## Abstracts

All Abstracts | Poster Abstracts | Talk Abstracts

### 1. Energy transportation and quantum correlation in a chain of ions

Ahmed Abdelrahman, University of California, Berkeley

view abstract +

We experimentally study energy transport across a chain of trapped ions of up to 37 ions. For this, we rapidly excite the radial local mode of one of the ions by pulsing a laser at the motional frequency. While the excitation is traveling through the ion crystal, we monitor the energy of other ions in the chain via sideband spectroscopy. We observe energy revivals persisting for for up to 40 ms, much longer than the typical transport time of 20 microseconds. The energy revivals are in well agreement with a normal mode decomposition of the ion motion. We also study the dynamics of quantum correlation of trapped ions. We establish quantum correlations between the internal degree-of-freedom of a single ion with its radial local mode with a pulse on the blue sideband. We then probe the coherence between the internal qubit and the local mode while the motional energy spreads across the crystal. Our studies show that the motion of trapped ions is a suitable candiate to study the dynamics of energy and quantum correlations in closed classical and quantum systems.

### 2. Remote Entanglement of Ba Ions

Carolyn Auchter, University of Washington

view abstract +

We present work toward entanglement of single Ba ions in traps separated by a few meters. A novel trap type with a parabolic mirror for light collection and a piezoelectric micropositioning system is used to achieve two results: reduction of micromotion and placement of the trap null at the focus of the parabolic mirror for improvement of light collection efficiency. Since entanglement is mediated by the interference of spontaneously emitted photons from each ion, light collection efficiency is essential to the rate and success of the experiment. This scheme can be extended to a loophole-free Bell Inequality test to be performed with traps separated by ~1 km. In addition to obtaining this fundamental result, generation of entanglement between different traps can be a useful technique for some quantum computing architectures. Results demonstrating the successful generation of an entangled ion and photon pair with fidelity of 0.84(1) are also presented.

### 3. Efficient open system control for near unitary maps

Charles Baldwin, University of New Mexico

view abstract +

A challenge in quantum control is to create a coherent process in the presence of decoherence, which is often not uniform throughout the Hilbert space. This presents a particular challenge in the context of optimal control where, through time-dependent Hamiltonians, the system explores a complicated path in Hilbert space. The goal is then to simultaneously drive the system to achieve the desired unitary map, while avoiding, to the maximum degree possible, loss, dissipation, and decoherence. Previous work on such open systems extend a d-dimensional Hilbert space to a d^2-dimensional space and optimize a propagator, based on the master equation, acting on the larger space. This extension allows all the dynamics to be captured but makes the numerical searches involved more costly. Building from the theory of quantum trajectories, we instead construct a $d$-dimensional non-unitary propagator with an effective non-Hermitian Hamiltonian from the master equation. This is the linear evolution corresponding to the unnormalized *no-jump* condition in a trajectory. By effectively minimizing the chance of a quantum jump, we minimize the probability for decoherence. We numerically demonstrate that optimizing the evolution of this propagator suppresses population in states with larger decoherence rates. While the propagator does not fully capture the dynamics of the open system, using it in the optimization returns a map that closely matches the full description of the system when the target is a unitary.

### 4. Optomechanical laser cooling with mechanical modulations

Pablo Barberis Blostein, Instituto de investigaciones en matematicas aplicadas y en sistemas, Universidad Nacional Autonoma de Mexico

view abstract +

We theoretically study the laser cooling of cavity optomechanics when the mechanical resonance frequency and damping depend on time. In the regime of weak optomechanical coupling we extend the theory of laser cooling using an adiabatic approximation.We discuss the modifications of the cooling dynamics and compare it with numerical simulations in a wide range of modulation frequencies.

### 5. Optimized nonconventional receiver for multi-state discrimination at the single-photon level

Francisco Elohim Becerra, University of New Mexico

view abstract +

Nonconventional receivers for nonorthogonal states based on single photon counting have the potential for state discrimination below the heterodyne measurement limit. These receivers can be used to optimize quantum communication protocols and increase the information transmitted in the communication channel. We discuss a measurement strategy for a receiver based on optimized adaptive measurements that can potentially discriminate four states below the heterodyne limit for input powers at the single-photon level, and analyze the performance of this strategy under realistic conditions.

### 6. Machine Learning For Quantum Computation in Quantum Lattice Gas

Elizabeth Behrman, Wichita State University

view abstract +

Authors Elizabeth C. Behrman and James E. Steck

J. Yepez, Vahala and Vahala and Soe show that a Bose-Einstein condensate, Type-II quantum lattice gas exhibits behavior that can be used for quantum computing. These physical systems are shown to behave as individual quantum bits, ψ = (up,down), in a 3D lattice according to the Schroednger wave equation with m=1/2 i hψ;dot = -KσΔ2ψ + [g|φ|2 – a]ψ; on a domain Ω. The first term on the right hand side models spatial tunneling between neighboring qbits, controlled by the spatially varying parameter K(x). The second term contains a nonlinear interaction controlled by the spatially varying parameters g(x) and a(x) (x is the spatial variable). φ = (1,1)·ψ We are using this as a quantum computer, programmed with quantum learning. Inputs are applied to defined regions in Ω, i.e. two small regions for a 2 input quantum gate. An output is measured on a separate region of Ω and the parameters K, g and a, are trained, rather than programmed, to give the correct computation. The probability amplitude ψ propagates through Ω as a quantum wave. J. Yepez et. al. have shown that the lattice can exhibit vortex and anti-vortex filaments and soliton type behavior. We will investigate whether training produces values of K a and g that create filaments and wave guides that serve as virtual synaptic pathways. In other words, training might create or "grow" pathways in the lattice that produce the desired computation. Preliminary simulations for a 2 input one output CNOT gate on a very course 2D mesh (40x50) verify our simulation and training algorithm. Results for a refined mesh applied to classical gates XOR, XNOR, CNOT, quantum gates, Toffoli, Fredkin, etc. will be ready for presentation at the conference.

### 7. Towards Tunable Many-Body Physics in a High-Cooperativity Optical Cavity

Gregory Bentsen, Stanford University

view abstract +

Atomic ensembles in optical cavities (often called “cavity QED” systems) show great promise as highly tunable laboratories in the study of quantum many-body physics. A short list of applications includes quantum metrology, quantum simulation, and implementation of protocols for quantum computing, such as error-correcting codes. The primary figure of merit for cavity systems is the single-atom cooperativity, which quantifies the coherence of the system. Here we present our ongoing work to construct an ensemble cavity QED system with single-atom cooperativity exceeding the total atom number N. A near-concentric cavity geometry will allow us to achieve this extreme strong-coupling condition together with excellent optical access: recent measurements of our cavity’s waist and finesse indicate a single-atom cooperativity of 150. Such a high cooperativity will permit exceptionally long coherent interaction times in a highly tunable many-body quantum system. We hope to leverage these long interaction times in quantum control schemes to generate non-Gaussian entangled states that are difficult (or impossible) to realize in existing experiments. Keywords: Cavity QED, Quantum Control, Non-Gaussian States, Many-Body Physics

### 8. Efficient Approximation of Diagonal Unitaries over Clifford+T Basis

Alex Bocharov, Microsoft Research

view abstract +

Jonathan Welch, Alex Bocharov, Krysta M. Svore: Diagonal Unitary (DU) Operators appear in a wide variety of quantum algorithms, from simple analytical potential operators for quantum simulation to complex oracles. We develop and examine methods for approximate decomposition of diagonal operators, focusing specifically on decompositions over the Clifford+T basis. Methods for exact decomposition of DU rely on networks of elementary CNOT entanglers which have negligible fault-tolerant cost compared to the T gate. As a result, the cost of the compiled circuit is entirely based on the fault tolerant cost of the single-qubit rotations, which can be exponential in the number of qubits. Here we present an algorithm to optimize the cost based on the phase context of the operator, where phase context is the finite alphabet of phases appearing along the diagonal. Our decomposition yields no more than k, where k is the size of the phase context, single-qubit rotations that are further approximated to a desired precision. Unlike exact methods, this decomposition can require a significant number of multi-controlled-NOT gates. However, these entangling gates have fixed fault-tolerant cost over the Clifford+T basis, independent of the target precision of the single-qubit phase approximations. The equivalent T-count of the resulting circuit is thus bounded by k C log_2(1/epsilon) + E(n,k), where n is the number of qubits, epsilon is the a desired precision, C is the quality factor of the implementation method (1<C<4) and E(n,k) is the total entanglement cost (in T gates). The optimal decision boundary between using our decomposition method and traditional ones is determined by partitioning the (k,n,epsilon) space into the area where the entanglement cost E(n,k) exceeds the epsilon-dependent cost of having to approximate up to $2^n$ distinct single-qubit axial rotations and the area where allowing cascaded entanglement is beneficial. Our simulations demonstrate that the latter area is significant, and that for practically important diagonal operators savings from using our method can be exponential in n when k << 2^n.

