## Abstracts

### 1. Quantum walks with neutral atoms: from quantum transport phenomena to the falsification of classical trajectory theories

Andrea Alberti, Institut für Angewandte Physik

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Quantum walks with neutral atoms: from quantum transport phenomena to the falsification of classical trajectory theories Andrea Alberti and Dieter Meschede Institut für Angewandte Physik der Universität Bonn, Wegelerstraße 8, 53115 Bonn, Germany The quantum walk is a prime example of quantum transport: a particle undergoing discrete shifts in space and time is delocalized over a very large Hilbert space. In our system we implement this type of transport using cold atoms moving in a deep optical lattice. By creating artificial electric fields, we observe textbook transport phenomena like spin orbit coupling, Bloch oscillations, or Landau-Zener tunneling in a single experiment. We unravel the unique character of electric quantum walks by studying very different transport regimes, which depend on the commensurability of the electric field [1]. We experimentally observe ballistic delocalization for rational fields and dynamical localization for irrational ones [2]. Physical insight into the "quantumness" of the walk is obtained by an analysis of decoherence phenomena [3] and application of ideal negative measurements, i.e. interaction-free measurements. Ideal negative measurements are the essential requisite to obtain a 6-sigma experimental violation of the Leggett-Garg inequality, which falsifies theories of motion based on classical trajectories [4]. The controlled interaction of exactly two quantum walkers remains a daunting but highly attractive experimental challenge. References: [1]: C. Cedzich, T. Rybá r, A. H. Werner, A. Alberti, M. Genske and R. F. Werner, Propagation of quantum walks in electric fields, Phys. Rev. Lett. 111, 160601 (2013) [2]: M. Genske, W. Alt, A. Steffen, A. H. Werner, R. F. Werner, D. Meschede, A. Alberti, Electric quantum walks with individual atoms, Phys. Rev. Lett. 110, 190601 (2013) [3]: A. Alberti, W. Alt, R. Werner and D. Meschede, Decoherence Models for Discrete-Time Quantum Walks and their Application to Neutral Atom Experiments, arXiv:1409.6145 [quant-ph] (2014), accepted in New J. Phys. [4]: C. Robens, W. Alt, D. Meschede, C. Emary, and A. Alberti, Quantum diffusion falsifies the concept of classical trajectories by violation of Leggett-Garg inequality, arXiv 1404:3912 (2014).

### 2. Polynomial Monogamy Relations

Grant Allen, University of California, San Diego

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Entanglement negativity naturally captures the monogamous nature of multiple qubits. Monogamy, at least to quantum physicists, tends to conjure up a linear inequality involving a party's correlations with the rest of the system. In this talk, we show that negativity only trivially saturates the inequality, and we find a much tighter inequality in general. Our methods then shed light on the shareability of negativity in larger systems.

### 3. Quantum-proof randomness extractors via hierarchies of semidefinite programs

Mario Berta, Institute for Quantum Information and Matter Caltech

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Randomness extractors are an important building block for classical and quantum cryptography as well as for device independent randomness amplification and expansion. However, for these applications it is often crucial that the extractors are quantum-proof, i.e., that they work even in the presence of quantum adversaries. In general, quantum-proof extractors are poorly understood: we only know that some standard constructions of extractors are quantum-proof and there is one example of an extractor (with quite bad parameters) that is not quantum-proof. We argue that in the same way as communication complexity and Bell inequalities (multi prover games), the setting of randomness extractors provides a operationally useful framework for studying the power and limitations of a quantum memory compared to a classical one. We start by recalling how to phrase the extractor property as a quadratic program with linear constraint, and show that this quadratic program can be approximated by a converging Lasserre type hierarchy of semidefinite programs (sdp). We then show that allowing non-commuting variables in the quadratic program naturally characterises quantum-proof extractors, and again give a converging (non-commutative) hierarchy of sdp relaxations. By construction, the first level of the commutative and the non-commutative hierarchy are the same whereas higher level relaxations are generally different. This gives a unifying approach to understand the stability properties of extractors against quantum adversaries. By studying the integrality gap of the first level sdp approximation we recover all known results about quantum-proof extractors and derive new dimension dependent stability and instability bounds. This submission is joint work with Omar Fawzi and Volkher Scholz (not online yet, but partly based on arXiv:1409.3563).

### 4. Steering many-body quantum dynamics

Tommaso Calarco, University of Ulm

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Quantum technologies are based on the manipulation of individual degrees of freedom of quantum systems with exquisite precision. Achieving this in a real environment requires pushing to the limits the ability to control the dynamics of quantum systems of increasing complexity. Optimal control techniques are known to enable steering the dynamics of few-body systems in order to prepare a desired state or perform a desired unitary transformation. I will present a recently developed optimal control method that allows doing so for a many-body quantum system undergoing e.g. a quantum phase transition in the non-adiabatic regime. This opens the way to a range of applications, from the suppression of defects in a superfluid-Mott-insulator transition with ultra-cold atoms in an optical lattice to the achievement of various quantum gates at the quantum speed limit. I will present detailed calculations we performed for different experimental scenario, together with the corresponding results obtained by experimental groups in different fields, from cold atoms to spin squeezing in atomic ensembles and diamond NV centers. Our control method also allows for exploring more general questions like the complexity of reversing quantum many-body dynamics, steering it back to its initial state even without the ability to revert the sign of the whole Hamiltonian. I will conclude by showing some recent results we obtained in this context, as well as further questions opened by our investigations.

