analytic results for Pauli-observable propagation in time-dependent disorder

**Presenting Author**: Adrian Chapman, CQuIC, New Mexico**Contributing Author(s)**: Akimasa Miyake

Matchgate circuits have been extensively studied due to (i) their classical simulability properties and (ii) their close connection to the physics of noninteracting fermions in one dimension. We extend (i) by introducing a classically efficient algorithm for the Lieb-Robinson commutator norm of a local observable under Heisenberg evolution by a nearest-neighbor matchgate circuit. This is surprising in light of the fact that the Heisenberg evolution itself cannot even be stored efficiently by a classical computer in general. We apply our result by (ii) to the study of fermions propagating through a one-dimensional lattice in the presence of spatio-temporally fluctuating disorder and demonstrate a method to classify this propagation into either the localized, diffusive, or ballistic dynamical phase. We find that our results coincide with known classifications of Anderson localization in the statically disordered case, but the localized phase can also be seen to survive in the presence of weakly fluctuating disorder. We expect our results to inspire the application of localization as a classical simulation technique for more general classes of quantum circuits.

(Session 12 : Saturday from 2:15pm - 2:45pm)

### Coupled layer construction of three dimensional topological codes with 'Fractons'

**Presenting Author**: Xie Chen, IQIM, Caltech

Three dimensional quantum codes can exhibit exotic topological properties compared to their two dimensional counterparts. In two dimensions, topological excitations are point like and can move freely in space, inducing nontrivial braiding statistics as they wind around each other. In three dimensions, topological excitations can also be point like. But it has been discovered that sometimes their motion are highly restricted, such that they can only move in a sub-dimensional manifold or their motion are correlated with each other. Such point excitations are dubbed 'fractons' and in this talk we try to address the question of where they come from. We show that one class of 'fractons' can emerge by coupling layers of two dimensional topological codes and inducing a condensation of 'particles loops'. By making connections between the 'fracton' topological order and the more conventional two dimensional ones, we are able to generalize 'fractons' models beyond the stabilizer framework.

(Session 12 : Saturday from 1:30pm - 2:15pm)

### Resonant transition based quantum computation

**Presenting Author**: Chen-Fu Chiang, State University of New York Polytechnic Institute**Contributing Author(s)**: Chang Yu Hsieh

In this article we assess a novel quantum computation paradigm based on the resonant transition (RT) phenomenon commonly associated with atomic and molecular systems. We thoroughly analyze the intimate connections between the RT-based quantum computation and the well-established adiabatic quantum computation (AQC). Both quantum computing frameworks encode solutions to computational problems in the spectral properties of a Hamiltonian and rely on the quantum dynamics to obtain the desired output state. We discuss how one can adapt any adiabatic quantum algorithm to a corresponding RT version and the two approaches are limited by different aspects of Hamiltonians' spectra. The RT approach provides a compelling alternative to the AQC under various circumstances. To better illustrate the usefulness of the novel framework, we analyze the time complexity of an algorithm for 3-SAT problems and discuss straightforward methods to fine tune its efficiency.

Read this article online: http://web.cs.sunyit.edu/~chiangc/Papers/RTQC_rev_1.pdf

### Quantum light matter interfaces using erbium doped yttrium orthosilicate

**Presenting Author**: Ioana Craiciu, IQIM, Caltech**Contributing Author(s)**: Evan Miyazono (co-first author),
Jake Rochman,
Tian Zhong and
Andrei Faraon

Rare earth quantum light-matter interfaces (QLMIs), consisting of optical resonators coupled to ensembles of rare earth ions, are uniquely suited for various quantum information applications, including quantum memories and quantum optical-to-microwave transducers. Among rare earths, erbium is particularly appealing due to its highly coherent resonance within a telecom band, allowing integration with existing optical communication technology and infrastructure. Micro-resonator QLMIs have various advantages over bulk rare earth crystals. They permit on-chip integration with other elements, such as microwave resonators for optical-to-microwave conversion. In the context of quantum memories, they provide enhanced coupling to the ions, and when the resonator is impedance matched to the ions, they can raise the theoretical memory efficiency to 100%. For spectral hole-burning based quantum memories, the coupling of rare earth ions to the resonator can provide improved memory initialization via Purcell enhancement of optical lifetimes. We present nano scale quantum light matter interfaces in erbium doped yttrium orthosilicate (Er:YSO). Our two types of devices take the form of nanobeam photonic crystal resonators milled directly into Er:YSO and of amorphous silicon ring resonators on Er:YSO. This latter hybrid design represents our newest efforts in a scalable on chip QLMI architecture. We have fabricated ring resonators with measured quality factors of over 10^5, and evanescent coupling to an ensemble of erbium ions characterized by a cooperativity of 0.54. The nanobeam resonator design has a measured quality factor of around 25,000, and a cooperativity of 2.4. We present simulation and experimental results of the optical properties of these cavities, and their coupling to erbium ions, including a demonstration of Purcell enhancement of the erbium telecom transition. We then analyze their potential as quantum memories.

Read this article online: http://scitation.aip.org/content/aip/journal/apl/108/1/10.1063/1.4939651

(Session 13 : Saturday from 3:15pm - 3:45pm)

### Toward a quasi-probability representation of matchgate circuits

**Presenting Author**: Ninnat Dangniam, Center for Quantum Information and Control (CQuIC), University of New Mexico **Contributing Author(s)**: Christopher Ferrie and Carlton Caves

Quantum circuits composed of a particular class of gates called matchgates range from circuits that are classically simulatable to those that can perform universal quantum computation. Matchgate computation can also be understood from a more physical point of view as a computation with fermionic modes. We attempt to construct a quasi-probability (phase space) representation of quantum theory in which classically simulatable matchgate circuits are represented positively i.e. non-contextually.

### Approximate reversal of quantum Gaussian dynamics

**Presenting Author**: Siddhartha Das, Louisiana State University**Contributing Author(s)**: Ludovico Lami, and Mark M. Wilde

Recently, there has been focus on determining the conditions under which the data processing inequality for quantum relative entropy is satisfied with approximate equality. The solution of the exact equality case is due to the work of Petz, who showed that the quantum relative entropy between two states stays the same after the action of a quantum channel if and only if there is a {\it reversal channel} that recovers the original states after the channel acts. Furthermore, this reversal channel can be constructed explicitly and is now called the "Petz recovery map". Recent developments have shown that a variation of the Petz recovery map works well for recovery in the case of approximate equality of the data processing inequality. Our main contribution here is a proof that bosonic Gaussian states and channels possess a particular closure property, namely, that the Petz recovery map associated to a bosonic Gaussian state and a bosonic Gaussian channel is itself a bosonic Gaussian channel. We furthermore give an explicit construction of the Petz recovery map in this case, in terms of the mean vector and covariance matrix of a given Gaussian state and the Gaussian specification of a given Gaussian channel.

### Experimental study of an optimized Kennedy receiver for multiple coherent states

**Presenting Author**: Matthew DiMario, Center for Quantum Information and Control (CQuIC), University of New Mexico**Contributing Author(s)**: F. E. Becerra

Non-Gaussian receivers for coherent states that have discrimination errors below the Quantum Noise Limit (QNL) are a valuable tool in communication. Discrimination of coherent states is fundamentally impossible to do with zero probability of error because of their intrinsic overlap. Therefore, the goal is to design and demonstrate discrimination strategies that minimize the error probability and outperform the perfect Heterodyne (QNL) measurements. We implement a strategy proposed by Sasaki et al. (PRA 86, 042328 (2012)) that is based on testing multiple hypotheses at once within a single-shot measurement to discriminate between quaternary phase-shift-keyed (QPSK) coherent states. The receiver is based on three displacement operations and single photon counting and in principle achieves errors below the QNL without the need for any feedback operations. The three displacement amplitudes are independently optimized to yield the absolute minimum overall probability of error given experimental imperfections. Our results align well with the theoretical predictions and allow us to identify how the critical parameters, such as visibility of the displacement operations and detection efficiency, influence the error probability. We are also able to identify what is required of these parameters for the strategy to out-perform a Heterodyne (QNL) measurement.

### Conditional mutual information of bipartite unitaries and scrambling

**Presenting Author**: Dawei Ding, Stanford**Contributing Author(s)**: Patrick Hayden, and Michael Walter

One way to diagnose chaos in bipartite unitary channels is via the tripartite information of the corresponding Choi state, which for certain choices of the subsystems reduces to the negative conditional mutual information (CMI). We study this quantity from a quantum information-theoretic perspective to clarify its role in diagnosing scrambling. When the CMI is zero, we find that the channel has a special normal form consisting of local channels between individual inputs and outputs. However, we find that arbitrarily low CMI does not imply arbitrary proximity to a channel of this form, although it does imply a type of approximate recoverability of one of the inputs. When the CMI is maximal, we find that the residual channel from an individual input to an individual output is completely depolarizing when the other input is maximally mixed. However, we again find that this result is not robust. We also extend some of these results to the multipartite case and to the case of Haar-random pure input states. Finally, we look at the relationship between tripartite information and its Renyi-2 version which is directly related to out-of-time-order correlation functions. In particular, we demonstrate an arbitrarily large gap between the two quantities.

Read this article online: https://arxiv.org/abs/1608.04750

### Speed limits for quantum control of local spin systems

**Presenting Author**: Jeffrey Epstein, UC Berkeley**Contributing Author(s)**: Birgitta Whaley

We show that the fundamental limits on quantum many-body dynamics from the Lieb-Robinson bound yield speed limits on two quantum control tasks, state transfer and entanglement sharing. We derive analytic speed limits on these tasks in nearest-neighbor coupled spin chains and lattices, providing optimal speeds for comparison with numerical optimal control results in the many-body setting.

### Protecting quantum information from noise -- a passive approach

**Presenting Author**: Ryan Epstein, Northrop Grumman

The steady improvement in coherence times and gate fidelities over the past several years has largely been due to reductions in noise and energy loss mechanisms. Achieving highly integrated quantum hardware, however, may necessitate tolerance of noisier signals and dirtier materials. Over the past couple of years, we have been looking at practical ways to design noise-resilience into quantum devices. In this talk, I’ll present theoretical work on methods for performing gates that are robust to control noise and that reduce qubit overhead and coupling complexity, building off of Bacon and Flammia’s Adiabatic Gate Teleportation technique. I’ll also talk about more fully noise-protected qubits and gates using blocks of qubits coupled together in Bacon-Shor-like codes.

(Session 9a : Friday from 5:15pm - 5:45pm)

### Practical, reliable error bars in quantum tomography

**Presenting Author**: Philippe Faist, Institute for Quantum Information and Matter, Caltech, Pasadena CA 91125, USA**Contributing Author(s)**: Renato Renner (Institute for Theoretical Physics, ETH Zurich, 8093 Switzerland)

Precise characterization of quantum devices is usually achieved with quantum tomography. However, most methods which are currently widely used in experiments lack a well-justified error analysis, especially in the regime of finite data. For example, maximum likelihood estimation does not provide any estimation of the error of the tomography procedure, and is typically complemented by an ad hoc method such as resampling/bootstrapping. We propose a new method which provides well-justified error bars. The error bars are practical, in that the error bars are typically of the same order of magnitude as those obtained by a resampling analysis. The error bars are determined for a figure of merit (such as the fidelity to a target state) which can be chosen freely. Our method takes as input the measurement data from the experiment, and runs an analysis based on the concept of confidence regions. We then introduce a new representation of the output of the tomography procedure, the quantum error bars. This representation is (i) concise, being given in terms of few parameters, (ii) intuitive, providing a fair idea of the "spread" of the error, and (iii) useful, containing the necessary information for constructing confidence regions. We present an algorithm for computing this representation and provide ready-to-use software. Our procedure is applied to actual experimental data obtained from two superconducting qubits in an entangled state, demonstrating the applicability of our method.