### 9. Quantum Simulation and Many-Body Physics with 2D Ion Crystals in a Penning Trap

Justin Bohnet, National Institute of Standards and Technology, Boulder

view abstract +

Abstract: Quantum simulations promise to reveal new materials and phenomena for experimental study, but few systems have demonstrated the capability to control ensembles in which quantum effects cannot be directly computed. We report on experiments characterizing a system of 100's 9Be+ ions in a Penning trap. These ions form 2D crystals in a triangular lattice and that may be used as a platform for intractable quantum simulations using the 9Be+ valence electron spins coupled with an effective Ising interaction. We characterize the new experimental apparatus using the coherence time of the ensemble and ion crystal stability using single site resolved imaging. We also report on the successful photodissociation of BeH+ contaminant ions that impede the use of such crystals for quantum simulation. Furthermore, we report on progress to bench-mark quantum effects of the spin-spin coupling using a spin-squeezing witness, laying the foundation for future experiments including observation of entanglement dynamics under the quantum Ising Hamiltonian, high efficiency molecular spectroscopy, and studies of quantum thermalization.

### 10. Limitations of Quantum Monte Carlo algorithms in simulating Quantum Adiabatic Optimization

Lucas Brady, University of California, Santa Barbara

view abstract +

We analyze how well imaginary-time path integral Quantum Monte Carlo (QMC) algorithms are capable of efficiently simulating Quantum Adiabatic Optimization (QAO) techniques for Hamiltonians with no sign-problem. Specifically, we look into cases where QAO is expected to succeed because the spectral gap of the adiabatic evolution is 'big', but where there could be issues for the classical QMC algorithms. First, we look at a counterexample presented by Hastings ["Obstructions to classically simulating the quantum adiabatic algorithm", Quantum Information & Computation, Vol 13, Issue 11-12, 2013] where QMC is predicted to fail, despite the fact that QAO would succeed. We implement the QMC for this problem and verify Hasting's results numerically. Next, we also use QMC algorithms to study the problem of finding the optimum of symmetric cost functions defined on the hypercube of bit strings. Specifically we look at cases where QAO techniques have to tunnel through barriers in the potential to reach the global minimum of the cost function. By varying the size of this barrier, we examine the transition point where the time complexity of the QAO algorithm switches from polynomial scaling to exponential. We compare this transition to the corresponding scaling of the QMC applied to this same problem.

### 11. Quantum Behavior of an Autonomous Maxwell’s Demon

Adrian Chapman, University of New Mexico

view abstract +

We consider a quantum generalization of the classical autonomous Maxwell's demon introduced by Mandal et al., and examine in this model the Second Law of thermodynamics, which does not neglect correlations. We treat the full quantum description using a matrix product operator formalism, which allows us to handle quantum and classical correlations in a unified framework. Applying this together with the replica trick from statistical mechanics, we approximate nonlocal quantities such as the erasure performed on the demon's memory register when it is so correlated. Finally, we examine how the demon may use these correlations as a resource to outperform its classical counterpart.

### 12. Equivalence of wave-particle duality to entropic uncertainty

Patrick Coles, University of Waterloo, Institute for Quantum Computing

view abstract +

Interferometers capture a basic mystery of quantum mechanics: a single particle can exhibit wave behavior, yet that wave behavior disappears when one tries to determine the particle's path inside the interferometer. This idea has been formulated quantitively as an inequality, e.g., by Englert and Jaeger, Shimony, and Vaidman, which upper bounds the sum of the interference visibility and the path distinguishability. Such wave-particle duality relations (WPDRs) are often thought to be conceptually inequivalent to Heisenberg's uncertainty principle, although this has been debated. Here we show that WPDRs correspond precisely to a modern formulation of the uncertainty principle in terms of entropies, namely the min- and max-entropies. This observation unifies two fundamental concepts in quantum mechanics. Furthermore, it leads to a robust framework for de riving novel WPDRs by applying entropic uncertainty relations to interferometric models.

### 13. Superradiant Lasers -- New Physics, New Technology

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

view abstract +

Superradiant (bad cavity) lasers using cold atoms can operate with less than one intra-cavity photon and with intrinsic Schawlow-Townes linewidths of 1 mHz or less, making them a promising candidate for improving precision measurements. Additionally, these lasers operate in a unique regime of laser physics where laser coherence is generated by spontaneous synchronization of the optical dipoles of an ensemble of atoms. Our rubidium superradiant Raman laser offers unique access to this atomic synchronization process. I will report recent studies of superradiant synchronization in two experiments, observing for the first time both synchronization of a lasing superradiant ensemble to an external driving field and spontaneous synchronization of two superradiant ensembles. I will also show recent progress towards a strontium superradiant laser, which could achieve the highly sought-after mHz linewidth.

### 14. Quantum Bochner's theorem for phase spaces built on projective representations

Ninnat Dangniam, University of New Mexico

view abstract +

Bochner's theorem gives the necessary and sufficient conditions on a characteristic function such that it corresponds to a true probability density function. In the Wigner phase space picture, quantum Bochner's theorem gives the necessary and sufficient conditions on the quantum characteristic function such that it corresponds to a valid quantum state and such that its Fourier transform is a true probability density. We extend this theorem to discrete phase space representations which possess enough symmetry to define a generalized Fourier transform.

### 15. Scalable quantum gates in trapped ion registers using optimal control of multimode couplings

Shantanu Debnath, University of Maryland

view abstract +

We perform high fidelity multipartite entanglement of ion subsets in a chain of five Yb+ qubits using optimal pulse shapes that couple to all modes of motion [1]. Pre-calculated optimized pulse shapes allows us to couple qubits through multiple collective modes of motion, keeping gate times short while scaling well with large qubit registers. A laser beam focused on a pair of adjacent qubits is modulated in phase and amplitude to drive high fidelity entangling gates for certain pulse solutions that can also be relatively insensitive to detuning errors [2]. We create entangled states in the GHZ class and witness genuine bipartite and tripartite entanglement using individual state detection. By combining pulse shaping with arbitrary individual optical addressing of qubits we are now poised to perform quantum algorithms on a static chain of many ions. This work was supported by grants from the U.S. Army Research Office with funding from IARPA, the DARPA OLE program, and the MURI Hybrid Quantum Circuits program; and the NSF Physics Frontier Center at JQI. [1] T. Choi et al.,Phys. Rev. Lett. 112, 19502 (2014). [2] D. Hayes, et al., Phys. Rev. Lett. 109, 020503 (2012).

### 16. Suppression of off-resonant carrier excitations via a standing wave gate beam

Thomas deLaubenfels, Georgia Tech Research Institute

view abstract +

Thomas E. deLaubenfels^{1,2},
Karl A. Burkhardt^{3},
Jason M. Amini^{1},
Kenneth R. Brown^{2,4},
Kenton R. Brown^{1},
J. True Merrill^{1},
Grahame D. Vittorini^{5},
Curtis Volin^{1},
Alexa W. Harter^{1}

1. Georgia Tech Research Institute, Atlanta, GA 30332, USA

2. School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, USA

3. Currently: Department of Physics, University of Texas, Austin, TX 78712, USA

4. Schools of Chemistry and Biochemistry, and Computational Science and Engineering,
Georgia Institute of Technology, Atlanta, GA 30332, USA

5. Currently: Joint Quantum Institute, University of Maryland Department of Physics and National Institute of Standards and Technology, College Park, Maryland 20742, USA

The motional dynamics of ions in radio-frequency traps lead to secular sidebands in their excitation spectra. The relative coupling strengths of the carrier and the secular sidebands are usually fixed by the Lamb-Dicke factor and the ion temperature. We present the results of an experiment in which the coupling strengths of the carrier resonance and 1st order secular sidebands may be selectively emphasized or suppressed relative to one another. Using ^{40}Ca+ ions trapped in a surface electrode trap, we excite the |S 1/2> -> |D 5/2> electric quadrupole transition with laser light that is normally incident to the trap's surface. The resulting retroreflection off the trap surface produces a standing wave. For a quadrupole transition, the carrier couples to the gradient of the electric field, and therefore its coupling strength is strongest at the nodes of the standing wave and suppressed at the anti-nodes. The sidebands, coupling to the magnitude of the field, are strongest at the anti-nodes and suppressed at the nodes. By moving the ion through the standing wave we alternatively suppress and excite the carrier and sideband transitions with the two sets of fringes 180 degrees out of phase. This technique could be used to suppress off-resonant carrier excitations in two qubit gates, and the fringes themselves provide a measure of the ion displacement that can be used to map out the potentials in the trapping region.

### 17. Combinatorial Results on the Stabilizer Polytope

Jeffrey Epstein, University of California, Berkeley

view abstract +

The subset of quantum algorithms known as stabilizer protocols is of practical interest because its members may be implemented in a fault-tolerant manner, and of theoretical interest because they can be simulated efficiently on a classical computer, yet still display uniquely quantum features such as contextuality. Stabilizer computation can be extended to universal quantum computation via the addition of distillable resource states known as magic states. In this work, we obtain results on the combinatorial structure of the stabilizer polytope, the set of convex combinations of pure states accessible to stabilizer protocols. We hope that these results will point the way towards new, more practical magic monotones for n-qubit states.

### 18. Towards generation of photons with orbital angular momentum correlation from atomic ensembles

Andrew Ferdinand, University of New Mexico

view abstract +

Photon pairs created in a four wave mixing (FWM) process in atomic systems are intrinsically compatible with atomic quantum memories, and can enable long-distance quantum communication based on atomic ensembles. Conservation of orbital angular momentum (OAM) in the FWM process allows for the generation of photons entangled in many OAM modes, potentially increasing the amount of information that can be communicated. We describe our progress towards generation of correlated photon pairs carrying OAM from an ensemble of Cesium atoms.