### 5. Spin Squeezing via Measurement -- a Useful Entanglement Resource

Kevin Cox, JILA, National Institute of Standards and Technology, and University of Colorado at Boulder

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I will report results from an experiment to generate and directly observe spin squeezing using a quantum non-demolition (QND) measurement. In a recent experiment, we directly observed 10.2(6) dB of spin squeezing with no background subtraction, one of the largest amounts of spin squeezing observed to date in any system. I will discuss these results as well as progress towards our next generation spin squeezing experiment and the potential applications of our scheme for precision measurement.

### 6. Taking Surface Electrode Traps to the Next Level

Spencer Fallek, Georgia Tech Research Institute

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Spencer D. Fallek, Nicholas D. Guise, J. True Merrill, Kelly E. Stevens, Kenton R. Brown, Jason M. Amini, Curtis Volin, and Alexa W. Harter Georgia Tech Research Institute, Atlanta, GA 30332, USA Robert E. Higashi, Son Thai Lu, Helen M. Chanhvongsak, Thi A. Nguyen, Matthew S. Marcus, Thomas R. Ohnstein, and Daniel W. Youngner Honeywell International, Golden Valley, Minnesota 55422, USA Surface electrode trap technologies have advanced rapidly in the past decade, providing an unprecedented ability to integrate complementary technologies for scalable quantum information systems. One limitation to this technology, as compared to 3D traps, is reduced light access due to wire bonds and trap die size. This has been a road block to increasing trap complexity. Approaches to improving light access in surface traps have included passing light through slots in the trap die and reducing the trap area using dense clusters of wire bonds (as demonstrated by Sandia National Laboratories' HOA trap built for the MUSIQC collaboration [1]). In collaboration with Honeywell International, we took the approach of removing the wire bonds from the trap and replacing them with through-the-wafer (TTW) vias that connect to back side ball-grid array (BGA) connections. Trench capacitors, integrated with the TTWs, provide RF grounding of the control electrodes to reduce intrinsic micromotion. With an overall die size of 1 mm x 3 mm, we can pass tightly focused beams across the trap surface without significant beam clipping. In this talk, I will report on characterization results of a BGA trap using 40Ca+ ions and on progress toward the Bernstein-Vazirani (BV) Algorithm using a chain of 171Yb+ ions in a second BGA trap. For the BV experiment, we use 40 mW of pulsed 355 nm light focused 60 μm above the trap surface to implement single and two qubit gates [2]. We have seen minimal charging effects on the trap in spite of the high UV power incident on the ion. When performing gate operations, the 355 nm Raman beams remain static and the ion chain is shuttled through the beams for addressing. Recent progress includes 93% fidelity two-qubit entanglement and low crosstalk single-qubit rotations on three ion chains. Our goal is to demonstrate the BV algorithm on three ions and then expand the algorithm to larger chains with swap gates.

[1] C. Monroe, et. al. Phys. Rev. A 89, 022317 (2014)
[2] R. Islam, et. al. Optics Lett. 39, 3238 (2014)

*This material is based upon work supported by the Georgia Tech Research Institute and the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA) under U.S. Army Research Office (ARO) contracts W911NF1010231 and W911NF1210605.

### 7. Hybrid diamond/gallium phosphide photonics for on-chip entanglement generation

Kai-Mei Fu, University of Washington

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Atomic-like solid-state defects are attractive candidates for quantum information processing due to the potential to integrate these defects into devices. However, the challenges associated with tuning the individual quantum properties of these defects, as well as the difficulty in realizing controlled interactions between defects, has thus far prohibited the realization of an on-chip defect-based quantum network. Here we present recent advances at UW toward the development of a hybrid photonics system aimed at realizing on-chip quantum photonic networks. A gallium phosphide (GaP) waveguiding layer is coupled to single NV centers created 20 nm from the diamond surface. The GaP photonic layer has the potential to provide efficient photon collection and active photon routing on the diamond chip. With this platform, we demonstrate photon collection from a single NV center into a micron-scale GaP cavity which is then routed to a bus waveguide. The photons are coupled off-chip through a grating coupler for device characterization. Current and projected device performance will be presented as well the implication for efficient NV electron spin entanglement generation.

### 8. Fault-tolerant quantum computation with constant overhead

Daniel Gottesman, Perimeter Institute

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The threshold theorem for fault tolerance tells us that it is possible to build arbitrarily large reliable quantum computers provided the error rate per physical gate or time step is below some threshold value. Most research on the threshold theorem so far has gone into optimizing the tolerable error rate under various assumptions, with other considerations being secondary. However, for the foreseeable future, the number of qubits may be an even greater restriction than error rates. The overhead, the ratio of physical qubits to logical qubits, determines how expensive (in qubits) a fault-tolerant computation is. Earlier results on fault tolerance used a large overhead which grows (albeit slowly) with the size of the computation. I show that it is possible in principle to do fault-tolerant quantum computation with low overhead, and with the overhead constant in the size of the computation. The result depends on recent progress on quantum low-density parity check codes.

### 9. The uncertainty principle in the light of quantum information

Gilad Gour, Institute for Quantum Science and Technology, University of Calgary

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Uncertainty relations are a distinctive characteristic of quantum theory that imposes intrinsic limitations on the precision with which physical properties can be simultaneously determined. The modern work on uncertainty relations employs entropic measures to quantify the lack of knowledge associated with measuring non-commuting observables. However, I will show here that there is no fundamental reason for using entropies as quantifiers; in fact, any functional relation that characterizes the uncertainty of the measurement outcomes can be used to define an uncertainty relation. Starting from a simple assumption that any measure of uncertainty is non-decreasing under mere relabeling of the measurement outcomes, I will show that Schur-concave functions are the most general uncertainty quantifiers. I will then introduce a novel fine-grained uncertainty relation written in terms of a majorization relation, which generates an infinite family of distinct scalar uncertainty relations via the application of arbitrary measures of uncertainty. This infinite family of uncertainty relations includes all the known entropic uncertainty relations, but is not limited to them. In this sense, the relation is universally valid and captures the essence of the uncertainty principle in quantum theory.