Read this article online: https://arxiv.org/abs/1509.06763

### Four wave mixing in a cold atomic ensemble for the generation of correlated photons pairs

**Presenting Author**: Andrew Ferdinand, CQuIC, New Mexico**Contributing Author(s)**: Francisco Elohim Becerra

Photon pairs generated by spontaneous four-wave mixing (FWM) in atomic ensembles provide a natural path toward quantum light-matter interfaces due to their intrinsic compatibility with atomic quantum memories. These photons are narrow band and have frequencies at or close to atomic resonances, and their temporal and spectral properties can be efficiently tailored to make them compatible with specific quantum memory protocols [1]. In addition, conservation of orbital angular momentum (OAM) in the FWM process enables the generated photons to form entangled qudits, which have applications in high-dimensional quantum information and communication. We study experimentally the generation of light from FWM in a cold ensemble of cesium atoms. We investigate theoretically the correlation and distribution of OAM modes occupied by photon pairs produced in spontaneous FWM as a function of experimentally accessible parameters of the process. These studies provide the basis for future investigations of photonic OAM correlation generated with FWM in atomic ensembles. [1] Du et al., Phys. Rev. Lett. 100, 183603. (2008)

(Session 13 : Saturday from 3:45pm - 4:15pm)

### Secrets of PRL

**Presenting Author**: Robert Garisto, Physical Review Letters, APS

I'll give a view inside of Physical Review Letters (PRL). I'll describe how the review process works, how we pick our highlighted papers, and how things have changed since -- notably how we are asking more of authors, referees, and ourselves. I will also present some illuminating statistics and talk about journal metrics. If there is time, I will give you some advice on how to succeed with your PRL submissions.

(Session 14 : Saturday from 5:30pm - 6:15pm)

### The statistical framework for "Chained Bell Inequality Experiment with High-Efficiency Measurements"

**Presenting Author**: Scott Glancy, National Institute of Standards and Technology**Contributing Author(s)**: P. Bierhorst, T. R. Tan, Y. Wan, S. Erickson, D. Kienzler, E. Knill, D. Leibfried, and D. J. Wineland

We recently performed correlation measurements on two 9Be+ ions that violate a chained Bell inequality obeyed by any local-realistic theory. The correlations can be modeled as derived from a mixture of a local-realistic probabilistic distribution and a distribution that violates the inequality. This poster describes the statistical framework used to quantify the maximum local-realistic fraction in the observed distribution without assuming fair-sampling of the measurements or that the distribution was independent and identical across trials. This framework excludes models of our experiment whose local-realistic fraction is above 0.327 at the 95 % confidence level. Supported by IARPA, ONR, and the NIST Quantum Information program

### Single-shot quantum resource theories

**Presenting Author**: Gilad Gour, Calgary

One of the main goals of any resource theory such as entanglement, quantum thermodynamics, quantum coherence, and asymmetry, is to find necessary and sufficient conditions (NSC) that determine whether one resource can be converted to another by the set of free operations. In this talk I will present such NSC for a large class of quantum resource theories which we call affine resource theories (ARTs). ARTs include the resource theories of athermality, asymmetry, and coherence, but not entanglement. Remarkably, the NSC can be expressed as a family of inequalities between resource monotones (quantifiers) that are given in terms of the conditional min entropy. The set of free operations is taken to be (1) the maximal set (i.e. consists of all resource non-generating (RNG) quantum channels) or (2) the self-dual set of free operations (i.e. consists of all RNG maps for which the dual map is also RNG). As an example, I will discuss the applications of the results to quantum thermodynamics with Gibbs preserving operations, and several other ARTs. Finally, I will discuss the applications of these results to resource theories that are not affine.

Read this article online: https://arxiv.org/abs/1610.04247

(Session 9b : Friday from 5:45pm - 6:15pm)

### QInfer: Statistical inference software for quantum applications

**Presenting Author**: Christopher Granade, Sydney**Contributing Author(s)**: Christopher Ferrie, Ian Hincks, Steven Casagrande, Thomas Alexander, Jonathan Gross, Michal Kononenko and Yuval Sanders

Characterizing quantum systems through experimental data is critical to applications as diverse as metrology and quantum computing. Analyzing this experimental data in a robust and reproducible manner is made challenging, however, by the lack of readily-available software for performing principled statistical analysis. In this talk, we introduce an open-source library, QInfer, to address this need and to improve the robustness and reproducibility of characterization experiments. We will show examples of how our library makes it easy to analyze data from tomography, randomized benchmarking, and Hamiltonian learning experiments either in post-processing, or online as data is acquired. We will discuss how QInfer also provides functionality for predicting the performance of proposed experimental protocols from simulated runs. By delivering easy-to-use characterization tools based on principled statistical analysis, QInfer helps address many outstanding challenges facing quantum technology. All source code and examples for this talk may be found online at qinfer.org.

Read this article online: https://arxiv.org/abs/1610.00336

(Session 9b : Friday from 3:45pm - 4:15pm)

### Semiclassical and quantum control of chaos

**Presenting Author**: Sacha Greenfield, Carleton College**Contributing Author(s)**: Alexei Stepanenko, Jessica Eastman, Andre Carvalho (Department of Quantum Science, Australian National University, Canberra, Australia), Bibek Pokharel and Arjendu Pattanayak (Department of Physics, Carleton College, Northfield, Minnesota)

Chaotic systems contain infinitely many unstable periodic trajectories that only appear for very particular initial conditions. Given a system starting at arbitrary initial conditions, we can “control” the system onto one of these trajectories by small, properly timed perturbations in system parameters. While previously only classical chaotic systems have been controlled, we aim to control chaos in a regime where the system is also quantum mechanical. We have controlled chaos in computer simulations of the classical and semiclassical damped driven double-well Duffing oscillators, and are currently implementing control using noisy semiclassical versions and stochastic Schrodinger equation trajectories of the same system.

### Rank deficiency and the Euclidean geometry of quantum states

**Presenting Author**: Jonathan A Gross, Center for Quantum Information and Control (CQuIC), University of New Mexico**Contributing Author(s)**: Carlton M Caves

Quantum state tomography requires characterizing a collection of parameters whose size grows rapidly with the size of the quantum system under consideration. In practice one hopes that prior information about the system can reduce the number of parameters in need of characterization—for example, one might expect to find high-quality quantum systems in states of low rank. Interest in tomographic schemes that return rank-deficient estimates leads us to explore some geometric properties of the space of quantum states that are analogous to solid angles in three-dimensional Euclidean geometry.

### Fundamental percolation thresholds for ballistic linear optical quantum computing

**Presenting Author**: Saikat Guha, Raytheon BBN Technologies

Any quantum algorithm can be implemented by an adaptive sequence of single node measurements on an entangled cluster of qubits in a square lattice topology. Photons are a promising candidate for encoding qubits but assembling a photonic entangled cluster with linear optical elements relies on probabilistic operations.

Read this article online: https://arxiv.org/abs/1701.03775

### Optical CNOT gate from two level system

**Presenting Author**: Dawit Hailu, Ben Gurion University of the Negev

The solution of a two level system driven by a Laser in the adiabatic limit is determined using third order Magnus expansion. We made the assumption that the laser is on resonance or close to resonance with the Bohr transition. As a consequence of which we are able to obtain a Hamiltonian which commute with itself at different times. We solve the problem using the Sylvester Formula where we make use of the eigenvalues. We propose that the dynamics mimics the behaviour of CNOT gate. To achieve this we make use of the observables (Population and coherences) as input/output of the gate.

### Improved spin squeezing of an atomic ensemble through internal state control

**Presenting Author**: Daniel Hemmer, Arizona**Contributing Author(s)**: Senthilnathan Lingasamy, Ezad Shojaee, Ivan Deutsch, and Poul Jessen

Squeezing of collective atomic spins is typically generated by quantum backaction from a QND measurement of the relevant spin component. In this scenario the degree of squeezing is determined by the measurement resolution relative to the quantum projection noise (QPN) of a spin coherent state (SCS). When starting from a SCS our current experiment generates ~3dB of metrologically relevant spin squeezing, closely matching theoretical predictions. Going forward, our main objective is to use control of the internal atomic spin to improve squeezing. For example, we can coherently map the internal spins from the SCS to a “cat” state, which increases the QPN by a factor of 2f=8 relative to the SCS [1]. This leads to increased backaction and entanglement produced by our QND measurement. The squeezing generated in the cat state basis can in principle be mapped back to the SCS basis where it will correspond to squeezing of the physical spin. A preliminary experimental result suggests that up to 8dB of metrologically useful squeezing can be generated in this way. However, more complex internal state preparation brings additional vulnerability to control errors. The main source of error for internal state control in our experiment appears to be fluctuating background magnetic fields at frequencies up to tens of kHz. We are currently developing a toolbox of composite pulses in order to diagnose and compensate for their presence. [1] L.M. Norris et al., Phys. Rev. Lett. 109, 173603 (2012)

### Realizable quantum spatial search

**Presenting Author**: Itay Hen, University of Southern California

Grover's unstructured search algorithm is one of the best examples to date for the superiority of quantum algorithms over classical ones. Its implementability however has been questioned by many due to its oracular nature. In this talk, I propose a mechanism to carry out a quantum adiabatic variant of Grover's search algorithm using a single boson placed in an optical lattice.

### Benchmarking a qutrit

**Presenting Author**: Ian Hincks, Institute for Quantum Computing, Waterloo, Canada**Contributing Author(s)**: Christopher Granade and David G. Cory

Randomized Benchmarking and related twirling-based protocols have become mainstays in assessing the quality of quantum logic gates. These protocols physically implement symmetrization by unitary groups in such a way as to exponentially reduce the number of parameters describing a gate or gateset down to just a few, including average fidelity or unitarity. In this talk, we provide a holistic account of performing randomized benchmarking on an Nitrogen Vacancy defect in diamond. This quantum system has three controllable energy levels, and several physical characteristics which make it ideal for experimentally studying quantum control and inference. We discuss methodologies of cosine-modulated gate design with numerical optimal control, characterizing Hamiltonian parameters with Bayesian inference, and driving microwave transitions in the non-linear regime of an amplifier. We find a 72-element Clifford subgroup, which is the smallest 2-design sufficient for the randomized benchmarking and unitarity protocols. We show the results of these experiments, emphasizing that rigorous statistical analysis improves the credibility of parameter estimates.

### Decoherence-free quantum computing in Kondo-coupled optical tweezers

**Presenting Author**: Leonid Isaev, JILA, NIST, CU Boulder**Contributing Author(s)**: Y. Lin, B. J. Lester, C. A. Regal, and A. M. Rey

We propose a basis for decoherence-free quantum computing that uses neutral atoms and encodes qubits in the collective atomic spin and motional degrees of freedom. The physical qubit consists of three spin-\(\frac{1}{2}\) atoms in a double-well, two localized in the lowest vibrational mode and one atom in an excited delocalized state, subject to a staggered Zeeman field whose direction is opposite in the two traps. An interplay between this field gradient and exchange interactions gives rise to a local singlet-triplet degeneracy, and defines a logical qubit subspace. For strong interactions this subspace enjoys full protection against longitudinal magnetic-field noise, and is protected by an energy gap against transverse spin-flipping perturbations. Arbitrary single-qubit rotations are performed by virtue of resonant transfer of two-atom singlet-triplet states between the wells. Moreover, a two-qubit entangling control-z gate can be implemented. We design a qubit initialization protocol that employs Landau-Zener adiabatic tunneling to efficiently create a spin-singlet state in one well, and argue that our proposal can be realized using optical tweezers to create the double-well, hyperfine states of bosonic \(^{87} {\rm Rb}\) atoms to implement spin degrees of freedom, and laser-induced AC Stark shifts to impose the Zeeman field gradient.

### A circuit-based quantum search algorithm driven by transverse fields

**Presenting Author**: Zhang Jiang, NASA Ames

We designed a quantum search algorithm, giving the same quadratic speedup achieved by Grover's original algorithm; we replace Grover's diffusion operator (hard to implement) with a product diffusion operator generated by transverse fields (easy to implement). In our algorithm, the problem Hamiltonian (oracle) and the transverse fields are applied to the system alternatively. We construct such a sequence that the corresponding unitary generates a closed transition between two states; one has a big overlap with the initial state (even superposition of all states), and the other has a big overlap with the target state. Let N = 2^{n} be the size of the search space. The transition rate is of order O(N^{-1/2}), yielding a O(N^{1/2}) algorithm. Our algorithm belongs to a class of algorithms recently proposed by Farhi et al., namely the Quantum Approximate Optimization Algorithm (QAOA).