### 19. A physical model for continuous decomposition of quantum measurements using feedback

Jan Florjanczyk, University of Southern California

view abstract +

Many experimental realizations exist of quantum systems exhibiting closed-loop control. It has also been shown by Oreshkov and Brun that using classical feedback to construct infinitesimal weak measurement "steps", one can decompose any generalized measurement into a continuous stochastic process. In this work, we consider how to realize such a construction in a physical setting. In particular, we consider a measurement apparatus consisting of a stream of probes interacting weakly with a quantum system. The measurement of each probe in the stream is fed back into the apparatus in one of two ways, either in determining the state of the next probe, or in tuning the interaction Hamiltonian. In both cases we consider a seemingly mild restriction on the weak measurement "steps", namely, that the steps be reversible until the procedure terminates. In the case of probe feedback this yields a very restricted class of possible decompositions, that is, only biased projective measurements. To model the interaction feedback case, however, we consider tuning linear control terms in the probe-system Hamiltonian. The reversibility condition in this case yields a quadratic system over a non-associative algebra generated by the control terms. We present an algorithm for finding closed subalgebras within any given control set and characterize the class of measurements decomposable by the restricted control sets.

### 20. Nonzero classical discord

Vlad Gheorghiu, Institute for Quantum Computing and University of Calgary

view abstract +

Quantum discord is the quantitative difference between two alternative expressions for bipartite mutual information, given respectively in terms of two distinct definitions for the conditional entropy. Whereas nonzero discord is touted as a form of quantum correlation, we show, by constructing a stochastic classical model of shared states, that discord indeed quantifies the presence of some stochasticity in the measurement process. We then establish an operational meaning of classical discord in the context of state merging with noisy measurement and thereby show the quantum-classical separation is not discord being nonzero but rather negative conditional entropy. This work is in collaboration with Barry C. Sanders and Marcos C. de Oliveira

### 21. Maximum Likelihood Estimation of Gaussian Quantum States

Scott Glancy, National Institute of Standards and Technology

view abstract +

Many experiments on quantum systems involve the preparation and measurement of Gaussian states of a multi-system continuous variable Hilbert space. Examples include optical and microwave systems involving squeezing and linear interactions and nanomechanical resonators described with second order Hamiltonians. The state space that these systems access is much smaller than the full Hilbert space and can be fully characterized with a 2N*2N covariance matrix and 2N means vector, where N is the number of individual modes or oscillators. We describe an algorithm for finding the maximum likelihood covariance matrix and means vector from homodyne (or quadrature) measurement data collected at arbitrary phases. The algorithm is similar to a diluted version of the R*rho*R algorithm of maximum likelihood density matrix tomography, and it increases likelihood at each iteration. We compare the performance of the maximum likelihood algorithm to a simpler, almost linear, estimator. [co authors: Nadav Kravitz and Emanuel Knill]

### 22. Characterization of a High Optical Access Microfabricated Ion Trap for Quantum Computing Applications

Richard Graham, University of Washington

view abstract +

One of the most promising building blocks for a technically scaleable ion trap quantum computer is the micro-fabricated planar ion trap. While demonstrating key requirement such as junctions for reordering ion chains, earlier designs had relatively poor optical access due to their planar geometry. This limited the ability to tightly focus laser beams and decreased fluorescence light signal/noise. Tight focusing is needed for individual ion addressing. Efficient fluorescence collection is critical for the fast qubit state detection required by most ion trap quantum computation architectures. We have recently begun working with a new generation High Optical Access (HOA) micro-fabricated surface trap made by Sandia National Labs. We are equipped to trap both barium and ytterbium ions in all regions of this trap. The barium-ytterbium system is a favored combination for future quantum computation applications. We report results characterizing fluorescence signal to noise, surface quality, ion transport, ion heating and loss rates. We have begun investigating the dynamics of barium-ytterbium ion chains.

### 23. In-Vacuum Electronics and Ball-Grid Arrays for Scalable Microfabricated Ion Traps

Nicholas Guise, Georgia Tech Research Institute

view abstract +

Microfabricated ion traps for quantum information research have grown to incorporate nearly 100 control electrodes. Each electrode requires an independent trapping potential, typically supplied by a digital-to-analog converter (DAC) and routed to the trap chip through a vacuum feedthrough, CPGA carrier, and wirebond connection. We report here on two new ion traps designed to scale more easily to traps of increasing complexity. The first trap integrates control electronics with an ion trap inside a vacuum system. Two 40-channel DAC integrated circuits, with supporting power regulation and custom filters, are decapsulated from commercial packages and mounted to a multilayer circuit board along with a surface electrode ion trap. We use a serial protocol for communication, such that only 9 vacuum feedthroughs are required to control the 80 in-vacuum channels. Scaling to larger systems would add 2 feedthroughs for every 40 DAC channels. The second ion trap utilizes ball-grid array connections to simplify signal routing and improve optical access to a trap chip. Through-substrate vias bring electrical signals from the back side of a trap die to a surface trap structure on the top side. Gold-ball bump bonds connect the back side of the trap die to an interposer for signal routing from a carrier. Trench capacitors are fabricated into the trap die, while wirebonds are moved to the interposer, allowing the trap die to be reduced to only the area required to produce trapping fields. The smaller trap dimensions (1.1mm x 3.2mm) enable tight focusing of an addressing laser beam for fast single qubit rotations. We characterize both traps with 40Ca+ ions and measure performance comparable to previous microfabricated traps in terms of ion storage lifetimes, mode frequency stabilities, and heating rates.

### 24. An array of transmon qubits for simulating the Bose-Hubbard model

Shay Hacohen-Gourgy, Quantum Nanoelectronics Laboratory, UC Berkeley. 2Departments of Physics and Applied Physics, Yale University

view abstract +

S. Hacohen-Gourgy, V. Ramasesh, C. De Grandi, S. M. Girvin, I. Siddiqi Chains of capacitively-coupled transmons can emulate the Bose-Hubbard Hamiltonian when one considers the full level-structure of the circuit. Here, each individual transmon plays the role of a lattice site, with the excitation level of each transmon corresponding to the number of bosons occupying that particular site. The transmon's anharmonicity gives rise to the attractive contact-interaction term, while the capacitive coupling realizes the hopping amplitude. We implement such a chain of capacitively-coupled transmons in a single 3D microwave cavity. For a fixed number N of excitations, the array has a ground state and a spectrum of excited states. Using cavity-assisted bath engineering, it should be possible to cool from an initial state in this subspace to the ground state. We present the current status of this goal.

### 25. A Device for Continuous-Time Quantum Error-Correction

Kung-Chuan Hsu, University of Southern California

view abstract +

Continuous-time quantum error-correction (CTQEC) is a study of protecting quantum information against decoherence, where both the decoherence and error-correction processes are considered continuous in time. Given any [[n,k,d]] quantum stabilizer code, we formulate a class of devices for implementing CTQEC involving weak coherent measurements and weak unitary corrections. In our scheme, one device is found that requires (n-k+1) ancillas in the measurement phase, and we believe that this amount of ancillas is the least that is required. Furthermore, we compare our device with other known approaches, particularly the ADL scheme. We show that, under a fair comparison, the performance is improved using our device. We also analyze the advantages and disadvantages of our device.

### 26. Quantum Coherence in Ultrastrong Optomechanics

Dan Hu, University of California, Merced

view abstract +

Ultrastrong light-matter interaction in an optomechanical system can result in nonlinear optical effects such as photon blockade. The system-bath couplings in such systems play an essential role in observing these effects. Here we study the quantum coherence of an optomechanical system with a dressed-state master equation approach. Our master equation includes photon-number-dependent terms that induce dephasing in this system. Cavity dephasing, second-order photon correlation, and two-cavity entanglement are studied with the dressed-state master equation.

### 27. Quantum Information Processing with Modular Networks

Ismail Inlek, University of Maryland / Joint Quantum Institute

view abstract +

Trapped atomic ions are qubit standards for the production of entangled states in quantum information science and metrology applications. Trapped ions can exhibit very long coherence times, while external fields can drive strong local interactions via phonons, and remote qubits can be entangled via photons. However, transferring quantum information across spatially separated ion trap modules for a scalable quantum network architecture relies on the juxtaposition of both phononic and photonic buses. We report the successful combination of these protocols within and between two ion trap modules on a unit structure of this architecture [1]. Importantly, trapped ions are the only experimental system to date where the remote entanglement generation rate exceeds the experimentally measured decoherence rate of the entangled state, paving the way for a scalable system with a non forbidding overhead in resources. We also report the experimental implementation of a technique to maintain phase coherence between spatially and temporally distributed quantum gate operations in such a system, a crucial prerequisite for scalability [2], and demonstrate a time-resolved photon detection technique to entangle frequency-distinguishable qubits and improve network robustness [3].