### 10. On the efficacy of weak measurements for tomography

Jonathan Gross, University of New Mexico, Center for Quantum Information and Control

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Recently there has been a fascination with weak measurements in the field of tomography. We conduct a detailed analysis of two specific schemes, so called "direct state tomography" and another scheme marketed as outperforming "standard" tomography with respect to fidelity considerations. Through the application of generalized measurement theory we clearly identify what weak measurements contribute beyond "standard" projective measurements and what simple techniques the application of weak measurements obscures.

### 11. Michelson-Morley test for electrons using a decoherence-free subspace for trapped ion

Hartmut Haeffner, University of California, Berkeley

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Lorentz symmetry is one of the corner stones of modern physics. As such it should not only hold for photons, but also for other particles such as the electron. Here we search for violation of Lorentz symmetry by performing an analogue of a Michelson-Morley experiment for electrons. We split an electron-wavepacket bound inside a calcium ion into two parts with different orientations. As the Earth rotates, the absolute spatial orientation of the wavepackets changes and anisotropies in the electron dispersion would modify the phase of the interference signal. To remove noise, we prepare a pair of ions in a decoherence-free subspace, thereby rejecting magnetic field fluctuations common to both ions. After a 23 hour measurement, we limit the energy variations to 11 mHz, verifying the isotropy of the electron's motion at the 1E-18 level, a 100 times improvement over previous work. Alternatively, we can interpret our result as testing the rotational invariance of the Coulomb potential. Assuming Lorentz symmetry holds for electrons and that the photon dispersion relation governs the Coulomb force, we obtain a fivefold improved limit on anisotropies in the speed of light. Our experiment demonstrates the potential of quantum information techniques in the search for physics beyond the Standard Model.

### 12. Role of classical hardness for quantum annealers

Itay Hen, University of Southern California

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Recent developments in quantum technology have led to the manufacturing of experimental programmable quantum annealing optimizers containing hundreds of quantum bits. These optimizers, also known as the "D-Wave" chips, promise to solve practical optimization problems potentially faster than conventional "classical" computers. The quantum nature of these optimizers has recently become the center of a heated debate within the Quantum Computing community (and well beyond it) about the claimed superiority of these annealers over traditional devices and the degree to which they exploit their quantum capabilities. In this context, specifically of importance is the question of how well quantum annealers perform on hard problems with rugged free-energy landscapes for which classical methods are expected to fail. I will describe attempts to identify such hard D-Wave-specific problems by means of state-of-the-art methods (multi spin coding, parallel tempering simulations and stochastic time-series analysis), and present results pertaining to the performance of various classical algorithms and the D-wave Two chip on these. This is a joint work with Victor Martin-Mayor.

### 13. A Platform of Rydberg-Dressed Cesium Atoms for Quantum Control Applications

Yuan-Yu Jau, Sandia National Laboratories

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Over the last decade, various ideas of using Rydberg-dressed atoms have been proposed for generating strong ground-state interactions between neutral atoms to realize quantum gates, entanglement of pair-wise qubits, and entanglement for spins in an atomic ensemble for quantum computing and quantum metrology applications. Compared to directly using Rydberg blockade for making quantum gates or producing entanglement, in principle Rydberg-dressed atoms are more insensitive to the various decoherence mechanisms and lead to a better quantum control fidelity. At Sandia, we have established an experimental system allowing us to singly trap Cs atoms and generate Rydberg dressing with a direct excitation laser at 318 nm. We have conducted a series of experiments with Rydberg-dressed Cs atoms using different principal quantum numbers of the Rydberg states with different experimental conditions. We will present our experimental progress of using Rydberg-dressed Cs atoms as the platform for future quantum control applications.

### 14. Informationally complete measurements from compressed sensing methodology

Amir Kalev, Center for Quantum Information and Control, University of New Mexico

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Determining quantum states and processes from a set of measurements is a fundamental problem in quantum information science. A set of such measurements is said to be informationally complete (IC) if, given sufficient statistics, they uniquely distinguish the desired density or process matrix from the set of all physical matrices. Because the standard protocols for quantum tomography (QT) scale poorly---growing exponentially with the number of subsystems---it is important to develop techniques that minimize the resources necessary for tomography. To this end, the methodology of compressed sensing (CS) has been ported from classical signal recovery and has been applied to the problem of QT. The CS paradigm applies under the assumption that there is an a priori knowledge that the signal has a concise representation, e.g., that it is a sparse vector or a low-rank matrix. Then, according to the CS methodology, one can reconstruct the signal, with very high accuracy, with a substantially reduced number of measurements, as long as the latter satisfy a restricted isometry property (RIP). However, for QT, the detailed nature of the relation between the CS measurements and IC measurements has not been made explicit. In this work, we rigorously establish the connection between RIP and IC through a key feature that arises in the quantum context: the positive semidefinite property of the density matrix (or of the process matrix). We show that due to the positivity of the density matrix, the CS measurements satisfy a special type of IC measurements. This relation has far reaching consequences for QT. First, it enables us to construct special type of IC measurements with tools provided by the CS methodology. By construction, the measurements are robust to noise. And second, with this result in hand, we are able to use simpler and more widespread numerical methods, as opposed to the specialized CS solvers, to achieve similar results. Hence, it becomes easier to employ algorithms that efficiently analyze QT data on large dimensional systems.