(Session 9c : Friday from 3:45pm - 4:15pm)

### Thresholds for universal concatenated quantum codes

**Presenting Author**: Tomas Jochym-O'Connor, California Institute of Technology**Contributing Author(s)**: Christopher Chamberland (IQC, University of Waterloo), Raymond Laflamme (IQC, University of Waterloo, Perimeter Institute)

Quantum computing algorithms will require fault-tolerance in order to suppress errors to sufficiently small levels for growing algorithmic complexity. Possible fault-tolerant implementations are far-ranging, all requiring qubit and computational resource overheads. Moreover, the level of precision required to implement a computation fault-tolerantly can differ greatly depending on the type of implementation used. In practice, the choice of fault-tolerant architecture will likely depend on the physical qubit architecture and the particular algorithm that is desired to be implemented, and as such it is of particular importance to understand the parameters at which fault-tolerant computation becomes possible for different proposals. The surface code is the leading contender for a fault-tolerant architecture due to the low weight of its stabilizer generators as well as its high fault-tolerance threshold rate, the physical error rate below which errors can be suppressed in an exponential manner. However, in order to complete a universal gate set for quantum computation, the surface code requires the preparation of a special ancillary state, a magic state. As such, to prepare a magic state with high fidelity, a process called magic state distillation is used, leading to high offline qubit overhead. In order to circumvent the need for magic state distillation, recent research efforts in quantum error correction have focused on finding alternative methods to implementing universal fault-tolerant gate sets. The first step towards determining whether these alternative methods will provide potential improvements over the surface code is to consider their fault-tolerance threshold. In this work, we present an upper bound on the asymptotic threshold for a concatenated scheme for universal fault-tolerant computation without magic state distillation. We show that the upper bound on the asymptotic threshold of \(1.28~\times~10^{-3}\) is competitive with other concatenated schemes, such as the Golay code.

Read this article online: https://arxiv.org/abs/1603.02704

### Dissipative quasi-local stabilization of generic pure quantum states

**Presenting Author**: Salini Karuvade, Dartmouth College**Contributing Author(s)**: Peter D. Johnson, Francesco Ticozzi, and Lorenza Viola

Dissipative control techniques with physically realizable resource constraints are attracting increasing attention across quantum information processing. A pure quantum state is called "dissipatively quasi-locally stabilizable" (DQLS) if it can be prepared by using purely dissipative continuous-time or discrete-time dynamics with respect to a fixed locality constraint. We characterize the DQLS nature of generic quantum states in finite dimensions for some simple yet important locality constraints, and provide conditions that must be satisifed if the states are DQLS, in more general cases. Our results shed light on approximate stabilization techniques for target pure states that are otherwise non-DQLS. Further, we describe how a state being DQLS ensures that the state is uniquely determined by its corresponding reduced states, illustrating a connection between the tasks of state preparation and local tomography. In the process, we give a constructive procedure for uniquely reconstructing a generic global state from its reduced neighborhood states, leveraging its stabilizability properties.

### Sub-shot noise measurement strategies for precision atomic sensors

**Presenting Author**: Mark Kasevich, Stanford

### Conditional mutual information and quantum steering

**Presenting Author**: Eneet Kaur, Louisiana State University**Contributing Author(s)**: Xiaoting Wang and Mark Wilde

Quantum steering has recently been formalized in the framework of a resource theory of steering, and several quantifiers have already been introduced. We propose the intrinsic steerability as an information-theoretic quantifier of steering that uses conditional mutual information to measure the deviation of a given assemblage from an assemblage having a local hidden-state model. We prove that this quantifier is a steering monotone (i.e., it is faithful, convex, and non-increasing under one-way local operations and classical communication). This suggests that the intrinsic steerability should find applications in protocols where steering is relevant. We then consider a restricted version of intrinsic steerability, which is a steering monotone under a restricted set of free operations. The restricted intrinsic steerability is additive with respect to tensor-product assemblages, and it is also monogamous.

### Symmetric Extendability of Quantum States and the Extreme Limits of Quantum Key Distribution

**Presenting Author**: Sumeet Khatri, Louisiana State University

We investigate QKD protocols with two-way communication that are based on the quantum phase of the well-known BB84 and six-state protocols. The quantum phase consists of the source sending quantum signals to the receiver, who measures them, leaving only classical data on both sides. Our goal is to find the highest value of the quantum bit error rate $Q$ for which two-way classical post-processing protocols on the data can create secret keys. Using the BB84 quantum phase, such protocols currently exist for $Q\leq\frac{1}{5}$. On the other hand, for $Q\geq\frac{1}{4}$ no such protocol can exist as the observed data is compatible with an intercept-resend channel. This leaves the interesting question of whether successful protocols exist in the gap $\frac{1}{5}\leq Q\leq\frac{1}{4}$. For the six-state protocol, the corresponding gap is known to be $\frac{5-\sqrt{5}}{10}\leq Q\leq\frac{1}{3}$. The current lower bounds have previously been shown to come from the symmetric extendability of the underlying quantum state shared between Alice and Bob after a two-way protocol called advantage distillation. Our work looks more generally at two-way post-processing protocols within the gap and asks the question of symmetric extendability of the states after them, for if they are symmetrically extendable then no secret key is possible. We have analytically constructed a symmetric extension throughout the gap for a particular class of protocols using a two-step procedure. Numerical analysis shows that for other arbitrary protocols the states are also symmetrically extendable throughout the gap. Moreover, for a very large percentage of protocols tested, our two-step construction works. We thus have very strong evidence to believe that there does not exist a two-way classical post-processing protocol to create a secret key beyond the current bounds, so that there is a point beyond which classical correlations of quantum origin are no longer useful in creating a secret key.

### Bounding the costs of quantum simulation of many-body physics in real space

**Presenting Author**: Ian Kivlichan, Harvard**Contributing Author(s)**: Nathan Wiebe, Ryan Babbush and Alán Aspuru-Guzik

Simulating many-particle dynamics, such as first-quantized quantum chemistry, with logarithmic dependence on the accuracy has proven to be a challenge. This is because the traditional approach, based on the quantum Fourier transform, introduces Hamiltonians with large max-norms. We solve this problem by using a new approach based on high-order finite difference formulae. This change makes the approach practical, and we further demonstrate that it can simulate n interacting particles using Õ(n^4) calculations of the pairwise interactions for a fixed spatial grid spacing, versus the Õ(n^5) time required by previous methods, assuming the number of particles is proportional to the number of orbitals. We also show that previous work has overlooked the fact that discretization errors can remove these exponential speedups, and address this by providing bounds on the discretization error and sufficient conditions to guarantee efficiency.

Read this article online: https://arxiv.org/abs/1608.05696

### Quantum circuits synthesis using lattices over number fields

**Presenting Author**: Vadym Kliuchnikov, Microsoft Research**Contributing Author(s)**: Sebastian Schoennenbeck

We present new algorithms for multiple qubit exact synthesis and exact state preparation. The algorithms work for the unitaries related to Clifford+T, Real Clifford+Controlled-H, and other similar gate sets. The algorithms run-time is polynomial in the bit-size of the input when the number of qubits is fixed. We prove the correctness of the algorithms for two qubits. For three and more qubits our algorithms either solve the problem in polynomial time or report that the solution was not found. We conjecture that the second outcome never happens based on empirical results. Experiments show that our algorithms produce circuits with a smaller number of T-gates than the algorithms for state preparation and exact synthesis by Giles and Selinger [10.1103/PhysRevA.87.032332].

### Q-plates for entangling photon spin and orbital angular momentum

**Presenting Author**: Hannah Knaack, Harvey Mudd College**Contributing Author(s)**: Morgan Mastrovich and Theresa W. Lynn

Photon polarization is a popular qubit variable, partially because it is so accessible, while orbital angular momentum is more difficult to manipulate and measure. However, the dimensionality of orbital angular momentum as a qudit is limited only by our technical ability to create and manipulate it. Q-plates shift orbital angular momentum in photons based on their incoming polarization, enabling the creation of entangled qubit-qudit systems on a single particle. A q-plate consists of a liquid crystal half-wave plates with a spatially varying axis. The “q” of the plate is defined by the number of complete revolutions the axis makes around the plate, and determines the magnitude of the angular momentum imparted. We are working to fabricate q-plates for use in quantum communications applications. We plan to create entanglement between the spin and orbital angular momentum degrees of freedom of a single photon, then to create multipartite entanglement on a photon pair produced by spontaneous parametric down-conversion.

### Squeezed state ansatz for quantum Sherrington-Kirkpatrick model and its applications to quantum annealing

**Presenting Author**: Sergey Knysh, NASA Ames

A question of fundamental importance in the physics of quantum annealing is its scalability. Recent work predicts a crossover from polynomial to exponential complexity for quantum annealing of spin glasses and relates the problem size at which this occurs to the "density" of spin glass bottlenecks [1]. An exact solution has been obtained for a toy problem, but rigorous analysis has remained elusive for realistic spin glass models where naive mean field fails. The present work takes a step in that direction by investigating thermodynamics of quantum Sherrington-Kirkpatrick model without resorting to replicas. The approach uses hard-core boson representation of a spin-1/2 model, with "modes" corresponding to delocalized eigenvectors of the interaction matrix. Hard-core nature of bosons is taken into account by appropriate renormalization factors. In this formulation, the ground state of paramagnetic phase is approximated by applying mode-dependent amount of squeezing/anti-squeezing to a vacuum, and the low-energy excitations correspond to Bogolyubov quasiparticles. Spin-glass phase is characterized by macroscopic occupation of a finite fraction of modes. Theoretical predictions are compared with known numerical results. [1] S. Knysh, "Zero-temperature quantum annealing bottlenecks in the spin-glass phase", Nature Communications 7, 12370 (2016).

(Session 9c : Friday from 5:15pm - 5:45pm)

### Joint measurement on the reflecting hyperplane in generalized probability theories

**Presenting Author**: Masatomo Kobayashi, Kyoto University**Contributing Author(s)**: Takayuki Miyadera

The existence of a pair of observables which is not jointly measurable is one of the most crucial aspects in quantum theory. The problem to find the necessary and sufficient conditions for effects to be coexistent is hard and has been only partially solved. It is, however, known that this peculiar property is not specific to the quantum theory in the general framework called Generalized Probability Theories. They have been studied from various points of view such as Bell's inequality, teleportaion, broadcasting and so on. In these articles, some authors indicated that the regular polygon systems are grouped into two series by the number of the vertexes, i.e. even or odd. We study the even-sided ones and show that the corresponding effect spaces have a nice symmetrical hyperplane which contains all (nontrivial) extremal effects and divides the whole effect space into reflection symmetric two subsets. We call it "reflecting hyperplane". Analyzing the coexistence problem in the polygon systems, we give necessary and sufficient conditions for a pair of effects on the hyperplane to be coexistent. Furthermore, we examine general systems (other than regular polygons) which have the reflecting hyperplane and show that the volume of the set of all effects coexistent with a nontrivial extreme effect is vanishing.

### Quantum optimal control of superconducting circuits

**Presenting Author**: Christiane Koch, Kassel

Quantum optimal control has grown into a versatile tool for quantum technology. Its key application is to identify performance bounds, for tasks such as state preparation or quantum gate implementation, within a given architecture. One such bound is the quantum speed limit, which determines the shortest possible duration to carry out the task at hand. Typical examples include the creation of entanglement or quantum error correction. To date, these tasks have been optimized for known, fixed parameters of the system. I will show that a fully numerical quantum optimal control approach can go even further and, using the most advanced control techniques, map out the entire parameter landscape for two superconducting transmon qubits. This allows to determine the global quantum speed limit for a universal set of gates with gate errors limited solely by the qubit lifetimes. While the interaction of qubits with their environment is typically regarded as detrimental, this does not need to be the case. I will show that the back-flow of amplitude and phase encountered in non-Markovian dynamics can be exploited to carry out quantum control tasks for a superconducting circuit that could not be realized if the system was isolated. The control is facilitated by a few strongly coupled, sufficiently isolated environmental modes. These can be found in a variety of solid-state devices other than superconducting circuits, for example in color centers in nanodiamonds or nanomechanical oscillators.