[1] Hucul et. al. Nat. Phys. DOI: 10.1038/nphys3150 (2014)

[2] Inlek et. al. Phys. Rev. A 90, 042316 (2014)

[3] Vittorini et. al. Phys. Rev. A 90, 040302(R) (2014)

### 28. Analytical Error Analysis of Clifford Gates by the Fault-Path Tracer Method

Smitha Janardan, Georgia Institute of Technology

view abstract +

Monte-Carlo methods for calculating failure rates of quantum circuits give accurate results but require large runtimes to achieve accurate results at low error rates. The malignant fault-point method of Aliferis, Gottesman, and Preskill runs independently of error rate but underestimates the failure rate. Our method, the Fault-Path Tracer (FPT), provides a collection of approximations that facilitate the trade-off between accuracy and efficiency. We apply gate-specific bistochastic matrices to the probability state, which accounts for error cancellation of Pauli errors. This circuit probability state can grow exceedingly large, therefore we introduce a variable transform that isolates key error combinations. In addition, these error combinations are divided recursively to further reduce memory usage. To determine the probability of a specific error combination, we rigorously apply the inclusion-exclusion principle to avoid overestimating the error rate. Our method is able to exactly match results from Monte Carlo simulations for the Bernstein-Vazirani algorithm with substantial improvements to timing performance. The FPT can be applied to any circuit made from Clifford operators and can analysis localized Pauli errors. Our method can also be used to calculate the performance of fault-tolerant error correcting codes.

### 29. Quasi-local frustration-free Markovian dynamics and stabilization of thermal graph states

Peter Johnson, Dartmouth College

view abstract +

Dissipative quantum state preparation with realistic quasi-local control resources is a task of growing importance in quantum control. Quasi-local frustration-free Lindblad dynamics are a promising candidate, having a low-complexity implementation and intrinsic model-robustness against quasi-local perturbations. We present necessary and sufficient conditions under which a target mixed state may be stabilized by quasi-local frustration-free Markovian dynamics. While it is not surprising that all product states are quasi-locally stabilizable, it turns out that relevant examples of mixed entangled states may also be quasi-locally stabilized. In particular, we consider thermal graph states, which are known to exhibit bound entanglement for a range of temperatures. We show that this class of states is quasi-locally stabilizable and analytically construct the Lindblad dynamics which prepare them.

### 30. Optimized pulse sequences that act as notch filters for time-dependent noise

Chingiz Kabytayev, Georgia Institute of Technology

view abstract +

We design pulse sequences for time-dependent amplitude or dephasing noise represented by a narrow Gaussian spectral peak in addition to a broad 1/ f noise spectrum. Employing a filter-transfer function formalism [1, 2, 3] allows us to perform a fast optimization based on the method of simulated annealing to obtain a high-fidelity control acting as a notch filter for single-qubit gates. We compare robustness of these control protocols to standard composite pulse sequences designed for static noise. We also compare our analytical results to numeric simulations of Bloch vector evolution and find good agreement. Our new pulse sequences dynamically-corrected gates improve the fidelity by two orders of magnitude. [1] Green T. et al., New. J. Phys. 15 095004 (2013) [2] C. Kabytayev et al., Phys. Rev. A 90, 012316 (2014) [3] A. Soare et al., Nature Phys. 10, 825–829 (2014)

### 31. Quantum Deep Learning

Ashish Kapoor, Microsoft Research

view abstract +

In recent years "deep learning" has had a profound impact on classical machine learning and artificial intelligence. Deep learning is a rich class of algorithms for learning complex representations of data and has been applied successfully in fields such as computer vision, speech recognition, and natural language processing. However, classical training of deep models faces a computational bottleneck: computation of the true gradient of L, where L is the "log-likelihood function", is classically intractable. Therefore, classical training can efficiently only approximate the gradient of L. Here we show that quantum computing provides an advantage over existing deep learning algorithms, in particular in the case of restricted and unrestricted Boltzmann machines. We develop two quantum machine learning algorithms that both accelerate the training of deep Boltzmann machines and improve the gradient computation. We show that a quantum computer can efficiently sample from the true gradient of L, bypassing the need for approximations entirely. We also show that unrestricted Boltzmann machines with intra-layer connections, can be efficiently trained on a quantum computer. Such models are known to be powerful for machine learning but efficient training algorithms are not known for them. We further provide extensive numerical evidence that our quantum algorithms produce models that outperform classical models with regard to the given objective function. Finally, one of the algorithms need not have access to a QRAM and requires a number of qubits that scales only with the number of nodes in the Boltzmann network, not the amount of training data. (Joint work: Nathan Wiebe, Ashish Kapoor, Krysta Svore).

### 32. Robust quantum logic in neutral atoms via adiabatic Rydberg dressing

Tyler Keating, University of New Mexico

view abstract +

The Rydberg blockade is a promising mechanism for the generation of quantum logic gates in neutral atoms, but in experimental efforts to produce such gates, Doppler shifts from atomic thermal motion routinely appear as major obstacles to achieving high fidelities. We study a scheme in which ground state atoms are adiabatically dressed with two, counter-propagating lasers to generate a controlled-Z gate that is robust to thermal motion. Neither adiabatic dressing nor the two-laser scheme lead to significant gains on their own, but taken together, they suppress Doppler errors by more than an order of magnitude. For reasonable parameters, with qubits encoded into the clock states of 133Cs, we predict that our protocol could produce a CZ gate in <10 μs with error probability on the order of 0.001.

### 33. Classical simulation of 2D coulomb crystals in a Penning Trap

Adam Keith, National Institute of Standards and Technology - Boulder

view abstract +

Trapped ions in a Penning trap are a very promising system for simulating condensed matter models due to a high spin-count, precise quantum control and low technical complexity. For example, previous work has shown engineered antiferromagnetic interactions by coupling the ions' spins to their collective motion – a step towards quantum simulation of quantum magnetism. Here, we extend previous analytical work studying the axial and planar normal modes at zero temperature. Using a molecular dynamics code with laser cooling, we estimate the planar mode temperatures and investigate coupling between different modes. We also discuss crystal stability. [co authors: Dominic Meiser, Emanuel Knill, John Bollinger]

### 34. EXACT SYNTHESIS OF SINGLE-QUBIT UNITARIES OVER CLIFFORD-CYCLOTOMIC GATE SETS

Vadym Kliuchnikov, Microsoft Research

view abstract +

Kliuchnikov Maslov and Mosca gave an efficient exact synthesis algorithm for single-qubit unitaries over the Clifford+T gate set. Their algorithm takes as input an exactly synthesizable unitary–one which can be expressed without error as a product of Clifford and T gates–and outputs a sequence of gates which implements it. The algorithm is optimal in the sense that the length of the sequence, measured by the number of T gates, is the smallest possible. Here we generalize this result to “Clifford-cyclotomic” gate sets; for each n we consider the gate set consisting of the Clifford group plus a z-rotation by π/n. We present an efficient exact synthesis algorithm which outputs a decomposition using the minimum number of π/n z-rotations. For the Clifford+T case n = 4 the set of exactly synthesizable unitaries was shown to be equal to the set of unitaries with entries over the ring Z[1/2,e^(iπ/4)]. We prove that this characterization holds for a handful of other small values of n but the fraction of positive integers for which it fails to hold is 100%.

### 35. (In)equivalence of color code and toric code

Aleksander Kubica, California Institute of Technology

view abstract +

A quantum error-correcting code with fault-tolerantly implementable non-Clifford logical gates is an indispensable ingredient for realization of universal quantum computation. At the moment, the topological color codes are the only known examples of topological stabilizer codes with transversally implementable non-Clifford logical gates. Thus, understanding similarities and differences between the topological color codes and ordinary topological quantum codes, such as the toric code, is an important problem. Here we prove that the topological color code on a d-dimensional closed manifold (without boundaries) is equivalent to multiple decoupled copies of the d-dimensional toric code up to local unitary transformations and adding/removing ancillas. Our result not only generalizes the proven equivalence for d = 2, but also provides an explicit recipe how to decouple independent components of the topological color code, highlighting the importance of “colorability” in the construction of the code. This result implies that the topological color code and the toric code belong to the same quantum phase according to the definition widely accepted in condensed matter physics community. Moreover, for a d-dimensional topological color code with boundaries, which admits transversal implementation of non-Clifford logical gates, we find that the code is equivalent to multiple copies of the toric code in d dimensions which are welded together along the (d-1)-dimensional boundaries. In particular, for d = 2, we show that the color code, defined on a lattice with three boundaries of distinct colors, is equivalent to a single copy of the toric code on a square lattice with boundaries, which is “folded” along a diagonal axis. Our findings may lead to a systematic method of composing known quantum codes to construct new codes with larger set of fault-tolerant logical gates. Our work also provides new insights into the classification of topological quantum field theories with boundaries in two or higher dimensions.

### 36. Practical variational tomography for critical 1D systems

Olivier Landon-Cardinal, IQIM, Caltech

view abstract +

We improve upon a recently introduced efficient quantum state reconstruction procedure targeted to states well-approximated by the multi-scale entanglement renormalization ansatz (MERA), e.g., ground states of critical models. The MERA description of a state is a quantum circuit which iteratively disentangles the state while condensing the entanglement into fewer particles at each renormalization step. MERA tomography iteratively learns this circuit by i) experimentally inferring density matrices on a constant number of renormalized particles and ii) numerically identifying the disentangling gates. We focus on point i), specifically on how to better extract information about renormalized particles from experimental measurements, studying critical spin-1/2 (qubits) systems for concreteness. Pauli observables on the experimental state renormalize into an overcomplete set of non-orthogonal operators on the renormalized particles. We show how to numerically select a subset of them which maximizes information extraction, thus dramatically reducing the required number of physical measurements. We numerically evaluate the number of measurements required to characterize the ground state of the critical 1D Ising (resp. XX) model. We find that MERA tomography on a 16-qubit (resp. 24-qubit) ground state requires fewer measurements than the qubyte experiment which performed brute-force tomography on 8 qubits. Joint work with Jong Yeon Lee (Caltech).