### 15. Two-particle quantum interference in tunnel-coupled optical tweezers

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Motional control of neutral atoms has a rich history and increasingly interest has turned to single-atom control. I will present work in which we begin by laser cooling single bosonic atoms to near their vibrational ground state in optical tweezer traps. Our recent work has explored the interference of these independently-prepared atoms in a limit where they can be considered non-interacting. We observe a massive-particle analog of the Hong-Ou-Mandel (HOM) effect when we arrange for atom tunneling to play the role of a balanced photon beamsplitter. The HOM signature is used to probe the effect of atomic indistinguishability on the two-boson dynamics for a variety of initial conditions. I will discuss the implication of these experiments for the assembly and control of a variety of quantum systems, ranging from nano-photonic interfaces to entanglement entropy measurements in many-body systems.

### 16. An Exchange-Only Qubit in Isotopically Enriched 28-Si

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We demonstrate coherent manipulation and universal control of a qubit composed of a triple quantum dot implemented in an isotopically enhanced Si/SiGe heterostructure, which requires no local AC or DC magnetic fields for operation. Strong control over tunnel rates is enabled by a dopantless, accumulation-only device design, and an integrated measurement dot enables single-shot measurement. Reduction of magnetic noise is achieved via isotopic purification of the silicon quantum well. We demonstrate universal control using composite pulses and employ these pulses for spin-echo-type sequences to measure both magnetic noise and charge noise. The noise measured is sufficiently low to enable the long pulse sequences required for exchange-only quantum information processing. Sponsored by United States Department of Defense. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressly or implied, of the United States Department of Defense or the U.S. Government. Approved for public release, distribution unlimited.

### 17. Neuromorphic photonic computation with multimode cavity QED

Benjamin Lev, Stanford University

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Photons in a multimode optical cavity can be used to mediate tailored interactions between atoms confined in the cavity. For atoms possessing multiple internal (i.e., "spin") states, the spin-spin interactions mediated by the cavity are analogous in structure to the RKKY interaction between localized spins in metals. Thus, it is possible to use spinful atoms in cavities to realize models of frustrated and/or disordered spin systems, including models that can be mapped on to the Hopfield neural network model and related models of associative memory. We explain how this realization of associative memory arises and discuss ways in which the properties of these models can be probed in this quantum optical setting.

### 18. Tamper-Resistant Cryptographic Hardware in the Isolated Qubits Model

Yi-Kai Liu, National Institute of Standards and Technology (NIST)

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Using quantum information, one can perform certain cryptographic tasks, such as quantum key distribution, with information-theoretic security. But other tasks, such as quantum bit-commitment and oblivious transfer, are provably impossible. We show how a special class of quantum devices -- "isolated qubits" -- can circumvent these limitations. Isolated qubits are qubits that have long coherence times, but can only be accessed using single-qubit gates and measurements; entangling operations are not allowed. (This definition is motivated by the properties of solid-state nuclear spins.) We show how isolated qubits can be used to construct "one-time memories," a kind of non-interactive oblivious transfer, as well as "one-time programs," programs that can only be run once, and reveal nothing about their internal structure.

### 19. Quantum Information Processing in surface electrode ion traps

Peter Maunz, Sandia National Laboratories

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Craig R. Clark, Matthew G. Blain, Jonathan Mizrahi, Susan M. Clark, Daniel L. Stick, Boyan Tabakov, Francisco Benito, Jonathan D. Sterk, Chris Tigges, Jay Van Der Wall, Ray Haltli, Andrew Hollowell, and Peter Maunz Micro-fabricated surface ion traps are an essential technology that will enable scaling of trapped ion quantum information processing to interesting mesoscopic system sizes. While micro-fabricated traps are inherently scalable, the surface geometry and close proximity of trapped ions to the trapping structure make their use for quantum information processing more challenging than macroscopic ion traps. In this talk, we will present progress toward mastering these challenges and establishing surface traps for quantum information processing. We will characterize the High-Optical-Access (HOA) trap, which is optimized for quantum information processing tasks, report on using an argon plasma to remove surface contaminants on traps and show a detailed experimental analysis of average and worst case fidelity of single qubit gates in 171Yb+. Furthermore, we will present the first two-ion gate in a Sandia surface trap. This work was supported by Sandia's Laboratory Directed Research and Development (LDRD) and the Intelligence Advanced Research Projects Activity (IARPA). Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the US Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

### 20. Experiments to observe the entangled particles inside macroscopic quantum states

Morgan Mitchell, ICFO - Institute of Photonic Sciences

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Macroscopic quantum phenomena, from the relatively familiar (squeezing) to the very exotic (high-Tc superconductivity) are thought to be produced by the collective actions of macroscopic numbers of entangled particles. Can we observe the microscopic, particulate entanglement underlying a macroscopic quantum state? I will describe two experiments, one with atoms and one with photons, that measure the entanglement of particles in a squeezed state. Using quantum non-demolition measurements on a spin ensemble, we produce a macroscopic spin singlet, an unpolarized squeezed state containing at least 500,000 entangled atoms. In another experiment, we extract photons from a polarization-squeezed beam and use quantum state tomography to directly observe pair-wise entanglement. We confirm the predicted large-scale entanglement: all photon pairs arriving within the squeezing coherence time are entangled.

### 21. How can Maxwell's demon harness quantum many-body correlations?

Akimasa Miyake, Center for Quantum Information and Control, University of New Mexico

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Maxwell's demon is the archetype which underscores the substantial role of information and correlations in the context of thermodynamics. While there is nothing paradoxical about the demon working as a refrigerator if one properly takes the increase of entropy in the demon's own memory into account, it is intriguing how different rules of information and correlations in quantum regime affect the thermodynamic performance of the demon. Here, we extend the memory of the Maxwell's demon to a collection of qubits, and characterize quantum advantages as well as potential limitations by so-called monogamy of entanglement which states that certain kinds of quantum correlations cannot be shared arbitrarily. This is a joint work with Adrian Chapman.