### Random bosonic states for robust quantum metrology

**Presenting Author**: Jan Kolodynski, ICFO**Contributing Author(s)**: M. Oszmaniec, R. Augusiak, C. Gogolin, A. Acin, and M. Lewenstein

We study how useful random states are for quantum metrology, i.e., whether they surpass the classical limits imposed on precision in the canonical phase sensing scenario. First, we prove that random pure states drawn from the Hilbert space of distinguishable particles typically do not lead to superclassical scaling of precision even when allowing for local unitary optimization. Conversely, we show that random pure states from the symmetric subspace typically achieve the optimal Heisenberg scaling without the need for local unitary optimization. Surprisingly, the Heisenberg scaling is observed for random isospectral states of arbitrarily low purity and preserved under loss of a fixed number of particles. Moreover, we prove that for pure states, a standard photon-counting interferometric measurement suffices to typically achieve resolutions following the Heisenberg scaling for all values of the phase at the same time. Finally, we demonstrate that metrologically useful states can be prepared with short random optical circuits generated from three types of beam splitters and a single nonlinear (Kerr-like) transformation.

Read this article online: https://arxiv.org/abs/1602.05407

(Session 9b : Friday from 4:45pm - 5:15pm)

### Three-dimensional color code thresholds via statistical-mechanical mapping

**Presenting Author**: Aleksander Kubica, IQIM, Caltech**Contributing Author(s)**: Michael Beverland,
Fernando Brandao,
John Preskill and
Krysta Svore

The color code is an example of a topological quantum error-correcting code which recently has gained a lot of attention due to achieving universality without magic-state distillation in three dimensions. Also, the color code illustrates a new and exciting idea of single-shot error correction which might drastically reduce time overhead of quantum computation. In this work we find fundamental bounds on the error-correcting capabilities of the three-dimensional color code, namely the threshold for optimal error correction of bit-flip/phase-flip noise with perfect measurements on the body-centered cubic lattice. In particular, the threshold associated with string-like (one- dimensional) and sheet-like (two-dimensional) logical operators is p_1 ≃ 1.9% and p_2 ≃ 27.5%, respectively. The aforementioned results were obtained by exploiting a connection between error correction and statistical mechanics. We performed parallel tempering Monte Carlo simulations of two previously unexplored three-dimensional statistical-mechanical models: the 4-body and the 6- body random coupling Ising models. We find their phase diagrams in terms of disorder strength and temperature. Our results put constraints on the practical use of the color code from the viewpoint of efficient decoders and bounding overhead.

(Session 9a : Friday from 4:15pm - 4:45pm)

### Preparation and coherent manipulation of pure quantum states of a single molecular ion

**Presenting Author**: Dietrich Leibfried, NIST, Boulder**Contributing Author(s)**: C. W. Chou, C. Kurz, D. B. Hume, P. N. Plessow and D. R. Leibrand

An amazing level of control is routinely reached in modern experiments with atoms, but similar control over molecules has been an elusive goal. We recently proposed a method based on quantum logic spectroscopy [1] to address this problem for a wide class of molecular ions [2]. We have now realized the basic elements of this proposal. In our demonstration, we trap a calcium ion together with a calcium hydride ion (CaH+) that is a convenient stand-in for more general molecular ions. We cool the two-ion crystal to its motional ground state and then drive the motional sidebands of Raman transitions in the molecular ion. A transition of the molecule is indicated by a single quantum of excitation in the secular motion of the pair. We can efficiently detect this single quantum with the calcium ion, which projects the molecule into the final state of the attempted sideband transition, leaving the molecule in a known, pure quantum state. The molecule can be coherently manipulated after the projection, and its final state read out by another quantum logic state detection. We demonstrate this by driving Rabi oscillations between rotational states. All transitions we address in the molecule are driven by a single, far off-resonant continuous-wave laser. This makes our approach applicable to control and precision measurement of a large class of molecular ions. Other QI projects in the NIST Ion Storage group will be briefly summarized. [1] P.O. Schmidt, et al. Science 309, 749 (2005) [2] D. Leibfried, New J. Phys. 14, 023029 (2012) *supported by ARO, IARPA, ONR, and the NIST Quantum Information program

(Session 11 : Saturday from 11:00am - 11:30am)

### Distinguishability of qubit and qutrit Bell states with projective and non-projective linear measurement

**Presenting Author**: Nathaniel Leslie, Harvey Mudd College**Contributing Author(s)**: Julien Devin and Theresa W. Lynn

We present new maximal distinguishability limits for qudit Bell states with projective and non-projective linear evolution and local measurement (LELM) devices. A well-known no-go theorem establishes that projective LELM detection schemes cannot reliably distinguish all four qubit Bell states; they can only reliably distinguish three. We show that only 3 out of 9 qutrit Bell states can be distinguished with projective LELM measurements. We also consider the case of non-projective measurements, and show that even general POVM-based LELM measurements cannot reliably distinguish all four qubit Bell states. We also establish that no more than 2d qudit Bell states may be distinguishable with general LELM measurements and in the qutrit case, at most 5 may be distinguishable.

### Quantum simulation of complex dynamics in a quantum kicked top

**Presenting Author**: Nathan Lysne, Arizona**Contributing Author(s)**: Kevin Kuper, Hannah Knaack and Poul Jessen

Recent advances in quantum control have enabled analog quantum simulation (AQS) as a means to study phase changes, order, and other complex many body phenomena. However, as experimental AQS grows in sophistication, new questions arise about our ability to verify the validity of a given simulation. In the absence of error correction, investigating the effects of imperfections on dynamics that is potentially chaotic and hypersensitive to errors is thus essential to understanding how much and in which ways we can trust AQS. The quantum kicked top (QKT) is an ideal model for such studies. We discuss results from recent experiments that use the d = 16 dimensional hyperfine manifold in the 6S1/2 electronic ground state of an individual Cs atom for AQS of a QKT with spin J = 15/2. As a baseline, we see close agreement between simulated and predicted dynamics in a mixed phase space over many tens of kicks. Prior work has shown the QKT dynamics reflects the separation between stable islands and sea of chaos in the classical QK, even in situations where the “fidelity” of the evolving QKT quantum state is poor. This suggests the former represents a “global” property that can be reliably simulated in the presence of errors, even when the microscopic behavior (the quantum state) cannot. We present data from experiments and numerical simulations in the presence of deliberately applied errors, showing that the frequency content of the perturbation plays a central role in the validity and robustness of AQS.

### Phase-tuned entangled state generation between distant spin qubits

**Presenting Author**: Clemens Matthiesen, UC Berkeley, Cambridge**Contributing Author(s)**: Robert Stockill, Megan Stanley, Lukas Huthmacher, Claire Le Gall, Pai Peng, Hartmut Haeffner, and Mete Atature

Entanglement is the central resource in quantum information processing, sensing and communication. Distribution of entanglement through non-local interactions, using photon interference and detection, is an attractive feature of flexible computation architectures where spatially separate nodes are locally controlled and connected via photonic channels. I will present very recent work from the Atatüre group in Cambridge on the generation of controllable entangled states between two electron spins confined in optically active indium-gallium-arsenide (InGaAs) quantum dots (QD) situated metres apart. The combination of a minimal single-photon state-projection scheme and the strong coherent light-matter interaction in these systems enables a distant entanglement rate of 7.3 kHz, the highest reported to date. With full control over the single-photon interference, we demonstrate the creation of entangled states with arbitrary phase. In the outlook I will discuss some limiting features of this semiconductor system [1], and highlight alternative venues for electron spin qubits trapped in vacuum [2]. [1] R. Stockill et al., Nature Comms 7, 12745 (2016). [2] P. Peng, C. Matthiesen, H Häffner, arXiv:1611.00130 [quant-ph] (2016).

(Session 13 : Saturday from 4:45pm - 5:15pm)

### Faithful conversion of propagating quantum bits to mechanical motion

**Presenting Author**: Karl Mayer, CU Boulder; NIST**Contributing Author(s)**: Adam Reed, John Teufel, Matt Reagor, Luke Burkhart, Wolfgang Pfaff, Rob Schoelkopf and Konrad Lehnert

Electromechanical devices are emerging as quantum information processing elements for superconducting circuits. By using a mechanical oscillator parametrically coupled to a microwave resonant circuit, these devices can store, amplify, and frequency-convert microwave fields. Experimental efforts to convert microwave fields to mechanical motion have so far been mostly limited to Gaussian states, such as coherent or squeezed states. We present experiments that demonstrate and characterize the conversion of non-Gaussian states, namely propagating microwave qubits prepared in mixed single-photon and superposition states. We perform state tomography to infer the density matrices for both the input states and the mechanical states after conversion, and compute the average fidelity for this conversion process to be in excess of 80%.

### Boson sampling of many-body quantum random walkers on a lattice

**Presenting Author**: Gopikrishnan Muraleedharan, Center for Quantum Information and Control (CQuIC), University of New Mexico**Contributing Author(s)**: Akimasa Miyake and Ivan H. Deustch

The Boson sampling problem introduced by Aaronson and Arkhipov showed quantum supremacy in terms of sampling complexity for the output distribution of photons scattering from a linear optical network. We study here an analogous problem in the case of multiple boson continuous-time quantum random walkers on a lattice, e.g., Bosonic atoms in an optical lattice. Results are presented for the special case of a 1D lattice with nearest neighbor and uniform hopping amplitude. We show that the permanent of the unitary time evolution operator can be approximated in \( O \left({{2T}\choose{T}}^3 \log N \right)\) time, using an algorithm developed by M. Shwartz [1]. Thus the sampling problem is easy as long as the time of evolution (T) is constant or at least logarithmic in N. When the time of evolution passes the logarithmic scale, the algorithm takes exponential time. It is not clear if the sampling problem is hard in this regime. Periodic and hard wall boundary conditions lead to the same result when number of lattice sites are substantially larger than the number of particles. When extended to arbitrary hopping amplitudes and on-site interactions, this corresponds to sampling complexity for a general Bose-Hubbard model. 1: Moshe Schwartz, "Efficiently computing the permanent and Hafnian of some banded Toeplitz matrices" , Linear Algebra and its Applications, Volume 430, Issue 4, 2009, Pages 1364-1374, ISSN 0024-3795, http://dx.doi.org/10.1016/j.laa.2008.10.029.

### Subradiance in the emission of atoms coupled to an optical nanofiber

**Presenting Author**: Austin Nar, Miami University**Contributing Author(s)**: Arkan Hassan and James Clemens

We investigate subradiance in the emission into an optical nanofiber of ultracold atoms trapped in a MOT surrounding the nanofiber. The atoms are coherently excited on resonance by a laser propagating orthogonally to the nanofiber. We present a classical random phase model which predicts subradiance and we also describe progress toward a quantum model which combines free space collective emission as described in Lehmberg, et. al [PRA 2 883] with the coupling to the nanofiber modes described by Le Kien, et. al [PRA 72 063815].

### Quantum algorithms for Gibbs sampling and hitting-time estimation

**Presenting Author**: Anirban Narayan Chowdhury, Center for Quantum Information and Control**Contributing Author(s)**: Rolando D. Somma

We present quantum algorithms for solving two problems regarding stochastic processes. The first algorithm prepares the thermal Gibbs state of a quantum system and runs in time that is polylogarithmic in the precision parameter, exponentially improving the precision dependence over known quantum algorithms. It also polynomially improves dependence on parameters such as system size and inverse temperature. The second algorithm estimates the hitting time of a classical Markov chain. For a sparse stochastic matrix, it provides quadratic improvement in complexity over a natural classical algorithm to estimate the hitting time. Both algorithms use tools recently developed in the context of Hamiltonian simulation, spectral gap amplification, and solving linear systems of equations.

Read this article online: https://arxiv.org/abs/1603.02940

### Scaling superconducting qubits: Toward a demonstration of quantum supremacy

**Presenting Author**: Matthew Neeley, Google

Our group has proposed an experiment to demonstrate "Quantum Supremacy", using a quantum device to perform a well-defined computational task that cannot be done in reasonable time on even the largest classical supercomputers (arXiv:1608.00263). This will require a device with 49 qubits arranged in a 7-by-7 grid and one- and two-qubit gate error rates below about 0.1%. I will outline our experimental progress toward this goal and describe the challenges associated with scaling superconducting qubit devices to the level of several tens of qubits and beyond.