### 37. Progress towards building an 174Yb BEC for Quantum Simulations at KRISS

Jae Hoon Lee, Korea Research Institute of Standards and Science

view abstract +

We report advancements in our experimental setup for an 174Yb BEC where we laser cool atoms exiting a Zeeman slower followed by evaporative cooling in an optical dipole trap. As we continue to construct our apparatus towards a BEC, we have developed a core-shell magneto-optical-trapping(MOT) scheme utilizing both the broad 1S0→1P1 transition and the narrow 1S0→3P1 transition in two spatially separated regions. Experimental implementation of this scheme showed both faster loading and high atom numbers, by more than two orders and one order of magnitude respectively, compared to conventional MOT schemes. We plan to further cool and transfer the atomic sample into a science chamber by displacing an optical dipole trap using an optically compensated zoom-lens. The atoms will be loaded into an optical lattice for quantum simulations.

### 38. Fisher Information Conservation in Multi-parameter Quantum Metrology

Nan Li, The Center for Quantum Information and Control

view abstract +

In order to estimate parameters encoded in quantum states, one usually performs quantum measurements and then constructs estimators of the parameters. For a single parameter scenario, the ultimate limit for such a scheme is quantified by the Fisher information in view of the celebrated Cramer-Rao bound. Whereas, for multiple parameters the Cramer-Rao bound can be quite loose and depends sensitively on the parameterization. Here we introduce an operational quantity which is invariant under re-parameterization and give tight bounds for specific scenarios.

### 39. Steady-state Mechanical Squeezing in an Optomechanical System via Duffing Nonlinearity

Jie-Qiao Liao, University of California, Merced

view abstract +

Quantum squeezing in mechanical systems is not only a key signature of macroscopic quantum eﬀects, but can also be utilized to advance the metrology of weak forces. Here we show that strong mechanical squeezing in the steady state can be generated in an optomechanical system with mechanical nonlinearity and red-detuned monochromatic driving on the cavity mode. The squeezing is achieved as the joint eﬀect of nonlinearity-induced parametric ampliﬁcation and cavity cooling, and is robust against thermal ﬂuctuations of the mechanical mode.

### 40. Strong atom-light interactions in 1D photonic crystals

Mingwu Lu, Quantum Optics Group

view abstract +

J. D. Hood, M. Lu, A. Goban, C.-L. Hung, M. J. Martin, A. C. McClung, J. A. Muniz, S.-P. Yu, O. Painter, and H. J. Kimble

We investigate opportunities that emerge from the integration of cold atoms with nano-scopic photonic crystal waveguides (PCWs). Significantly, PCWs enable the light-matter interaction to be engineered for both trapping and strong atom-photon coupling [1,2], thereby opening new avenues for novel quantum transport and quantum many-body phenomena [3,4]. Beyond our initial observations in Ref. [5], we have succeeded in trapping Cesium atoms along the length of 1D PCWs. The atoms are localized approximately 110nm above the surface of the PCW with trap lifetime of approximately 50ms. Trapped atoms are probed by light in a guided mode of the device. By way of both steady-state transmission spectra and transient decay after short-pulse excitation, we infer that the peak decay rate for one trapped atom is G1D/G* = 1.0 ± 0.1, where G1D (G*) is the atomic spontaneous emission rate into the guided (all other) mode (s). We discuss progress towards trapping atoms at the center of the PCW, for which G1D/G* ~ 5, as well as advances in device fabrication to achieve optical quality factors Q ~ 106.

[1] C.-L. Hung, S.M. Meenehan, D. E. Chang, O. Painter, and H. J. Kimble, New J. Phys. 15, 083026 (2013).

[2] S.-P. Yu, J. Hood, J. Muniz, M. Martin, R. Norte, C.-L. Hung, S. M. Meenehan, J. D. Cohen, O. Painter, and H. J. Kimble, Appl. Phys. Lett. 104, 111103 (2014).

[3] D. Chang, L. Jiang, A. Gorhskov, and H. J. Kimble, New J. Phys. 14, 063003 (2012).

[4] J. S. Douglas, H. Habibian, A. V. Gorshkov, H. J. Kimble, and D. E. Chang, arXiv:1312.2435 (2013).

[5] A. Goban, C.-L. Hung, S.-P. Yu, J. D. Hood, J. A. Muniz, J. H. Lee, M. J. Martin, A. C. McClung, K. S. Choi, D. E. Chang, O. Painter, and H. J. Kimble, Nature Comm. 5, 3808 (2014).

### 41. Ultra-broadband Josephson traveling-wave parametric amplifier for microwave quantum measurement

Chris Macklin, QNL, University of California, Berkeley

view abstract +

C. Macklin (1), K. P. O. Brien(2), M. E. Schwartz(1), D. Hover(3), V. Bolkhovsky(3), S. Tolpygo(3), G. Fitch(3), T. Weir(3), W. D. Oliver(3), X. Zhang(2), I. Siddiqi(1)

(1) - QNL, University of California, Berkeley;

(2) - NSEC, University of California, Berkeley;

(3) - MIT Lincoln Laboratory.

Josephson parametric amplifiers (JPAs) have enabled near-quantum-limited detection of cryogenic single-photon-scale microwave signals. However, the bandwidth over which the system noise temperature approaches the quantum limit is relatively narrow due to the gain-bandwidth tradeoffs inherent in resonator-based parametric amplifiers. To sidestep this limitation, we have developed a new type of JPA based on a nonlinear transmission line: the Josephson traveling-wave parametric amplifier (JTWPA). We present theoretical and experimental results on the amplifier performance of the JTWPA, demonstrating gain in excess of 20 dB over an instantaneous bandwidth of more than 2 GHz with a 1 dB compression power of -100 dBm. We measure the noise performance of the JTWPA using traditional noise power techniques as well as fiducial quantum measurements using a circuit QED system in the weak measurement regime, finding a system noise temperature with the JTWPA less than a factor of 3 above the quantum limit. Due to its large bandwidth and input compression power, the JTWPA brings near-quantum-limited measurement closer towards the level of generality and practicality offered by semiconductor amplifiers.

### 42. Van Trees Information in Quantum Metrology

Esteban Martínez, Instituto de Investigaciones en Matemáticas Aplicadas y Sistemas de la Universidad Nacional Autónoma de México

view abstract +

When you want to estimate, using quantum measurements, which parameter is a random variable, Quantum Van Trees information can be used to find a lower bound in the error. However, in general it is impossible to find a quantum measurement strategy that reaches the lower bound. We propose a modification of the definition Quantum Van Trees that we believe can be used to find the quantum measurement strategy that gives the lowest error.

### 43. Optimal feedback for remote entanglement

Leigh Martin, University of California at Berkeley

view abstract +

Recent experiments in superconducting qubits have demonstrated measurement as a resource for entanglement, even when qubits are spatially separated to a significant degree. We consider the problem of using measurement combined with feedback to deterministically entangle remote qubits. This constraint forces us to consider only local feedback, which leads us to a unique control-theory problem. Within this constraint, we derive a series of protocols for this system which generate entanglement as quickly as possible. By considering the both discrete and continuous measurement, a transition between two distinct protocols emerges, which allow one to approach unit fidelity even with non-unit efficiency readout. We find that even in the presence of expected experimental imperfections, it should be possible to achieve high-fidelity entanglement using capabilities that have already been demonstrated experimentally.

### 44. Refining a Polarization- and Entanglement-Based Quantum Eraser for Undergraduate Lab Courses

Morgan Mastrovich, Harvey Mudd College

view abstract +

Presenters: Morgan Mastrovich and Siddarth Srinivasan Co-author: Theresa W. Lynn The quantum eraser is a powerful tool for conveying the essentials of quantum physics. In an apparatus in our upper-level teaching labs, a polarization-based quantum eraser experiment is performed with single photons produced as members of entangled pairs, via spontaneous parametric down conversion. Furthermore, the which-way information is obtained not from the signal photons that traverse the interferometer, but from the idler photons that are polarization entangled with the signal photons. This experiment has made many fundamentals of quantum mechanics and quantum information directly accessible to undergraduate students in their coursework. However, this style of polarization-based quantum eraser experiment, both at our campus and elsewhere, has exhibited unexpected partial persistence of interference fringes in the presence of which-way information. We report on recent investigations of this phenomenon and progress in eliminating the persistent fringes, thus increasing the experiment's value as a pedagogical tool.

### 45. Resource quality of a symmetry-protected topologically ordered phase for quantum computation

Jacob Miller, Center for Quantum Information and Control, University of New Mexico

view abstract +

We investigate entanglement naturally present in the 1D topologically ordered phase protected with the on-site symmetry group of an octahedron as a potential resource for teleportation-based quantum computation. We show that, as long as certain characteristic lengths are finite, all its ground states have the capability to implement any one-qubit gate operation perfectly as a key computational building block. This feature is intrinsic to the entire phase, in that perfect gate fidelity coincides with perfect string order parameters under a state-insensitive renormalization procedure. Our approach may pave the way toward a novel program to classify quantum many-body systems based on their operational use for quantum information processing.