### 22. Local and Remote Networks of Trapped Ions

Christopher Monroe, Joint Quantum Institute and University of Maryland

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Laser-cooled and trapped atomic ions are standards for quantum information science, acting as qubits with unsurpassed levels of quantum coherence while also allowing near-perfect measurement. When qubit state-dependent optical forces are applied to a collection of atomic ions, their Coulomb interaction is modulated in a way that allows the entanglement of the qubits through quantum gates that can form the basis of a quantum computer. Similar forces allow the simulation of quantum magnetic interactions, and recent experiments have implemented transverse Ising or XY models with up to 20 trapped ions, and this seminar will cover recent experimental results, from studies of equilibrium ground states [1,2] and dynamics [3,4] to the implementation of certain interacting spin-1 models [5] that may show certain topologically-ordered ground states. Soon these experiments will be extended to >20 spins, where no classical computer can predict its behavior, particularly the many-body dynamics. Scaling to even larger numbers can be accomplished by coupling trapped ion qubits to photons [6,7], where entanglement can be formed over remote distances for applications in quantum communication, quantum teleportation, and modular quantum computation.
[1] R. Islam, et al., Science 340, 583 (2013).
[2] P. Richerme, et al., Phys. Rev. Lett. 111, 100506 (2013).
[3] P. Richerme, et al., Nature 511, 198 (2014).
[4] C. Senko, et al., Science 345, 430 (2014).
[5] C. Senko, et al., arXiv 1410.0937 (2014).
[6] L.-M. Duan and C. Monroe, Rev. Mod. Phys. 82, 1209 (2010).
[7] D. Hucul, et al., Nature Physics doi:10.1038/nphys3150, arXiv 1403.3696 (2014).

### 23. Quantum control and squeezing of collective spin

Enrique Montano, University of Arizona

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Enrique Montano, Daniel Hemmer, Poul Jessen. Center for Quantum Information and Control (CQuIC). College of Optical Sciences and Department of Physics, University of Arizona. Ben Baragiola, Leigh Norris, Ivan Deutsch. Center for Quantum Information and Control (CQuIC). Department of Physics and Astronomy, University of New Mexico. Quantum control of many body atomic spins is often pursued in the context of an atom-light quantum interface, where a quantized light field acts as a "quantum bus" that can be used to entangle distant atoms. One key challenge is to improve the coherence of the atom-light interface and the amount of atom-light entanglement it can generate, given the constraints of working with multilevel atoms and optical fields in a 3D geometry. We are currently exploring new ways to achieve this, through rigorous optimization of the spatial geometry, and through control and optimization of the internal atomic state. Our basic setup consists of a quantized probe beam passing through an atom cloud held in a dipole trap, first generating spin-probe entanglement through the Faraday interaction, and then using backaction from a measurement of the probe polarization to squeeze the collective atomic spin. In this scenario the relevant figure of merit is the signal-to-noise ratio for a measurement of the collective spin projection noise in the presence of probe shot noise. With an optimized free-space geometry we readily achieve a signal-to-noise ratio of 10dB, and by using a 2-color probe scheme to suppress tensor light shifts we can translate this into as much as 7dB of metrological squeezing. It is possible to further increase atom-light coupling by "amplifying" the initial projection noise per atom through a suitable internal state preparation. For example, by preparing the atom ensemble in a "cat" state, the spin projection noise can be increased by a factor of 2f (8 for Cs) relative to the commonly used spin coherent state. Under the right conditions such an increase in projection noise can lead to stronger measurement backaction and increased atom-atom entanglement. If so, we can in principle use further internal-state control to map this entanglement to a basis where it corresponds to improved squeezing of, e.g., the physical spin-angular momentum or the collective atomic clock pseudospin. In practice, controlling the collective spin of N~10^6 atoms in this fashion is an extraordinarily difficult challenge because errors in the control of individual atoms tend to be highly correlated. We will discuss recent, encouraging progress towards the preparation and detection of projection noise limited "cat" states, and the general prospect of using the internal atomic structure as a resource for ensemble control.

### 24. Fully reconfigurable gate architecture for Si/SiGe spin qubits

Jason Petta, Princeton University

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Depletion mode architectures for gate-defined quantum dots have been successful in the implementation of single, double and triple quantum dots. However, scaling up to more complicated devices presents serious lithographic challenges. I will present a reconfigurable, accumulation mode lateral quantum dot device architecture. The same device can be operated as a few electron single quantum dot or a few electron double quantum dot. High sensitivity single electron charge sensing is achieved using a nearby quantum dot as a charge detector. I will also describe recent efforts to couple semiconductor quantum dots to microwave cavities.

### 25. Hyper-Accurate Gate Set Tomography

Kenneth Rudinger, Sandia National Laboratories

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Standard quantum tomography is limited by its reliance on precalibrated states/measurements/operations, which are unavailable in many physical qubit systems. Gate set tomography (GST) is a tomographic framework introduced to solve this problem of self-referential calibration. Previous work demonstrated that GST can successfully reconstruct quantum states and processes with reasonable accuracy, using closed-form linear inversion of data obtained from short sequences of quantum operations. In this talk, we demonstrate algorithms for "long-sequence GST", which enable efficient analysis of data from experiments involving long sequences of gates. We also show how to choose long sequences that amplify every possible error in the gate set. Together, these techniques produce GST estimates whose accuracy is limited not by 1/sqrt(N) (where N is the number of measurements), but by 1/L, where L is the length of the longest gate sequence. We show simulations and experimental results (including trapped-ion, neutral atom, and semiconductor qubits) that confirm accuracy better than 1e-4 in the gate elements. This work was supported in part by the Laboratory Directed Research and Development 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.