Read this article online: arXiv:1608.00263

### Multipartite entanglement in stabilizer tensor networks

**Presenting Author**: Sepehr Nezami, Stanford University**Contributing Author(s)**: Michael Walter

Tensor network models reproduce important structural features of holography, including the Ryu-Takayanagi formula for the entanglement entropy and quantum error correction in the entanglement wedge. In contrast, only little is known about their multipartite entanglement structure, which has been of considerable recent interest. In this work, we study random stabilizer tensor networks and show that here the tripartite entanglement question has a sharp answer: The average number of GHZ triples that can be extracted from a stabilizer tensor network is small, implying that the entanglement is predominantly bipartite. As a consequence, we obtain a new operational interpretation of the monogamy of the Ryu-Takayanagi mutual information and an entropic diagnostic for higher-partite entanglement. Our technical contributions include a spin model for evaluating the average GHZ content of stabilizer tensor networks and a novel formula for the third moment of random stabilizer states.

Read this article online: https://arxiv.org/pdf/1608.02595.pdf

### Higher moments of stabilizer states

**Presenting Author**: Sepehr Nezami, Stanford University**Contributing Author(s)**: Michael Walter

Stabilizer states are a fundamental tool in quantum information theory. In the past years, there has been renewed interest in their statistical properties, motivated by a number of important applications. Celebrated results include a characterization of their third and fourth moments in the multiqubit case (e.g.,Zhu/Webb/Kueng&Gross, QIP 2016). In this work, we present a simple explicit expression for all higher moments of stabilizer states in odd prime power dimensions. Previously, it was only known that they form a 2-design but not a 3-design (i.e. that their second but not their third moments agree with the Haar measure). In contrast, and significantly for applications, our formula allows the computation of a t-th moment even when the stabilizer states fail to be a t-design. Our key technical result is a version of Schur-Weyl duality for the Clifford group. Whereas the commutant of the tensor power action of the unitary group is spanned by the permutation action, we show that for the Clifford group the commutant has a natural description in terms of discrete symplectic phase space, unraveling a new and surprising algebraic structure. We sketch possible applications of our result to quantum information theory and signal recovery.

### Quantum error correction of reference frame information

**Presenting Author**: Sepehr Nezami, Stanford**Contributing Author(s)**: Patrick Hayden and Grant Salton

The existence of quantum error correcting codes is one of the most counterintuitive and potentially technologically important discoveries of quantum information theory. But standard error correction refers to abstract quantum information, i.e. information that is independent from the physical incarnation of the systems used for storing the information. There are, however, other forms of information that are physical, one of the most ubiquitous being reference frame information. Here we analyze the problem of error correcting physical information. The basic question we seek to answer is whether such error correction is possible, and, if yes, the limitations to which it is subjected. The issue is highly nontrivial given the fact that the systems that need to be used for transmitting physical information must contain the physical quantity we are interested in, so all actions applying to them, including the encoding/decoding necessary for error correction, are subjected to limiting constraints.

Read this article online: https://www.dropbox.com/s/xfo6vh8tmo3xao4/main.pdf?dl=0

(Session 9a : Friday from 5:45pm - 6:15pm)

### Spectroscopy of quantum and non-Gaussian noise

**Presenting Author**: Leigh Norris, Dartmouth**Contributing Author(s)**: Gerardo Paz-Silva and Lorenza Viola

Precisely characterizing the decoherence effects arising from coupling to a noisy environment is essential for designing optimized error correction strategies and validation protocols for realistic quantum information processors. This challenge has prompted much of the recent interest in quantum noise spectroscopy, which seeks to estimate the spectral properties of noise affecting a target quantum system. Despite considerable theoretical and experimental advances, this effort has largely been confined to the case of classical, Gaussian phase noise on a single qubit. We overcome these limitations by introducing quantum noise spectroscopy protocols for both quantum and non-Gaussian phase noise. For realistic systems that include a pair of excitons coupled to a phonon bath and a qubit undergoing quadratic dephasing at an optimal point, we numerically demonstrate reconstruction of the asymmetric spectra unique to quantum environments and the polyspectra associated with higher order cumulants of non-Gaussian noise. In both cases, spectral reconstructions enable us to accurately predict the dynamics of qubits coupled to these noise sources. In addition to the practical value in characterizing a larger class of noise processes, this work highlights dynamical and spectral signatures unique to quantum and non-Gaussian noise sources.

Read this article online: http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.116.150503, https://arxiv.org/pdf/1609.01792v2.pdf

(Session 10 : Saturday from 9:15am - 9:45am)

### Heuristics for machine learning in quantum compression

**Presenting Author**: Jonathan Olson, Harvard University**Contributing Author(s)**: Jonathan Romero and Alan Aspuru-Guzik

Machine learning (ML) is a powerful technique for discovering and classifying features in large data sets. However, the somewhat ad-hoc nature of ML algorithms cultivates a heavy dependence on the heuristics of these methods. In this talk, we discuss and introduce new general heuristics for quantum machine learning in the context of data compression.

### Band-limited quantum optimal control

**Presenting Author**: Adrian Orozco, Center for Quantum Information and Control (CQuIC), University of New Mexico**Contributing Author(s)**: Grant Biedermann, Mike Martin and Ivan Deutsch

Control of quantum systems is important for the development of quantum technology. Many researchers have explored a variety of functional analytic methods for synthesizing optimal control waveforms that evolve a quantum system from an initial state to a final target state. In particular, the GRadient Ascent Pulse Engineering (GRAPE) method has proven to be a powerful platform for synthesizing these controls. However, in the standard GRAPE algorithm controls are designed in the time domain and there is no direct way of limiting its bandwidth, which is important in practical applications. In addition, for higher dimensional Hilbert spaces GRAPE requires more time steps to completely specify the system’s state. As the total coherence time is limited, the bandwidth will increase when augmenting the number of time steps. These concerns are greatly important when implementing these designed controls in the laboratory. We circumvent these problems by expanding the control via a truncated Fourier series constraining the bandwidth through its Fourier coefficients. A gradient ascent method is used to numerically optimize the Fourier coefficients of a piecewise constant control that lead to the desired evolution of our quantum state. A weakly dressed symmetric Rydberg ensemble model is used to investigate the effect of expanding the control in this way [1]. We find that the control waveform can be designed to have two important characteristics for practical applications; a band-limited power spectrum and constrained control amplitudes during the entire evolution. Furthermore, we find that the total number of time steps (total evolution time) can be restricted for a particular range of Hilbert space dimensions without imparting additional constraints to experimental apparatus. 1. T. Keating, C. H. Baldwin, Y.-Y. Jau, J. Lee, G. W. Biedermann, and I. H. Deutsch, Phys. Rev. Lett. 117, 213601 (2016).

### Quantum algorithm for linear differential equations with exponentially improved dependence on precision

**Presenting Author**: Aaron Ostrander, QuICS, University of Maryland**Contributing Author(s)**: Dominic Berry, Andrew Childs and Guoming Wang

Recently quantum algorithms for Hamiltonian simulation have been proposed which have complexity logarithmic in the inverse error. Hamiltonian simulation is just a special case of simulating the ordinary differential equation dx/dt=Ax+b where A is anti-Hermitian and b=0. For more general A, the complexity of such a simulation is less well understood. Berry proposed a quantum algorithm for ODEs using linear multistep methods that is polynomial in the inverse error. This algorithm encoded the simulation problem in a linear system and used a quantum linear systems algorithm (QLSA) to solve the system. Recently, QLSAs which scale logarithmically in the inverse error have been proposed. However, this exponential improvement in solving linear systems does not necessarily translate to an exponential improvement for algorithms that use the QLSA as a subroutine. In fact, Berry’s algorithm has polynomial scaling regardless of which QLSA is used. This is because there are other error-dependent parameters in the algorithm that contribute to the complexity. In this work, we revisit the problem of solving linear differential equations and propose a new QLSA-based algorithm that scales logarithmically in the inverse error. Our approach is based on evolving according to the propagator exp(At) by approximating it using a Taylor series.

### Optimal control for quantum metrology with time-dependent Hamiltonians

**Presenting Author**: Shengshi Pang, University of Rochester**Contributing Author(s)**: Andrew N. Jordan

Due to its importance in many areas of physics, quantum metrology has attracted a growing attention in recent years. Most of the current researches on quantum metrology were focused on systems with time-independent Hamiltonians. For systems with time-dependent Hamiltonians, however, little has been known due to the complexity of dynamics. In this work, we study quantum metrology with general time-dependent Hamiltonians to bridge this gap. We obtain the maximum quantum Fisher information for general parameters in time-dependent Hamiltonians, and find that proper Hamiltonian control on the system is necessary to reach the maximum Fisher information. We derive the optimal Hamiltonian control in general, and show that it is generally an adaptive and feedback-based control. With a minimal example of a qubit in a rotating magnetic field, we surprisingly find that the time scaling of quantum Fisher information reaches T^4 in estimating the rotation frequency of the field, which significantly breaks the traditional limit of T^2 time scaling for quantum Fisher information with time-independent Hamiltonians. This suggests a dramatic difference between quantum metrology with time-dependent Hamiltonians and time-independent Hamiltonians, and also shows the advantage of quantum control in enhancing quantum metrology. We conclude by considering the effect of level crossings in the derivative of the Hamiltonian with respect to the parameter of interest, and point out that additional control on the Hamiltonian is necessary for that case.

Read this article online: https://arxiv.org/abs/1606.02166

### Open quantum systems with arbitrary initial conditions

**Presenting Author**: Gerardo Paz-Silva, Griffith University (Australia)**Contributing Author(s)**: Michael Hall and Howard Wiseman

The theory of Open Quantum Systems is concerned with the prediction and control of the dynamics of a quantum system in the presence of interactions with external degrees of freedom. This is a highly non-trivial problem, and in its study two assumptions are usually made: (A1) the state of system and bath is factorizable at time t=0, and (A2) certain knowledge of the bath, e.g., of the bath correlations, is assumed despite (by definition) not being fully accessible. Seeking to replace the assumption character of (A2) by measurable information, recent years have seen the emergence of the so-called Quantum Noise Spectroscopy protocols. These, provided (A1) holds, use the measurable response of a quantum system to its bath and different control scenarios, in order to extract information regarding the bath correlations (with respect to the reduced density matrix of the bath). In this talk, by introducing a new universal density matrix decomposition we show how (A1) can be naturally removed from current calculations methods, such as master equations, and, additionally, how the notion of Quantum Noise Spectroscopy can be extended to the case where system and bath are initially correlated. Thus, we show how (A1) and (A2) can in principle be simultaneously discarded from the set of assumptions made in the theory of Open Quantum Systems. We further discuss consequences and applications of our decomposition method to quantum steering and to the understanding of quantum channels.

### Performance of quantum annealers on hard scheduling problems

**Presenting Author**: Bibek Pokharel, University of New Mexico**Contributing Author(s)**: Davide Venturelli (NASA Ames Research Center), Eleanor Rieffel (NASA Ames Research Center)

Quantum annealers have been employed to attack a variety of optimization problems. We compared the performance of the current D-Wave 2X quantum annealer to that of the previous generation D-Wave Two quantum annealer on scheduling-type planning problems. Further, we compared the effect of different anneal times, embeddings of the logical problem, and different settings of the ferromagnetic coupling across the logical vertex-model on the performance of the D-Wave 2X quantum annealer. Our results show that at the best settings, the scaling of expected anneal time to solution for D-WAVE 2X is better than that of the DWave Two, but still inferior to that of state of the art classical solvers on these problems. We discuss the implication of our results for the design and programming of future quantum annealers.

### Random quantum circuits with varying topologies and gate sets

**Presenting Author**: Anthony Polloreno, Rigetti Quantum Computing**Contributing Author(s)**: Nicholas Rubin, Robert Smith, and William Zeng

We build on recent results using sampling from the output of random unitary matrices as a metric for quantum supremacy. We first investigate the relationship between the choice of gate set and the circuit depth required to converge to the Porter-Thomas distribution. In particular, we note that convergence is possible using iSWAP gates in place of CZ gates. Next we explore the effects of varying qubit connectivity on the convergence behavior of random circuits. We address the feasibility of these schemes with near-term superconducting qubit hardware.