### 46. Steady-state entanglement between distant transmons, stabilised against high transmission loss

Felix Motzoi, University of California, Berkeley

view abstract +

Being able to stabilise entanglement over long distances and long times provides numerous advantages over pulsed experiments (avoiding variability, synchronisation, and calibration issues) while providing an important resource on-demand, which can then be potentially distilled and used to construct a quantum network. We show how existing superconducting technologies can be entangled over distances of tens of meters providing resilient stabilisation even in the presence of high inefficiency of the transmission channel. This can be achieved both in the dispersive and near-resonant cavity regimes using simple protocols that employ correlated environmental interactions and symmetry breaking. These require only a single-frequency drive that interacts sequentially with each cavity-qubit system. The dispersive regime protocol uses feedback while the near-resonant regime protocol is autonomous.

### 47. Prediction, Retrodiction, and Smoothing for a Continuously Monitored Superconducting qubit.

Kater Murch, Washington University, St. Louis

view abstract +

The quantum state of a superconducting transmon qubit inside a three-dimensional cavity is monitored by reflection of a microwave field on the cavity. Measurement outcomes at different times are correlated, and knowledge of later measurement outcomes can be used to provide statistical information about earlier probe results. For a driven, damped and continuously monitored quantum system, the information inferred from measurement data yields a quantum trajectory given by the matrix, which is conditioned on probe results until a time t. Further probing after t can be incorporated into an auxiliary matrix E. We show that the combination of the density matrix and E make nontrivially different and more precise predictions for the outcomes of measurements in the past. Our experiments verify the predictions of both projective and weak value (weak) measurements conditioned on full measurement records.

### 48. Quantum algorithms for shortest paths problems in structured instances

Aran Nayebi, Stanford University

view abstract +

Joint work with Virginia Vassilevska Williams Abstract: We consider the quantum time complexity of the all pairs shortest paths (APSP) problem and some of its variants. The trivial classical algorithm for APSP and most all pairs path problems runs in O(n^3) time, while the trivial algorithm in the quantum setting runs in \tilde{O}(n^{2.5}) time, using Grover search. A major open problem in classical algorithms is to obtain a truly subcubic time algorithm for APSP, i.e. an algorithm running in O(n^{3-c}) time for constant c >0. To approach this problem, many truly subcubic time classical algorithms have been devised for APSP and its variants for structured inputs. Some examples of such problems are APSP in geometrically weighted graphs, graphs with small integer edge weights or a small number of weights incident to each vertex, and the all pairs earliest arrivals problem. In this paper we revisit these problems in the quantum setting and obtain the first nontrivial (i.e. O(n^{2.5-c}) time) quantum algorithms for the problems. Full paper available at: http://arxiv.org/abs/1410.6220

### 49. Algebraic quantum error correction: A unified theory

Sepehr Nezami, Stanford Institute For Theoretical Physics

view abstract +

Authors:
Sepehr Nezami, Grant Salton, Patrick Hayden

Abstract:
We present a novel, generalized framework for codeword stabilized quantum error correction that reproduces all known stabilizer codes as well as codeword stabilized quantum codes as special cases. Our formalism also extends to non-abelian groups and non-abelian stabilizers. For instance, we found a new, non-abelian CWS error correcting code based on a non-abelian stabilizer that was not known to have error correcting capability. Our algebraic framework is sufficiently general that it includes all known algebraic quantum codes, but it contains enough structure that it can be used to find new codes and analyze their error correcting properties. Furthermore, our formalism includes continuous variable stabilizer codes, qudit CWS codes, and new continuous variable CWS codes. Our approach is to extend the notions of error correction to arbitrary group actions on a state space, making only minimal assumptions to keep the framework as general as possible.

### 50. Design and fabrication of a surface trap for freely rotating rings of ions

Crystal Noel, University of California, Berkeley

view abstract +

We present the design and fabrication of an r.f. trap using planar electrodes with the goal to trap on the order of 100 ions in a small ring structure of diameters ranging between 100~$\mu$m and 200~$\mu$m. In order to minimize the influence of trap electrode imperfections, we aim at trapping the ions around 400~$\mu$m above the trap electrodes. Calculating the ion dynamics, we study various imperfections causing a break in the rotational symmetry. We conclude that the considered imperfections can be controlled sufficiently well to allow for freely rotating ion ring even at energies comparable to the ground state energy of the rotational degree-of-freedom. We also present micro-fabrication methods developed to preserve the rotational symmetry of the trap electrodes using vias beneath the silicon electrodes.

### 51. Fundamental filter functions for open-loop noise filtering and identification

Leigh Norris, Dartmouth College

view abstract +

Transfer-function techniques motivated by control engineering are an important tool for obtaining a physical picture of the controlled dynamics in the frequency domain and for quantitatively analyzing control performance. Recent work [Paz-Silva & Viola, arXiv:1408.3836] has shown that arbitrary transfer filter functions may be built out of a computationally tractable set of fundamental filter functions, which suffices to characterize the error suppression capabilities of the control protocol in both the time and frequency domain. Here, we will demonstrate the usefulness of this general framework by focusing on realistic single-qubit noisy control scenarios. In particular, the design of dynamical-decoupling protocols for noise spectroscopy beyond the standard stationarity and/or Gaussianity assumptions will be addressed.

### 52. Spin squeezing and optimal internal spin control in an ensemble of qudits

Leigh Norris, Dartmouth College

view abstract +

We study the production of spin squeezed states in a large ensemble of cold, trapped alkali atoms with hyperfine spin f interacting with optical fields. By restricting the state of each atom to a qubit embedded in the 2f+1 dimensional hyperfine spin, we model spin squeezing of the ensemble through QND measurement of the collective spin. This formalism also enables us to explore the effect of control over the internal hyperfine spin of the atoms. State preparation using such control increases the entangling power of the atom-light interface for f>1/2, substantially enhancing spin squeezing. Dissipative dynamics on the system include optical pumping due to spontaneous emission, which is a fundamental barrier to achieving large spin squeezing in atomic ensembles. While most works ignore optical pumping or treat it phenomenologically, we employ a master equation derived from first principles. This sheds light on a variety of interesting effects, including transfers of coherence outside the embedded qubit that occur for atoms with f>1/2. We can account for these transfers of coherence by modeling each atom as a qutrit embedded in the 2f+1 dimensional hyperfine spin. Using a numerical search, we identify state preparations that maximize the spin squeezing generated by QND measurement in the presence of optical pumping.

### 53. Characterizing General Linear Transformations on bosonic modes

Shashank Pandey, Center for Quantum Information and Control, Department of Physics and Astronomy, University of New Mexico.

view abstract +

In this work we consider the following scenario: We are given some set of input signal bosonic modes and we wish to transform their mean by an arbitrary linear transformation T.
In general such a transformation will not be symplectic and cannot be implemented unitarily, we reduce it to its essential nonsymplectic parts, discuss how it could be implemented both in a probabilistic or deterministic way and also study the noise on the output.

Probabilistic: We find that such transformations T can be reduced to nonsymplectic operations that can be thought of as a set of amplifications, rotations and inversions. The simple
procedure to implement them relies on probabilistic amplifiers combined with other simpler processes, each of those results in noise on the output.

Deterministic: To implement the transformation T deterministically we construct its symplectic completion using auxiliary modes and find a set of basic canonical hamiltonians that suffice to produce any such transformation. Finally we characterize the noise properties of such transformations through a fictitious state on the auxiliary modes.

### 54. Can postselection improve the precision of weak measurement?

Shengshi Pang, University of Southern California

view abstract +

The advantage of weak measurements with postselection in precision of parameter estimation is under a heated debate recently. It is known that postselecting the system in a weak measurement can amplify the interaction parameter by the weak value. However, to obtain a large weak value, the postselection efficiency is usually very low, which may cancel the benefit of the weak value amplification. Therefore, whether postselection can really improve the precision of a weak measurement is a subtle problem. In this work, we study this problem in detail for two typical estimation strategies: one is simply averaging the measurement results, which is a suboptimal estimation strategy; the other is the well-known maximum likelihood estimation (MLE), which is an asymptotically optimal strategy since it minimizes the variance of the estimate. For the first strategy, we obtain and compare the maximum signal-to-noise ratio (SNR) for both postselected and non-postselected weak measurements, and show that the postselection can increase the SNR when the initial pointer state is a squeezed coherent state but cannot when the initial pointer state is a normal coherent state. This implies that to improve the precision of weak measurement by postselection, some nonclassicality in the pointer state is necessary. For the second estimation strategy, we consider the Fisher information for both types of weak measurements, and find that the Fisher information of a postselected weak measurement is generally larger than that of a non-postselected weak measurement, but they become equal when the initial system state approaches an eigenstate of the system observable. From these two results, we conclude that the postselection can indeed offer advantage in precision when the estimation strategy is suboptimal, but such advantage will vanish when the estimation strategy is optimized.

### 55. Fault-tolerant logical gates in quantum error-correcting codes

Fernando Pastawski, California Institute of Technology

view abstract +

Recently, Bravyi and König have shown that there is a trade-off between fault-tolerantly implementable logical gates and geometric locality of stabilizer codes. They consider locality-preserving operations which are implemented by a constant-depth geometrically-local circuit and are thus fault-tolerant by construction. In particular, they shown that, for local stabilizer codes in D spatial dimensions, locality preserving gates are restricted to a set of unitary gates known as the D-th level of the Clifford hierarchy. In this talk I will present a version of their result applicable to subsystem codes and explain several extensions arising thereof.