### 26. When can we trust analog quantum simulators?

Mohan Sarovar, Sandia National Laboratories, Livermore

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Many quantum information technologies are rapidly maturing to the point where they are capable of analog quantum simulation. In fact, several AMO experiments have made non-trivial observations about quantum many body models based on analog simulation of the models [e.g. Trotzky et al. Nature Physics, 8 325 (2012), Richerme et al. Nature, 511 198 (2014)]. However, unlike digital quantum simulation, there is no notion of controlling errors in analog simulation and this has raised questions about when the results from analog simulators can be trusted [Hauke at al. Rep. Prog. Phys. 75, 082401 (2012)]. In this talk I will relate the question of whether an analog quantum simulation is robust to the phenomenon of parameter space compression. This enables the development of a technique for assessing when a particular analog quantum simulation will be robust to experimental uncertainty and errors. I will present ongoing work applying this technique to several quantum many body models to assess their robustness to experimental uncertainty during analog simulation. This is joint work with Jun Zhang and LiShan Zeng.

### 27. Topology and Non-Local Quantum Engineering with Ultracold Atoms

Monika Schleier-Smith, Stanford University

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A conceptually appealing vision for fault-tolerant quantum computation involves encoding information in non-local, topological properties of a many-particle quantum system. Motivated by this prospect, I will present recent experiments employing atom interferometry to measure geometric phases imprinted in the band structure of an optical honeycomb lattice. Using a Bose-Einstein condensate as a momentum-resolved probe, we have directly detected the singular quantized Berry flux of a Dirac cone. Major outstanding challenges are to combine suitable geometric phases with interactions to realize topologically ordered states; and to develop methods of accessing non-local degrees of freedom. With the latter challenge in mind, I will present plans for engineering non-local interactions among cold atoms via strong coupling to a single optical resonator mode. These highly coherent and controllable interactions will also provide new opportunities for entanglement-enhanced metrology and for fundamental studies of many-particle quantum dynamics.

### 28. Quantum Bath Engineering with Superconducting Qubits

Irfan Siddiqi, University of California, Berkeley

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Uncontrolled interaction with a noisy environment typically results in decoherence processes that suppress quantum behavior, and typically drive a system of quantum bits toward their ground state. We consider the case of superconducting transmon qubits coupled to microwave frequency cavities, with the latter providing both a channel for quantum state readout and a dynamic quantum bath which can be configured through the application of microwave irradiation. With appropriately chosen drive pulses and readout protocols, we show that such an environment can mediate autonomous cooling to both superposition and entangled states for up to three qubits coupled to a single cavity, and two qubits in separate cavities connected by a coaxial cable. We discuss the fidelity of these operations and routes for future optimization.

### 29. Recent progress in trapped ion quantum information at NIST

Daniel Slichter, National Institute of Standards and Technology

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Qubits formed from the hyperfine states of trapped atomic ions exhibit long coherence times, and can be precisely controlled using lasers and/or microwave fields. However, scaling up to systems with dozens or hundreds of trapped ions presents a variety of experimental challenges. Here, we report progress on several projects for improving and scaling both control and readout of trapped ion qubits, including trap-integrated photon detectors, single-mode fibers for delivery of high-power UV laser light, and all-microwave single-qubit and two-qubit gates. We also describe other current work, including fast ion transport in multi-zone traps, studies of anomalous motional heating from trap surfaces, and the development of a new open-source experimental control platform suitable for complex experiments requiring agile frequency synthesis and many channels of nanosecond-timed digital I/O. This work is supported by IARPA, ONR, and the NIST Quantum Information Program.

### 30. High-precision Quantum Algorithms

Rolando Somma, Los Alamos National Laboratory

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I will describe a simple, efficient method for implementing various operations on a quantum computer to solve problems in Hamiltonian simulation, linear algebra, physics, and more. The most important properties of our method is that its cost depends only logarithmically on the inverse of the desired precision and it does not require using phase estimation as in previous approaches, with a significant reduction in the number of gates needed to solve the problem.

### 31. Optically measuring and coupling quantum systems in a cavity

Dan Stamper-Kurn, University of California, Berkeley

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Cavity quantum electrodynamics generally lets one direct the interactions between polarizable objects and light, increasing the relevance of a single optical mode. As such, optical cavities improve our ability to extract information about a quantum object through its interaction with light, and also our ability to cause quantum objects to interact with one another remotely by exchanging photons. I will discuss studies of cavity optomechanics using gases of ultracold atoms trapped within a high finesse Fabry-Perot resonator. Cavity-based measurement allows us to detect forces as the standard quantum limit, a long-time goal for optomechanical systems. We also demonstrate coherent coupling between distinct mechanical objects, mediated by cavity photons, and also characterize the simultaneous influence of measurement on this interaction.

### 32. Entanglement is not Enough

Leonard Susskind, Stanford University

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Two things make quantum physics very different from classical physics: entanglement, and the capacity for exponential complexity. The role of entanglement in the quantum theory of black holes is well established. But entanglement is not enough; long after entanglement has reached its maximum, complexity in a chaotic quantum system continues to increase. The increase of complexity is deeply related to the interiors of black holes in ways that suggest deep connections between complexity and space-time geometry. I will explain some of the ways in which quantum information theory is leading you a much deeper understanding of black holes. Entanglement and quantum computational complexity play a key role in the emergence of space behind the horizon.