### Optimal digital dynamical decoupling for general decoherence via Walsh modulation

**Presenting Author**: Haoyu Qi, Louisiana State**Contributing Author(s)**: Jonathan Dowling and Lorenza Viola

We provide a general framework for constructing digital dynamical decoupling sequences based on Walsh modulation, applicable to arbitrary qubit decoherence scenarios. Building on the equivalence between the Walsh formalism and the recently introduced concatenated-projection approach, we identify a family of optimal Walsh sequences which can be exponentially more efficient, in terms of the required total pulse number for fixed cancellation order, than known sequences based on concatenated design. Optimal sequences for a given cancellation order are highly non-unique, their performance depending sensitively on the control path. We provide an analytical upper bound to the achievable decoupling error, and argue how suitable path-optimized sequences within the optimal Walsh family can substantially outperform concatenated decoupling, while respecting realistic timing constraints. We validate these conclusions by numerically computing the average fidelity in a toy model capturing the essential feature of hyperfine-induced decoherence in a quantum dot.

(Session 9a : Friday from 4:45pm - 5:15pm)

### Spin squeezing on nanophotonic waveguides

**Presenting Author**: Xiaodong Qi, CQuIC, New Mexico**Contributing Author(s)**: Jongmin Lee, Yuan-Yu Jau, and Ivan H. Deutsch

Strong coupling between atoms and photons is a prerequisite for quantum information processing protocols ranging from quantum metrology to quantum communication and computation. This strong coupling effect can be achieved using nanophotonic waveguides whereby an ensemble of atoms are trapped in the evanescent field. In this talk, I will present our recent progress in the theoretical study of implementing spin squeezing using optical nanofibers (ONF) and square waveguides (SWG) with both birefringence and Faraday interactions as QND measurement. Various geometries of protocols will be discussed based on the analysis of optical depth per atom on ONF and SWG platforms. In calculating the spin squeezing parameter, we have established a set of stochastic master equations to describe the individual and collective spin dynamics. Our simulation shows that ~10 dB of spin squeezing can be reached with a few thousands of atoms on these nanophotonic waveguides. Using the fundamental TE and TM modes, the SWG could generate more spin squeezing compared to the ONF platform. Our result can be generalized to other nanophotonic platforms, for the implementation of non-Gaussian states, and to improve quantum sensing precision using spin squeezing techniques.

### Pump-probe spectroscopy in near-resonance optical lattices

**Presenting Author**: Anthony Rapp, Miami University**Contributing Author(s)**: Preston Ross, Ethan Clements, Andrew Hachtel, and Samir Bali

We observe vibrational and Brillouin resonances in the transmission spectrum of a weak light beam probing a near-resonance optical lattice. We discuss future measurements on novel Brownian ratchets in our lab.

### Investigations of quantum heuristics for optimization

**Presenting Author**: Eleanor Rieffel, NASA Ames Research Center**Contributing Author(s)**: Stuart Hadfield, Zhang Jiang, Salvatore Mandra, Davide Venturelli, and Zhihui Wang

We explore the design of quantum heuristics for optimization, focusing on the quantum approximate optimization algorithm, a metaheuristic developed by Farhi, Goldstone, and Gutmann. We develop specific instantiations of the of quantum approximate optimization algorithm for a variety of challenging combinatorial optimization problems. Through theoretical analyses and numeric investigations of select problems, we provide insight into parameter setting and Hamiltonian design for quantum approximate optimization algorithms and related quantum heuristics, and into their implementation on hardware realizable in the near term.

### Practical transmission matrix of a multimode fiber

**Presenting Author**: Nate Ristoff, Center for Quantum Information and Control (CQuIC), University of New Mexico**Contributing Author(s)**: F. E. Becerra

Transmission of information through multimode fibers can provide a path to achieving higher capacity than what is currently possible with single mode fibers. However, cross talk between different spatial modes makes information transmission challenging. Therefore a method to reverse intermodal cross talk is required to ensure information transmission with high fidelity. States of light with spatial structure in Laguerre Gaussian (LG) modes are an ideal basis to investigate experimentally the communication capacity of such multimode fibers due to the orthogonality between modes and the infinite size of the basis. The mode structure of LG beams have radial and orbital angular momentum (OAM) degrees of freedom and thus both must be included in a modal decomposition. We investigate a protocol previously used to characterize the output of a few mode fiber and extend it to the study the transmission of light through a fiber with many modes (highly multi-mode fiber) with the goal of increasing information transmission. This protocol allows for a fast determination of the transmission matrix of a multi-mode fiber with a modest number of measurements. In addition, this method does not require a second beam to act as a local oscillator to retrieve inter-modal phase information. This protocol could in principle allow for implementing real time tracking of the transmission matrix of the fiber so that a disturbance in the fiber can be detected and corrected to avoid loss of information.

### Factoring using 2n+2 qubits with Toffoli based modular multiplication

**Presenting Author**: Martin Roetteler, Microsoft**Contributing Author(s)**: Thomas Haener and Krysta M. Svore

We describe an implementation of Shor's quantum algorithm to factor n-bit integers using only 2n+2 qubits. In contrast to previous space-optimized implementations, ours features a purely Toffoli based modular multiplication circuit. The circuit depth and the overall gate count are in O(n^3) and O(n^3 log(n)), respectively. We thus achieve the same space and time costs as Takahashi et al., while using a purely classical modular multiplication circuit. As a consequence, our approach evades most of the cost overheads originating from rotation synthesis and enables testing and localization of faults in both, the logical level circuit and an actual quantum hardware implementation. We implemented and simulated a Toffoli network for the entire controlled modular multiplication piece of Shor's algorithm in LIQUi|>, for real-world bit-sizes of up to 8,192. Asymptotically, our new (in-place) constant-adder, which is used to construct the modular multiplication circuit, uses only dirty ancilla qubits and features a circuit size and depth in O(n log(n)) and O(n), respectively. Our resource estimates determine also the constants for the scaling of the circuit size.

Read this article online: https://arxiv.org/abs/1611.07995

(Session 9c : Friday from 5:45pm - 6:15pm)

### Experimental demonstration of robust phase estimation near the Heisenberg limit

**Presenting Author**: Kenneth Rudinger, Sandia**Contributing Author(s)**: Shelby Kimmel (QuICS, University of Maryland), Daniel Lobser (Sandia National Laboratories), and Peter Maunz (Sandia National Laboratories)

High-fidelity gate operations are one of many requirements for full-scale quantum computation. A variety of benchmarking and tomographic protocols have been developed to aid in the characterization and improvement of these operations. In this talk, we will discuss robust phase estimation (RPE), a particular protocol that can be used to learn the phases of quantum operations to very high accuracy. Unlike many other phase estimation protocols, RPE requires no ancillae nor near-perfect state preparation or measurement. We demonstrate the first published experimental implementation of RPE on a single-qubit system (a trapped Yb\(^+\) ion), and use it to learn the phases of X and Y rotations to within \(\sim10^{-4}\) radians. This accuracy requires only 352 experimental samples per phase, and exhibits Heisenberg-like scaling. We also explore how this accuracy appears to outperform the original theoretical bounds on RPE. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04 94AL85000.

(Session 11 : Saturday from 11:30am - 12:00pm)

### Investigating the quantum approximate optimization algorithm's advantage over classical algorithms

**Presenting Author**: Ciaran Ryan-Anderson, CQuIC New Mexico, Sandia**Contributing Author(s)**: Yang Jiao and Ojas Parekh

The Quantum Approximate Optimization Algorithm (QAOA) is designed to find approximate solutions to combinatorial optimization problems. The approximation quality of QAOA is a function of the parameters to the algorithm, one of which corresponds to the depth of a quantum circuit realizing QAOA. Recently, in [1], it has been shown that even when QAOA is used in its lowest-depth form, it can produce distributions that are hard to sample from classically. This indicates that QAOA can demonstrate some level of ``Quantum Supremacy," at least for the task of sampling from a distribution. However, QAOA is foremost an optimization algorithm, and QAOA's complexity as an optimization algorithm is largely open. In this work we investigate QAOA's advantage over classical algorithms from an optimization perspective. This work was supported by the Laboratory Directed Research and Development (LDRD) program at Sandia National Laboratories. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. [1] E. Farhi and A. W. Harrow, Quantum supremacy through the quantum approximate optimization algorithm, (2016), arXiv:1602.07674.

(Session 9c : Friday from 4:15pm - 4:45pm)

### Entanglement from topology in Chern-Simons theory

**Presenting Author**: Grant Salton, Stanford University**Contributing Author(s)**: Brian Swingle and Michael Walter

The way in which geometry encodes entanglement is a topic of much recent interest in quantum many-body physics and the AdS/CFT duality. This relation is particularly pronounced in the case of topological quantum field theories, where topology alone determines the quantum states of the theory. In this work, we study the set of quantum states that can be prepared by the Euclidean path integral in three-dimensional Chern-Simons theory. Specifically, we consider arbitrary 3-manifolds with a fixed number of torus boundaries in both abelian U(1) and non-abelian SO(3) Chern-Simons theory. For the abelian theory, we find that the states that can be prepared coincide precisely with the set of stabilizer states from quantum information theory. This constrains the multipartite entanglement present in this theory, but it also reveals that stabilizer states can be described by topology. In particular, we find an explicit expression for the entanglement entropy of a many-torus subsystem using only a single replica, as well as a concrete formula for the number of GHZ states that can be distilled from a tripartite state prepared through path integration. For the nonabelian theory, we find a notion of "state universality", namely that any state can be prepared to an arbitrarily good approximation. The manifolds we consider can also be viewed as toy models of multi-boundary wormholes in AdS/CFT.

Read this article online: https://arxiv.org/abs/1611.01516

### On chip nonlinear quantum devices

**Presenting Author**: Linda Sansoni, Paderborn

In the last years the challenge of showing quantum supremacy has greatly attracted the interest of the scientific community. In this context the adoption of integrated photonic platforms has shown a great potential to finally confirm the advantage of using quantum resources compared to classical ones. Integrated photonics is indeed an optimal candidate for the experimental implementation of highly complex and compact quantum circuits. Despite the enormous development in this field, one of the major issues still remains a reliable and efficient generation of quantum states of light. Integrated waveguide sources have suitable features for this purpose as high brightness and stability. Nevertheless requirements as generation of light on different spatial modes or the possibility to operate the devices outside the lab, are still a major challenge. Here we present how we address these challenges by exploiting new waveguide designs in lithium niobate substrates and the adoption of fiber-hybrid technology. Our devices range from multichannel sources of entangled states to a fully plug and play source of heralded single photons. With these achievements we bring the quantum technology to a next level of development and a step closer to the adoption of a fully integrated platform for quantum information applications.

### Scalable macromodeling for superconducting circuits

**Presenting Author**: Michael Scheer, Rigetti Quantum Computing**Contributing Author(s)**: Max Block, Eyob Sete, Nick Rubin, Nikolas Tezak, Matt Reagor, and Chad Rigetti

Modeling and simulation tools enable more rapid exploration of the superconducting quantum circuit parameter space than would be possible with fabrication and measurement alone. A variety of promising modeling schemes for these circuits have been proposed but their scalability and validity for many qubit systems has not been demonstrated. We give a detailed discussion of a superconducting circuit modeling technique that allows for rapid simulation of several qubits. We compare the predictions made by this and several other models to the measured parameters of many qubits. We evaluate these models in terms of their accuracy and resource requirements and discuss their utility for designing many-qubit systems.

### Determining the effective dimension of a quantum state space

**Presenting Author**: Travis Scholten, Sandia National Labs**Contributing Author(s)**: Robin Blume-Kohout

Quantum state tomography of multiple qubits or optical modes usually relies on techniques to reduce the number of parameters being fit. For example, quantum compressed sensing searches for low-rank estimates, and in optical tomography, the (formally infinite-dimensional) Hilbert space is truncated in some physically- motivated manner. Is it possible to reduce the number of parameters in some other way, using maximum likelihood estimation? Under the assumptions of local asymptotic normality, we have found two useful ways of doing so. The first uses model selection based on the loglikelihood ratio statistic, and allows one to choose the best Hilbert space dimension directly. The second uses the idea of the statistical dimension of the quantum state space to calculate its "effective" dimension. Surprisingly, both results imply that tomography of low-rank true states almost always yields estimates whose dimension is small, even when the estimator does not explicitly impose that constraint.