### 56. Surprises in the quantum-classical connection for nonlinear systems

Arjendu Pattanayak, Carleton College

view abstract +

We report on several recent results that show surprises in the Quantum-Classical connection for nonlinear systems, including in particular (a) the existence and source of chaos demonstrated via computed Lyapunov exponents for quantum systems with classically regular counterparts and (b) demonstration that the entanglement behavior of a 2-qubit system can display complete correspondence with the classical phase-space.

### 57. Tunable Quantum Speed-Up of Field Evolution in an Open Optical Cavity QED System

Burkley Patterson, Joint Quantum Institute

view abstract +

The quantum speed of state evolution is an important parameter in quantum information, with fundamental and technological implications. We are studying the quantum speed of an open cavity QED system. We perform second order correlation measurements of the intensity escaping the cavity. We focus on the cavity field coupled to an atomic polarization (N two-level atoms), which we treat as a tunable environment. Changing the number of atoms changes the quantum speed of the cavity field as it returns to steady state. Our results show that we can manipulate the quantum speed by tailoring the environment, which opens the possibility of implementing optimal quantum control. Work supported by the NSF of USA.

### 58. Controlling Quantum Chaos

Bibek Pokharel, Carleton College

view abstract +

The existence of quantum trajectory chaos has been established for an open nonlinear oscillator via Lyapunov exponents and Poincare sections computed using the Quantum State Diffusion formalism. This form of chaos lends itself to being controlled using the classical Ott-Grebogi-Yorke feedback protocol which traps the chaotic trajectory at an unstable fixed point of the evolution by a timely feedback in the system parameters. A coupled set of stochastic ordinary differential equations, accurate in the parameter regime used, are derived within a semi-classical approximation to the full quantum evolution. These ODEs allow us to estimate the feedback needed to control the quantum evolution. We report on progress using this hybrid technique towards controlling the observed quantum chaotic trajectories.

### 59. Dispersive mode response due to nanofiber-trapped atoms

Xiaodong Qi, University of New Mexico

view abstract +

Strong coupling between atoms and photons is a prerequisite for quantum information processing protocols ranging from quantum-limited metrology to quantum communication and computation. This strong coupling regime can be achieved in a nanofiber platform whereby ensembles of atoms are trapped in a two-side chain through the evanescent field of a nanofiber. In this work, we study the atom-photon interface in the dispersive regime, where the atoms' spin state is coupled to the photons' polarization through the index of refraction. We calculate this dispersive interaction first through the dyadic Green function method that allows and finds the nanofiber-guided fields scattered from the tensor-polarizable atoms. We study the phase shift and polarization rotation of the guided light due to the nanofiber-trapped atoms. Compared with the free-space laser trapped atomic cloud systems, our results show that the nanofiber platform will yield a much stronger coupling between the atoms and photons. Moreover, we present the emission rate surface of the nanofiber modes to show that the nanofiber platform has a good controlability even only considering a scalar atomic polarizability. Then we give an equivalent approach from the Heisenberg picture and apply the input-output formalism to simplify the calculations. Finally, we design an atomic state and atom number read-out protocol in the clock-state subspace, in which we demonstrate the high-sensitivity nature of the platform. This model could be used to design efficient quantum data buses, quantum gates and quantum memories benefiting from the strong entanglement between nanofiber modes and atomic ensembles.

### 60. Two dimensional coulomb crystals in an oblate ion trap for quantum simulations

Anthony Ransford, University of California Los Angeles

view abstract +

We present a novel trap design that is insensitive to micromotion along the symmetry axis where quantum operations will be performed. The RF potential and pseudo potential of this trap design are modeled. This trap is amenable to the study of Ising model interactions which can be mapped to the phonon modes with tunable power law behavior. The trap allows for new Coulomb crystal configurations that can be used to investigate frustrated magnetism.

### 61. Using symmetry groups in quantum information

Ravi Rau, Louisiana State University

view abstract +

In quantum information, symmetries of the operators and states of multiple qubits or higher-dimensional spins have not been much exploited. The SU(2) group for a single qubit, and its associated geometrical Bloch sphere are familiar but not similar pictures of SU(4) for two-qubit or higher SU(N). Examples will be given of such pictures and especially of sub-group symmetries that can be very useful for calculating entanglement, discord, and other properties. One is an interesting SU(2) X SU(2) X U(1) symmetry of X states of two qubits and an easy iterative generalization for multiple qubits.

### 62. QuDirac.jl

Jarrett Revels, American University

view abstract +

J.R. Revels, N.L Harshman

We present QuDirac.jl, an open-source, type-centric framework for computational analysis and simulation of quantum systems written in the Julia programming language. Most existing computational quantum mechanics libraries are representation-dependent, working solely with arrays of coefficients in fixed bases to determine the effects of quantum transformations. QuDirac.jl leverages recent advances in dynamically-typed programming environments and just-in-time (JIT) compilation to perform representation-free versions of these calculations. The library also facilitates idiomatic manipulation of abstract states and operators by implementing type constructs for bras and kets - the building blocks of standard Dirac notation. Additional features include:

- Lazily evaluated, user-defined inner products over an extensible type hierarchy of spaces
- Persistent and factorizable tensor product structures for all quantum ob jects
- Subspace extraction, analysis, and transformation via generic selection functions on state and operator labels
- Operator generation and representation from user-defined functions

### 63. Local records and global entanglement: A quantum state decomposition for redundantly recorded information

C. Jess Riedel, Perimeter Institute

view abstract +

We show that there is a unique maximal decomposition of a pure multi-partite (N>2) quantum state into a sum of states which are "locally orthogonal" in the sense that the local reduced state for a term in the sum lives in its own orthogonal subspace for each subsystem. Observers can make local measurements on any subsystem and determine which "branch" they are on. The Shannon entropy of the resulting branch weights defines a new measure of global, GHZ-like entanglement, which is insensitive to local pairwise entangling operations and vanishes when there is no piece of information recorded at every subsystem. In the bi-partite (N=2) case, this decomposition reduces to the (not necessarily unique) Schmidt decomposition and the entropy reduces to the entropy of entanglement.

### 64. Quantum computing by color-code lattice surgery

Ciaran Ryan-Anderson, University of New Mexico, Center for Quantum Information and Control, Sandia National Laboratories

view abstract +

We present how to use lattice surgery to enact a universal set of fault-tolerant quantum operations with color codes. Along the way, I will also show how to improve existing surface-code lattice-surgery methods. Lattice-surgery methods use fewer qubits and the same time or less than associated defect-braiding methods. Per code distance, color-code lattice surgery uses approximately half the qubits and the same time or less than surface-code lattice surgery. Color-code lattice surgery can also implement the Hadamard and phase gates in a single transversal step—much faster than surface-code lattice surgery can. I will show that against uncorrelated circuit-level depolarizing noise, color-code lattice surgery uses fewer qubits to achieve the same degree of fault-tolerant error suppression as surface-code lattice-surgery when the noise rate is low enough and the error suppression demand is high enough. 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.

### 65. Will it Cool? Normal Mode Thermometry in Sympathetically Cooled Ion Chains

Tomasz Sakrejda, University of Washington

view abstract +

We are investigating the use of co-trapped Ytterbium and Barium ions to build a scalable quantum computer. The ground state hyperfine levels of Ytterbium-171 will be used as qubits, while Barium-138 will be used to sympathetically cool the system. We wish to understand the scaling of cooling efficacy with refrigerant ion number and chain configuration. We perform motional sideband excitation measurements with a narrowband laser, extracting normal mode occupation numbers for different configurations and ion number ratios. We also present progress toward implementation of motional quantum gates in these mixed species ion chains using a mode-locked frequency-doubled YAG laser.

### 66. Towards multi-heterodyne dispersive detection of ultracold gas dynamics

Bianca Sawyer, Dodd-Walls Centre for Photonic and Quantum Technologies, University of Otago

view abstract +

Trapped ultracold gases have long been utilized as a highly controllable experimental testbed for the investigation of exciting and fundamental quantum phenomena. The manipulation and control of such systems may benefit significantly from (partial) information gained in measurement with off-resonant light [1]. For example, quantum non-demolition measurement can be used to engineer spin-squeezed states of atomic ensembles, leading to quantum noise limited interferometry [2, 3]. We present a non-destructive interrogation system that uses frequency modulation spectroscopy to measure the quantum state-dependent phase shift incurred on an off-resonant optical probe when transmitted by an atomic medium. This robust and powerful tool has been routinely used to track a number of dynamical processes in trapped ultracold gases. Our applications include following the atomic density during an evaporative cooling sequence [4], performing gradient magnetometry [5], optimising quantum state preparation and identifying magnetic Feshbach resonances. We are currently extending the capabilities of our scheme by developing an asymmetric dual-frequency probe, followed by multi-heterodyne IQ detection to simultaneously monitor atoms in two different internal states. Additionally, we are investigating the use of feedback protocols in our ultracold gas experiment to perform reliable quantum state preparations, e.g. via adiabatic rapid passage in the presence of an arbitrary magnetic bias field.