### 33. Efficient Synthesis of Universal Probabilistic Quantum Circuits

Krysta Svore, Microsoft Research

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Techniques to efficiently compile high-level quantum algorithms into lower-level fault-tolerant circuits are crucial for the implementation of a scalable quantum computer. Several universal gate sets can be used for compilation, including Clifford+T, T = [1 0; 0 e^{i \pi/4}], Clifford+K, K = [1 0; 0 e^{i \pi/6}], and Clifford+V, V=\1/\sqrt{5} (Id+2iZ). While in principle the Solovay-Kitaev algorithm can solve the synthesis problem for any universal gate set, the synthesized circuits have a large upper bound on the circuit depth of O(log^{3.97} (1/e), where e is the precision, and a classical compilation time that is almost cubic in \log(1/e). Fortunately, for each of the above-mentioned bases (using separate algorithms), elementary number theory can be leveraged to obtain an optimal or near-optimal depth circuit. For Clifford+T, for example, the number of T gates (and compilation time) is close to 3 log_2(1/\e) for single-qubit Z rotations. In this talk, we show that this constant can be further reduced; this comes as a surprise as there is an information-theoretic lower bound that establishes that there are Z-rotations that require 3 log_2(1/e) many T gates to reach an approximation precision e. By (1) allowing measurements and adaptive decisions on earlier results and (2) allowing to operate on more than one qubit through the use of an ancilla, we show that this bound can be surpassed using so-called Repeat-Until-Success" (RUS) circuits. We show that with a single framework we can synthesize RUS circuits over the above three bases and achieve an expected gate count of log_b(1/e)+O(log(log(1/e))), where b is related to an expansion property of the underlying basis; b is defined so that for a given depth t the number of unique circuits scales as Theta(b^t). Specifically, b=2 for Clifford+T, b=4 for Clifford+K, and b=5 for Clifford+V. Based on arxiv:1404.5320 and arxiv:1409.3552.

### 34. Microwave Optomechanical Circuits

John Teufel, National Institute of Standards & Technology

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By incorporating microfabricated mechanical resonators into superconducting microwave circuits, we use microwave photons to prepare and measure quantum states of motion. At NIST, we are developing this emergent technology toward an array of applications including: force sensing, quantum-limited microwave amplification, frequency conversion, thermometry, and processing of quantum information. I will discuss recent progress toward each of these goals as well as recent experiments which merge these mechanical circuits with supercondicting qubits.

### 35. Distributed Management of Density Matrices

Rodney Van Meter, Keio University

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The density matrix (d.m.) of a quantum state is a statistical construct, describing our best understanding of the actual state based on our prior experience with, and constant monitoring of, the experimental apparatus and its ability to store and manipulate quantum states. An operational problem arises when a multi-particle state is held in physically distributed locations and each node must make real-time decisions on the disposition of the quantum state, as in a quantum repeater network. Each node holding part of the state may independently choose to manipulate the state, affecting its fidelity. Software systems must concern themselves with the discrepancy between (in a two-party state) Alice's notion of the d.m., Bob's notion of the d.m., and the d.m. that would be compiled by an observer Orville not subject to relativistic constraints on information. We have developed a set of principles for guiding the implementation, and compare four methods for meeting the constraints: by contract, by centralized control, by distributed calculation and decision, and by direct monitoring. Simulations including direct monitoring will be presented.

### 36. Area Laws and the complexity of quantum states

Umesh Vazirani, U.C. Berkeley

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One of the great challenges posed by the laws of quantum mechanics is that the complexity of quantum states in general grows exponentially in the number of particles. Are there large classes of quantum states that do not suffer from exponential complexity? A sweeping conjecture, called the area law, asserts that states of special interest in condensed matter physics, ground states of gapped local Hamiltonians have limited entanglement. Whereas the area law is rigorously proved for a one dimensional chain of particles, establishing it for two and three dimensional systems remains a central open question in quantum Hamiltonian complexity. At the other end of the spectrum is the generalized area law, where the interaction graph of the local Hamiltonian can be arbitrary - the generalized area law asserts that the entanglement entropy for a subset of vertices scales as its edge cut-set (the area) rather than the cardinality of the subset (volume). I will outline a recently discovered counter-example to the generalized area law. The construction is based on quantum expanders, and has a beautiful alternate description in terms of a very efficient communication complexity protocol. It is insightful to view the construction in the context of the proof of the area law in one dimension, which I will briefly sketch, leading to a discussion of prospects for two dimensional systems. Based on joint work with Itai Arad, Alexei Kitaev and Zeph Landau, and with Dorit Aharonov, Aram Harrow, Zeph Landau, Daniel Nagaj and Mario Szegedy.

### 37. Dissipative quantum state preparation with quasi-local resources

Lorenza Viola, Dartmouth College

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Techniques for quantum reservoir and dissipation engineering are playing an increasingly important role in controlling open quantum systems. Implications range from dissipative quantum state preparation and quantum computation, to non-equilibrium quantum phases of matter and quantum thermodynamics. In this talk, I will describe progress toward developing a general control-theoretic framework for the analysis and synthesis of quasi-local open-system dynamics that admits a desired quantum state as its unique asymptotically stable state, with focus on continuous-time Markovian dynamics and entangled target states. In particular, after reviewing existing necessary and sufficient conditions for quasi-local stabilization of a pure state, I will discuss the additional challenges that the stabilization problem entails for a general mixed target state, and present recent rigorous results for a natural class of frustration-free Lindblad dynamics.