Read this article online: https://arxiv.org/abs/1609.04385

### Quantum effects in vibrational energy harvesting

**Presenting Author**: John Scott, Carleton College**Contributing Author(s)**: Moses Misplon, Max Trostel, and Arjendu Pattanayak (Department of Physics, Carleton College, Northfield, Minnesota)

Vibrational energy harvesting is a promising means of recovering energy from random external excitation by coupling these to an electrical harvesting circuit via a mechanical oscillator. We have explored a model bistable vibrational energy harvester in detail to elucidate the dynamical mechanisms which lead to the best performance, especially as it relates to higher energy orbits and chaos. Further, recent advances in nanoelectromechanical systems engineering indicate that such systems could operate at a scale where quantum mechanical effects are non-trivial. Using a semiclassical approximation to quantum state diffusion model, we explore the effects of these quantum effects and find that these can lead to a substantial increase in the efficiency with which the harvester is able to convert energy.

### Flux-noise insensitive and flux-tunable superconducting qubit

**Presenting Author**: Eyob Sete, Rigetti Quantum Computing**Contributing Author(s)**: Matthew Reagor, Nicolas Didier, and Chad Rigetti

Fast high-fidelity two-qubit gates are an essential component of a universal quantum computer. Tunable qubits are promising candidates to realize such gates. However, tunability often comes at the expense of increased noise-sensitivity for a qubit, thus degrading gate performance. We propose a superconducting circuit that mitigates a dominant noise source for a class of tunable qubits. The circuit consists of a SQUID with asymmetric junctions and shunted using a superinductor. We show that flux ‘sweet spots’ can be engineered at the frequency of operation by varying the junction asymmetry and the applied magnetic flux. This device coupled with a fixed frequency qubit allows a realization of fast high-fidelity two-qubit gates.

### Distribution of Bell inequality violation vs. multiparty quantum correlation measures

**Presenting Author**: Kunal Sharma, Louisiana State University **Contributing Author(s)**: Tamoghna Das, Aditi Sen De, and Ujjwal Sen

Violation of a Bell inequality guarantees the existence of quantum correlations in a quantum state. A pure bipartite quantum state, having nonvanishing quantum correlation, always violates a Bell inequality. Such correspondence is absent for multipartite pure quantum states. For a shared multipartite quantum state, we establish a connection between the monogamy of Bell inequality violation and genuine multi-site entanglement as well as monogamy-based multiparty quantum correlation measures. We find that generalized Greenberger-Horne-Zeilinger states and another single-parameter family states which we refer to as the "special Greenberger-Horne-Zeilinger" states have the status of extremal states in such relations.

Read this article online: https://arxiv.org/pdf/1512.01477v1.pdf

### Measurement of correlations in a symmetric many-body quantum state via continuous measurement

**Presenting Author**: Ezad Shojaee, Center for Quantum Information and Control (CQuIC), University of New Mexico**Contributing Author(s)**: Amir Kalev and Ivan Deutsch

Continuous measurement on an ensemble of quantum systems in the presence of dynamical control is a fast and robust way to reconstruct the one-body reduced density matrix of a many-body quantum state [1-4]. We expand this protocol in order to reconstruct the correlations in a symmetric many-body state of multiple qubits. In this continuous weak measurement, the many-body system is probed collectively, weakly enough not to erase the initial conditions over the duration of the measurement, but strongly enough to map the information about the initial state in the measurement outcome. This can be achieved by subjecting the system to an external control which differentiate states with different initial correlations. The problem of extracting the correlation from this record is an inverse problem which is tricky in the strong back-action regime because the measurement back-action on the state disturbs it in a way which depends on the correlations. The conditions and requirements for reconstruction of correlations and the information-gain/disturbance tradeoff are the subject of the present work. [1] Andrew Silberfarb, Poul S. Jessen, and Ivan H. Deutsch, Phys. Rev. Lett. 95, 030402 (2005) [2] Greg A. Smith, Andrew Silberfarb, Ivan H. Deutsch, and Poul S. Jessen Phys. Rev. Lett. 97, 180403 (2006) [3] Carlos A Riofrío, Poul S Jessen and Ivan H Deutsch, Journal of Physics B: Atomic, Molecular and Optical Physics, 44, 15 (2011) [4] A. Smith, C. A. Riofrío, B. E. Anderson, H. Sosa-Martinez, I. H. Deutsch, and P. S. Jessen, Phys. Rev. A 87, 030102(R) (2013)

### Entanglement detection on an NMR quantum-information processor using random local measurements

**Presenting Author**: Amandeep Singh, Indian Institute of Science Education and Research, Mohali, Punjab, INDIA**Contributing Author(s)**: Arvind and Kavita Dorai

Random local measurements have recently been proposed to construct entanglement witnesses and thereby detect the presence of bipartite entanglement. We experimentally demonstrate the efficacy of one such scheme on a two-qubit NMR quantum information processor. We show that a set of three random local measurements suffices to detect the entanglement of a general two-qubit state. We experimentally generate states with different amounts of entanglement, and show that the scheme is able to clearly witness entanglement. We perform complete quantum state tomography for each state and compute state fidelity to validate our results. Further, we extend previous results and perform a simulation using random local measurements to optimally detect bipartite entanglement in a hybrid system of 2⊗3 dimensionality.

Read this article online: http://journals.aps.org/pra/accepted/c5076Nc8Kba17315a20d68544acaa5679b4d7332a, https://arxiv.org/abs/1610.02472

### Attainability of the quantum information bound in pure state models

**Presenting Author**: Fabricio Toscano, Instituto de Fisica, Universidade Federal do Rio de Janeiro (UFRJ), Brasil**Contributing Author(s)**: W. P. Bastos and R. L. de Matos Filho

The attainability of the quantum Cramer-Rao bound, that is the fundamental limit of precision in quantum parameter estimation, involves two steps. The first step is the saturation of the classical Cramer-Rao bound (CCR) associated with the Fisher information associated with the probabilities distributions of a particular positive-operator valued measure (POVM). This saturation depends on the nature of the estimator used to process the data drawn from the set of probabilities in order to estimate the true value of the parameter. Those estimators that saturates the CCR bound are called efficient estimators or asymptotically efficient estimators when the saturation only occurs in the limit of a very large number of measured data (a typical example of this type is the maximum likelihood estimator). The second step is independent on the nature of the estimator and consists in the saturation of the so called quantum information bound (QIB), that occurs when the Fisher information of a suitable POVM coincide with quantum Fisher information associated with the final quantum state where the parameter was imprinted. Braunstein and Caves [1] have shown that the QIB can be always be achieved if the suitable quantum measurement is a von Neumann projective measurement in the eigenvectors basis of an observable called symmetric logarithmic derivative. The problem is that this measurement require the knowledge of the value of the parameter to be estimated. Mainly two approaches have been adopted in order to deal with the fact that the optimal POVM depends on the true value of the parameter. The first one relies on adaptive quantum estimation schemes that could, in principle, asymptotically achieve the QCR bound. The second one looks for the families of density operators where the parameter is imprinted, for which the use of an specific POVM that does not depend on the true value of the parameter leads to the saturation of the QIB. This is known as the search for the global optimal POVM that saturates the QIB independently of the true value of the parameter. For full-rank density operators, Nagaoka [2] showed that saturation of the quantum information bound by using a POVM that does not depend on the true value of the parameter is only possible for the so called quasi-classical family of density operators. He also presented complete characterisation of the quantum measurements that guarantee the saturation for this family. Therefore, the problem of finding the states and the corresponding optimal measurements that lead to the saturation of the QIB, independently of the true value of the parameter, in the case of one-parameter families of full-rank density operators has been already solved. However, for the opposite case of pure states (rank-one density operators), the complete characterisation of the families of states and the corresponding measurements that lead to the saturation of the QIB, independently of the true value of the parameter, is still an open question in the case of arbitrary Hilbert spaces. It is important to remark that inside the families of pure states the QFI reaches its largest values. Here, we consider quantum state families of pure density operators in which the true value of the parameter is imprinted by a unitary evolution whose generator is arbitrary but with discrete spectrum and independent of the true value of the parameter. Thus, we present the complete solution to the problem of which are all the initial states and the corresponding families of global projective measurements that allow the saturation of the QIB, within the pure quantum state families considered. Also, we show that within all the states that saturate the quantum information bound those corresponding to the Heisenberg limit allow the maximum retrieval of information of the parameter in the final state. [1] S. L. Braunstein and C. M. Caves, Physical Review Letters 72, 3439 (1994). [2] H. Nagaoka, in Chapter 9 of ``Asymptotic Theory of Quantum Statistical Inference: Selected Papers'' (2005).

Read this article online: https://arxiv.org/abs/1701.09144

### Attainability of the quantum information bound in pure state models

**Presenting Author**: Fabricio Toscano, Instituto de Fisica, Universidade Federal do Rio de Janeiro (UFRJ), Brasil **Contributing Author(s)**: Wellison P. Bastos and Ruynet L. de Matos Filho

The attainability of the quantum Cramer-Rao bound [QCR], the ultimate limit in the precision of the estimation of a physical parameter, requires the saturation of the quantum information bound [QIB]. This occurs when the Fisher information associated to a given measurement on the quantum state of a system which encodes the information about the parameter coincides with the quantum Fisher information associated to that quantum state. Braunstein and Caves [PRL 72, 3439 (1994)] have shown that the QIB can always be achieved via a projective measurement in the eigenvectors basis of an observable called symmetric logarithmic derivative. However, such projective measurement depends, in general, on the value of the parameter to be estimated. Requiring, therefore, the previous knowledge of the quantity one is trying to estimate. For this reason, it is important to investigate under which situation it is possible to saturate the QCR without previous information about the parameter to be estimated. Here, we show the complete solution to the problem of which are all the initial pure states and the projective measurements that allow the global saturation of the QIB, without the knowledge of the true value of the parameter, when the information about the parameter is encoded in the system by a unitary process.

Read this article online: https://arxiv.org/abs/1701.09144

(Session 9b : Friday from 5:15pm - 5:45pm)

### Quantum process tomography of optical unitaries

**Presenting Author**: Kevin Valson Jacob, Louisiana State University**Contributing Author(s)**: Sushovit Adhikari and Jonathan Dowling

Characterizing quantum evolutions are of prime importance in quantum information. In the emerging area of photonic quantum technologies, this amounts to determining the unitary matrix which transforms the mode operators of a linear optical circuit. We propose a loss-tolerant method to fully characterize such unitaries by using only single photons. By inputting a single photon in a given input mode and finding the probability for it to be detected in all output modes, we find the moduli of all the matrix elements of the unitary. To find the phases of the matrix elements, we need the matrix elements to 'interfere' with each other. This is found by measuring the phase difference between two different paths taken by a photon. To implement this, we can either send in a photon superposed between any two input modes, or measure the output photon in a different mode basis. The former can be implemented by placing a 50:50 beamsplitter before the unknown unitary while the latter can be implemented by placing a beamsplitter after the unitary. We develop a scheme which optimizes the number of experimental configurations necessary for the full tomography of a `d' dimensional unitary. Although the Hilbert space is exponentially large in the dimension, only \(O(d^2)\) measurements suffice.

### Detecting non-Markovian effects in quantum computing architectures

**Presenting Author**: Andrzej Veitia, Oregon**Contributing Author(s)**: Marcu P. da Silva and Steven van Enk

We present a family of tests for detection of non-Markovian effects in quantum gate sequences. A central feature of our method is its insensitivity to state preparation and measurement errors (SPAM). Although our method is not scalable, we will discuss its application to few-qubit systems as a means of detecting spatial correlations in a quantum computing architectures

(Session 9b : Friday from 4:15pm - 4:45pm)

### Chained Bell inequality experiment with high-efficiency measurements

**Presenting Author**: Yong Wan, NIST**Contributing Author(s)**: T. R. Tan, S. Erickson, P. Bierhorst, D. Kienzler, S. Glancy, E. Knill, D. Leibfried, and D. J. Wineland

Recent Bell test experiments that have demonstrated violation of Bell inequalities, have successfully falsified theories of local realism [1-3]. A chained Bell inequality experiment [4], a generalization of the standard Clauser-Horne-Shimony-Holt experiment, utilizes 2N different pairs of measurement settings. The correlations observed in such an experiment can be modeled as a mixture of a local-realistic distribution and a “non-local” distribution that maximally violates the inequality. Using a chained Bell inequality, one can set an upper limit on the fraction of the mixture that satisfies local realism [5-7]. Here, we describe a chained Bell inequality experiment on trapped ions. An entangled pair of trapped Be+ ions is generated using a Mølmer-Sørensen gate [8]. The individual measurement settings are randomized and applied to the ions via single qubit operations. The ions are measured individually with high efficiency. We quantify the local-realistic fraction to be below 0.327 at the 95% confidence level without the fair-sampling or independent-and-identical-distributions assumptions. This work was supported by IARPA, ONR, and the NIST Quantum Information Program. [1] B. Hensen et al., Nature 526, 682 (2015). [2] L. K. Shalm et al, Phys. Rev. Let. 115 250402 (2015). [3] M. Giustina et al., Phys. Rev. Let. 115 250401 (2015). [4] P. M. Pearle, Phys. Rev. D 2, 1418 (1970). [5] A. C. Elitzur, S. Popescu, and D. Rohrlich, Phys. Lett. A 162, 25 (1992). [6] J. Barrett, A. Kent, and S. Pironio, Phys. Rev.Lett. 97, 170409 (2006). [7] P. Bierhorst, J. Phys. A: Math. Theor. 49 215301 (2016). [8] J. P. Gaebler et al., Phys. Rev. Lett. 117, 060505 (2016).