### 38. Quantum Bootstrapping via Compressed Quantum Hamiltonian Learning

Nathan Wiebe, Microsoft Research

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Recent work has shown that quantum simulation is a valuable tool for learning empirical models for quantum systems. We build upon these results by showing that a small quantum simulators can be used to characterize and learn control models for larger devices for wide classes of physically realistic Hamiltonians. This leads to a new application for small quantum computers: characterizing and controlling larger quantum computers. Our protocol achieves this by using Bayesian inference in concert with Lieb-Robinson bounds and interactive quantum learning methods to achieve compressed simulations for characterization. Whereas Fisher information analysis shows that current methods which employ short-time evolution are suboptimal, interactive quantum learning allows us to overcome this limitation. We illustrate the efficiency of our bootstrapping protocol by showing numerically that an 8-qubit Ising model simulator can be used to calibrate and control a 50 qubit Ising simulator while using only about 750 kilobits of experimental data.

### 39. Fidelity of recovery and geometric squashed entanglement

Mark Wilde, Louisiana State University

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We define the fidelity of recovery of a tripartite quantum state on systems A, B, and C as a measure of how well one can recover the full state on all three systems if system A is lost and a recovery operation is performed on system C alone. This quantity is helpful in making concrete the notion of an approximate quantum Markov chain. The surprisal of the fidelity of recovery (its negative logarithm) is an information quantity which obeys nearly all of the properties of the conditional quantum mutual information I(A;B|C), including non-negativity, monotonicity under local operations, duality, and a dimension bound. We then define an entanglement measure based on this quantity, which we call the geometric squashed entanglement. We prove that the geometric squashed entanglement is an entanglement monotone, that it vanishes if and only if the state on which it is evaluated is unentangled, and that it reduces to the geometric measure of entanglement if the state is pure. We also show that it is subadditive, continuous, and normalized on maximally entangled states. Our results for the bipartite case can be extended to a multipartite fidelity of recovery and a multipartite geometric squashed entanglement. This is joint work with Kaushik P. Seshadreesan.

### 40. Causation and the Two Theorems of John Bell

Howard Wiseman, Griffith University

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Abstract: Fifty years ago John Bell published a theorem [1] which has been described as "the most profound discovery in science" [2]. However, the question as to what his theorem says about the world is still much disputed by physicists and philosophers [3]. Bell's original answer [1] was the joint assumptions of determinism and locality. His later answer [4] was the single assumption of local causality (which, confusingly, he sometimes also called locality). Different "camps" of physicists "operationalists and realists respectively "prefer the different versions of Bell's theorem. Which of Bell's notions, locality or local causality, expresses the causal structure of Einstein's theory of relativity? I will argue for the answer: neither [5,6]. Both notions require an additional causal assumption, and the one required for local causality is a stronger one. I will discuss how the different assumptions fit with the ideologies of the two camps, and how they can best be reconciled. [1] J. S. Bell, "On the Einstein-Podolsky-Rosen paradox", Physics 1, 195-200 (1964). [2] H. P. Stapp, "Are superluminal connections necessary?", Nuovo Cim. 40B, 191 (1977). [3] J. Phys. A 47, issue 42: Special Issue "50 years of Bell's theorem" (2014). [4] J. S. Bell, "The Theory of Local Beables", Epistemological Lett. 9, 11-24 (1976). [5] H. M. Wiseman, "The two Bell's theorems of John Bell", in [4], article 424001. [6] H. M. Wiseman, "Bell's theorem still reverberates", Nature 510, 467-9 (2014).

### 41. Quadratic forms in quantum Hall states

Jon Yard, Microsoft

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A promising approach to the construction of a fault-tolerant quantum computer aims to manipulate quantum information through the braiding of bulk quasiparticle excitations in strongly-correlated two-dimensional topologically ordered systems such as fractional quantum Hall states. The bulk excitations in such 2+1-dimensional topological phases are protected from noise by a finite energy gap, whereas the edges, which are actually what are probed in experiments, support gapless excitations. However, the same bulk topological phase can have multiple distinct edge phases. To make matters worse, a general classification of edge phases corresponding to a possible bulk phase is not currently known. In this talk, I will illustrate how the mathematical theory of integral quadratic forms yields a natural and complete mathematical classification of the bulk-boundary correspondence for abelian topological phases. For these states, edge phases correspond to integral lattices, while the bulk phase only depends on an invariant of the edge lattice called its genus by Gauss. I will also discuss ongoing research on a physical interpretation for an arithmetic refinement of the genus called the spinor genus. This is joint work with Cano, Cheng, Conrad, Mulligan, Nayak and Plamadeala.

### 42. Nanophotonic quantum memory based on rare-earth-doped crystals

Tian Zhong, California Institute of Technology

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Rare earth ions (REIs) are promising candidates for implementing solid-state quantum memories and quantum repeater devices. Moreover, their high spectral stability, long coherence times, and small inhomogeneous broadening make REIs a good choice for integration in an on-chip quantum nano-photonic platform. Here we demonstrate photon storage in an Yttrium orthosilicate Y2SiO5 (YSO) photonic crystal nano-beam resonator with mode volume of 1.6 cubic wavelength. The coupling of the 883 nm 4I9/2-4F3/2 transition of Neodymium (Nd) ions to the nano-resonator results in a 40 fold enhancement of the transition rate (Purcell effect), and increased optical absorption (~80%) - adequate for realizing efficient photon storage via cavity impedance matching. Optical coherence times T2 up to 100 μs with low spectral diffusion were measured for ions embedded in the nano-beams, which are comparable to those observed in unprocessed bulk samples. This indicates that the remarkable coherence properties of REIs are preserved during nanofabrication process. Multi-temporal mode photon storage using stimulated photon echo and atomic frequency comb (AFC) protocols were then implemented in these Nd:YSO nano-resonators. Lastly, our current technology can be readily transferred to Erbium (Er) doped YSO devices, therefore opening the possibility of efficient on-chip optical quantum memory at 1.5 μm telecom wavelength.