### Experimental time-optimal universal control of spin qubits in solids

**Presenting Author**: Xiaoting Wang, Louisiana State**Contributing Author(s)**: Jianpei Geng,
Yang Wu,
Kebiao Xu,
Fazhan Shi,
Yijin Xie,
Xing Rong and
Jiangfeng Du

Quantum control of systems plays an important role in modern science and technology. The ultimate goal of quantum control is to achieve high-fidelity universal control in a time-optimal way. Although high-fidelity universal control has been reported in various quantum systems, experimental implementation of time-optimal universal control remains elusive. Here, we report the experimental realization of time-optimal universal control of spin qubits in diamond. By generalizing a recent method for solving quantum brachistochrone equations [X. Wang et al., Phys. Rev. Lett. 114, 170501 (2015)], we obtained accurate minimum-time protocols for multiple qubits with fixed qubit interactions and a constrained control field. Single- and two-qubit time-optimal gates are experimentally implemented with fidelities of 99% obtained via quantum process tomography. Our work provides a time-optimal route to achieve accurate quantum control and unlocks new capabilities for the emerging field of time-optimal control in general quantum systems.

Read this article online: http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.117.170501

### Quantum approximate optimization algorithm on a one-dimensional model

**Presenting Author**: Zhihui Wang, NASA Ames Research Center (QuAIL)**Contributing Author(s)**: Zhang Jiang, Stuart Hadfield, and Eleanor Rieffel

A recently proposed class of quantum algorithm, the Quantum Approximate Optimization Algorithm (QAOA), holds great potential in tackling challenging combinatorial optimization problems on a gate model quantum computer. In QAOA, the problem Hamiltonian and a non-commuting driving Hamiltonian are applied alternatively. With an optimized time sequence for each piece, the optimal output of the problem Hamiltonian is approximated. We study QAOA on the model of a ring of disagreement. We provide analysis of QAOA for any level. Through transformation to the Fermionic representation, the evolution of the system under QAOA translates into quantum optimal control of a noisy spin ensemble. We show that the optimal controls lie within a defined subspace as a result of the symmetry in the system and hence the search effort can be focused on a lower-dimensional space. A well-known result of quantum control is that the control landscape admits only global optima. That result relies on the controllability of the system, i.e., given time, the set of provided controls can drive the system between any two states. In QAOA, however, at a finite level, the structure of the controls is constrained and does not guarantee full control over the system. We show that, nevertheless, the search space is still trap-free. While this is a study of a simple model, it may reveal underlying structure of the algorithm and inspire more efficient variants of QAOA.

### Elucidating reaction mechanisms on quantum computers

**Presenting Author**: Nathan Wiebe, Microsoft**Contributing Author(s)**: Markus Reiher, Dave Wecker, Matthias Troyer, and Krysta Svore

It is well known that quantum simulation promises exponential speedups for finding full configuration interaction (FCI) solutions for quantum chemistry over the best known classical algorithms. But when will this be useful? How large or a quantum computer will we need to achieve this? Here we provide estimates that show that a reasonable sized quantum computer can be used to help understand how biological nitrogen fixation works, which is a problem that requires an FCI solution. This understanding could lead to a new generation of energy efficient methods for making fertilizer that would be significant industrially. Our work considers the overheads of fault tolerance and circuit synthesis and also introduces fundamentally new circuits for simulating chemical dynamics with lower depth and introduces new methods for parallelizing phase estimation over independent quantum computers. These latter contributions help address the biggest drawback of non-variational quantum eigensolvers: their inability to be parallelized.

Read this article online: https://arxiv.org/abs/1605.03590

### Oscillatory localization of quantum walks

**Presenting Author**: Thomas Wong, University of Texas at Austin

We examine an unexplored quantum phenomenon we call oscillatory localization, where a discrete-time quantum walk with Grover's diffusion coin jumps back and forth between two vertices. We then connect it to the power dissipation of a related electric network. Namely, we show that there are only two kinds of oscillating states, called uniform states and flip states, and that the projection of an arbitrary state onto a flip state is bounded by the power dissipation of an electric circuit. By applying this framework to states along a single edge of a graph, we show that low effective resistance implies oscillatory localization of the quantum walk. This reveals that oscillatory localization occurs on a large variety of regular graphs, including edge-transitive, expander, and high-degree graphs. As a corollary, high edge connectivity also implies localization of these states, since it is closely related to electric resistance.

Read this article online: http://journals.aps.org/pra/abstract/10.1103/PhysRevA.94.062324

### Bell nonlocality vs. EPR steering in polarization-entangled photons

**Presenting Author**: Chen Jie Xin, Harvey Mudd College**Contributing Author(s)**: Evan Atchison and Theresa W. Lynn

Violation of a Bell inequality, or Bell nonlocality, is a signature of only a restricted class of two-qubit entangled states. States with too little entanglement to be Bell nonlocal may nevertheless be EPR steerable: measurements performed on one subsystem can influence probabilities of measurement outcomes on the other subsystem, thus ‘steering’ the second subsystem. Surprisingly, given the mutual nature of bipartite entanglement, certain two-qubit entangled states are actually one-way steerable, with only one subsystem able to steer the other. EPR steering, both mutual and one-way, could be useful as a signature of partial entanglement in a variety of quantum communication or distributed quantum computing schemes. We study EPR-steerable states of photon pairs entangled in polarization, produced via spontaneous parametric down-conversion. By varying the entanglement purity, we map out a range of entangled states that may be Bell nonlocal and steerable, Bell local but steerable, or Bell local and not EPR steerable. The simplicity of the experimental approach makes it suitable for an undergraduate advanced laboratory.

### The surface code with a twist

**Presenting Author**: Theodore Yoder, MIT**Contributing Author(s)**: Isaac H. Kim

The surface code is one of the most successful approaches to topological quantum error-correction. It boasts the smallest known syndrome extraction circuits and correspondingly largest thresholds. Defect-based logical encodings of a new variety called twists have made it possible to implement the full Clifford group without state distillation. Here we investigate a patch-based encoding involving a modified twist. In our modified formulation, the resulting codes, called triangle codes for the shape of their planar layout, have only weight-four checks and relatively simple syndrome extraction circuits that maintain a high, near surface-code-level threshold. They also use 25% fewer physical qubits per logical qubit than the surface code. Moreover, benefiting from the twist, we can implement all Clifford gates by lattice surgery without the need for state distillation. By a surgical transformation to the surface code, we also develop a scheme of doing the same gates on surface code patches in an atypical planar layout, though with less qubit efficiency than the triangle code. Finally, we remark that logical qubits encoded in triangle codes are naturally amenable to logical tomography, and the smallest triangle code can demonstrate high-pseudothreshold fault-tolerance to depolarizing noise using just 13 physical qubits.

Read this article online: http://web.mit.edu/~tjyoder/Public/surface-code-twist.pdf

(Session 9a : Friday from 3:45pm - 4:15pm)

### Universal fault-tolerant computing with Bacon-Shor codes

**Presenting Author**: Theodore Yoder, Massachusetts Institute of Technology

We present an optimized universal gate set, consisting of Hadamard and controlled-controlled-Z (CCZ), on Bacon-Shor subsystem codes. For concatenated Bacon-Shor codes, our gates possess a provably high asymptotic threshold under adversarial noise. For topological Bacon-Shor codes, our gates do not possess a threshold, but fail to do so only to the extent that a Bacon-Shor topological memory also fails. The smallest Bacon-Shor code has particularly simple implementations of our universal gates with the smallest space-time footprint of any known universal scheme by nearly 50% while also using no postselected state creation. We discuss possible implementation in ion trap architectures, where we find our CCZ is roughly three times faster than a magic-state version, a difference that translates to implementations of Shor's algorithm.

Read this article online: http://web.mit.edu/~tjyoder/Public/universal-fault-tolerant-draft.pdf

### Multiparameter estimation with single photons

**Presenting Author**: Chenglong You, Louisiana State University**Contributing Author(s)**: Sushovit Adhikari, Margarite LaBorde, Jonathan Dowling, and Jonathan Olson

It was suggested in [Phys. Rev. Lett. 111, 070403] that optical networks with relatively simple preparation and measurement devices – single photon Fock states and on-off detectors -- can show significant improvements over classical strategies for multiparameter estimation when the number of modes in the network is small. This was further developed in [arXiv:1610.07128] for the case of single parameter estimation, and shown to be sub-shotnoise only for n<7. In this paper, we show that this simple strategy can give asymptotically post-classical sensitivity for multiparameter estimation even when the number of modes is large. Additionally, we consider the effects of several other measurement techniques that can increase the efficiency of this device.

### Quantum digital simulator interacting with a bath

**Presenting Author**: Yi-Cong Zheng, Centre for Quantum Technologies, Yale-NUS college**Contributing Author(s)**: Hui-Khoon Ng

For a quantum digital simulator simulating a closed many-body quantum system, we ask the following questions: if both systems interacting with the same bath in the same way, will the dynamics of the target system and simulator behave somewhat close to each other? In this paper, we study the open system dynamics of both target system and their digital simulator by solving their time-convolutionless non-Markovian master equations and comparing their density matrices every simulation cycle. We give conditions when their stroboscopic behavior are close to each other analytically: that is, the gate period needs to be much smaller than both bath correlation time and the simulation cycle; meanwhile, the simulation cycle needs to be either much longer or much shorter than the bath correlation time. Numerical simulation of the open system dynamics for a simplified Kitaev toric code model in a thermal boson bath is carried out to verify the validity of these conditions, surprisingly, the fast speed of gate sequence alone is not enough to keep the nature of decoherence process. This result may shed light on developing new methods of quantum error correction and Gibbs state preparation.^{1}

### A nanophotonic platform integrating quantum memories and single qubits based on rare-earth ions

**Presenting Author**: Tian Zhong, IQIM, Caltech**Contributing Author(s)**: Jonathan Kindem, John Bartholomew, Jake Rochman, and Andrei Faraon

The integration of rare-earth ions in an on-chip photonic platform would enable quantum repeaters and scalable quantum networks. Here we demonstrate a nanophotonic platform consisting of yttrium vanadate (YVO) photonic crystal nanobeam resonators coupled to a spectrally dilute ensemble of Nd ions. The cavity acts as a memory when prepared with spectral hole burning, meanwhile it permits addressing of single ions. For quantum memory, atomic frequency comb (AFC) protocol was implemented in a Nd:YVO nanocavity cooled to 475 mk. We measure an efficiency at 2% at a storage time of ~100 ns with an efficient WSi superconducting nanowire detector (SNSPD). The small mode volume of the cavity results in a peak atomic spectral density of <10 ions per homogeneous linewidth, suitable for probing single ions when detuned. The high-cooperativity coupling of a single ion yields a strong signature (20%) in the cavity reflection spectrum. We estimate a signal-to-noise ratio exceeding 10 for addressing a single Nd ion. This, combines with the AFC memory, constitutes a promising platform for preparation, storage and detection of rare-earth qubits on the same chip.

(Session 13 : Saturday from 4:15pm - 4:45pm)

**SQuInT Chief Organizer**

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Mark M. Wilde, Assistant Professor LSU

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Gloria Cordova

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Ivan Deutsch, Regents' Professor

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