- I.H. Deutsch, and P.S. Jessen, "Quantum control and measurement of atomic spins in polarization spectroscopy", Opt. Commun. 283, 681-94 (2010)
- M.H. Schleier-Smith, I.D. Leroux, and V. Vuletic, "States of an ensemble of two-level atoms with reduced quantum uncertainty", Phys. Rev. Lett. 104, 073604 (2010)
- J. Appel et al., "Mesoscopic atomic entanglement for precision measurements beyond the standard quantum limit", Proc. Natl. Acad. Sci. USA 106, 10960-5 (2009)
- B.J. Sawyer, A.B. Deb, T. McKellar, and N. Kjaergaard, "Reducing number fluctuations of ultracold atomic gases via dispersive interrogation", Phys. Rev. A 86, 065401 (2012)
- A.B. Deb, B.J. Sawyer, and N. Kjaergaard, "Dispersive probing of driven pseudo-spin dynamics in a gradient field", Phys. Rev. A 88, 063607 (2013)

### 67. Device-Independent Tripartite Quantum Key from Three-Player Quantum Games

Mahrud Sayrafi, University of California, Berkeley

view abstract +

Quantum entanglement, one of the most counter-intuitive phenomena in quantum theory, has long been studied in information theoretic contexts. It is known that use of entanglement in multiparty game strategies can lead to arbitrarily large advantage over classical players. These violations of classical bounds, known as Bell's inequalities, are due to the nonlocal nature of the correlations. Here we introduce a protocol for key distribution among three players who share nothing other than entangled quantum states. Further, we present partial results in enabling any two players to use partial entanglement to produce a key independent of the third player in order to make the protocol resilient against a corrupted player. This research contributes to the study of non-locality in the reduced bipartite state of an entangled state that maximally violates a tripartite inequality.

### 68. Wiring up charged particles

Philipp Schindler, UC Berkeley

view abstract +

Presenting authors: S. Möller, P. Schindler, D.Gorman, R. Masuda, N. Daniilidis and H. Häffner Coupling charged particles to electronic devices opens up new possibilities for quantum hybrid systems. In particular, ultracold trapped ions and superconducting quantum electronics present a promising constituents for a hybrid quantum information processor. Such a device would allow access to the advantages of both architectures: The exquisite and fast control of superconducting electronics combined with the astonishing coherence times of atomic systems. Furthermore, the well established laser-cooling toolbox can be transferred onto superconducting quantum electronic devices. We report on our experimental results towards an interface between a single ion and a superconducting resonator. We confine a single Ca ion in a surface trap at 200 um distance from a pick-up wire. This wire is connected to a superconducting tank circuit with resonance frequency of around 2MHz and a quality factor of above 30000. We have successfully trapped a single ion and coupled its motion to the electronic resonator. We expect to cool the mode of the resonator by more than two orders of magnitude when coupling it to a continuously Doppler-cooled ion. The long-term goal is to reach the quantum regime where the resonator is cooled close to its motional ground state. At cryogenic temperatures this regime can only be reached if the resonance frequency is on order of several GHz. Since the ion's motional frequency is typically a couple of MHz, a frequency conversion scheme is required to overcome this mismatch. We propose a parametric up-conversion mechanism exploiting the non-linear the trapping potential. This method converts the frequency before the signal enters any solid state device thus avoiding the excessive low-frequency noise present in these systems.

### 69. Lost in (Hilbert) Space: Model Selection for Quantum Tomography

Travis Scholten, University of New Mexico, Sandia National Laboratories

view abstract +

Reconstructing the quantum state of a continuous variable system (e.g., an optical mode) using quantum tomography presents a unique problem: the dimension of its Hilbert space is infinite. Its density matrix has infinitely many parameters, which cannot all be estimated from finite data. Brute force reconstruction (e.g., via the Radon transform or deconvolution) produces undesirable overfitting artifacts. Smoothing is one solution, but lacks a good theoretical justification. I introduce a statistically well-motivated approach based on model selection and log likelihoods. Maximum likelihood estimates in a sequence of D-dimensional subspaces (spanned by the first D Fock states) are ranked by their log likelihood. This ranking allows one to find an estimate whose dimension is smaller while simultaneously providing a good fit to data. I apply this method to heterodyne tomography and demonstrate the method can indeed eliminate overfitting by choosing a good dimension (D) in which to reconstruct optical states. Sandia 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 No. DE-AC04-94AL85000.

### 70. Generating entanglement via measurement between two remote superconducting qubits

Mollie Schwartz, Quantum Nanoelectronics Laboratory, University of California, Berkeley

view abstract +

M.E. Schwartz, N. Roch, F. Motzoi, C. Macklin, R. Vijay, A.E. Eddins, A.N. Korotkov, K.B. Whaley, M. Sarovar, I. Siddiqi Measurement has traditionally been viewed as a means to restore classical behavior to a quantum system: a quantum superposition, once observed, transforms into a single classical state. However, for some systems it is possible to design a measurement that projects instead into an entangled state, thereby purifying, rather than destroying, quantum correlations. We present the use of a continuous measurement to generate entanglement between two superconducting qubits that are separated by more than a meter of cable, demonstrating that quantum information be transferred over the metallic wires that comprise a low-loss channel for microwave photon propagation. We further take advantage of a nearly quantum-limited amplification chain to generate a faithful, time-resolved record of single quantum trajectories of our system. We use these trajectories to track the evolution of a single joint quantum state under the influence of measurement. Studying the statistics of these trajectories and of the ensemble of measurements provides insight into the dynamics of measurement-induced entanglement in an extended quantum network. This work was funded by the ARO and by the Fannie and John Hertz Foundation.

### 71. Quantum Phase Transition of a Multi-connected Superconducting Jaynes-Cummings Lattice Model

Kangjun Seo, University of California, Merced

view abstract +

Superconducting quantum devices have excellent connectivity, tunable couplings and long decoherence times as demonstrated by recent experiments. These devices provide a powerful platform for constructing analog quantum simulators to study novel quantum many-body effects. In this work, we present a multi-connected Jaynes-Cummings lattice model, where the qubits and resonators are arranged alternatively. In a one-dimensional configuration, this model bears an intrinsic symmetry between the left and right qubit-resonator couplings under a mirror reflection of the lattice. Different from the coupled cavity array (CCA) model, the qubit-resonator couplings in our model induce both onsite Hubbard nonlinearity and hopping along the lattice. Here we study the phase transition of this model using the exact diagonalization method. By analyzing the off-diagonal long-range order of the single-particle density matrix and the energy gap, we show that this model can demonstrate a Mott insulator "superfluid" Mott insulator transition with symmetric critical points. The reentry to the Mott insulator phase originates from the symmetry between the couplings. We also discuss the implementation of the phase transitions with the superconducting devices, including the state preparation and detection schemes. 1. K. Seo and L. Tian, eprint arXiv:1408.2304.

### 72. Distinguishability of Qudit Hyperentangled States with Linear Evolution and Local Measurement

Victor Shang, Harvey Mudd College

view abstract +

Presenters: Victor Shang, Theresa W. Lynn

Additional Co-Author: Calvin Maldonado

We present recent progress in determining optimal distinguishability of hyperentangled qudit Bell states using linear evolution and local measurement (LELM). Previous work in our group has established an upper bound on the number of hyper-Bell state classes that can be reliably distinguished, provided that Bell state classes are always disjoint. We have recently undertaken a combination of computational and analytic approaches to two remaining questions: whether the assumption of disjoint classes holds in general, and whether the associated upper bound is achievable. In the case of hyperentangled qubit degrees of freedom, Bell state classes are in fact always disjoint, and the upper bound is realizable with a conceptually simple detection apparatus. We present recent work to resolve these questions for hyperentangled qudit degrees of freedom, including the experimentally important (qubit)x(qutrit) case.

### 73. Enhanced collective spin squeezing via internal spin control in the presence of decoherence.

Ezad Shojaee, University of New Mexico

view abstract +

In this work, we model the generation of collective spin squeezing via quantum non-demolition (QND) measurement in an of ensemble cesium atoms, enhanced through control of the internal spin state of the atoms. The Faraday interaction generates the requisite entanglement between the light and the atoms, and measurement backaction and squeezing arises by monitoring the polarization state of the transmitted light. The strength of the measurement backaction depends on the ability of the polarimeter to distinguish different projections of the collective spin given the shot-noise resolution of the probe. Internal spin control can enhance the atomic projection noise variance when compared to photon shot noise, and thus enhance the entangling strength of the interaction [1]. However, different internal states can be more susceptible to decoherence. To study this trade-off, we simulate the system based on a stochastic master equation, which describes the QND measurement and the effects of optical pumping. The latter includes both population transfers, as well as transfer of coherences between magnetic sublevels. We investigate how different spin preparations would generate different amounts of metrologically relevant squeezing and how robust they are to the decoherence due to the photon scattering.

- Leigh M. Norris, et al. Phys. Rev. Lett. 109, 173603 Published 23 October 2012

### 74. High-rate Rydberg-based quantum repeater

Neal Solmeyer, The Army Research Laboratory

view abstract +

Neal Solmeyer(1), Xiao Li(2), Qudsia Quraishi(1)

1 Army Research Laboratory, 2800 Powder Mill Rd., Adelphi, MD 20783
2 Joint Quantum Institute, Univ. of MD, College Park, MD 20740
Networking of quantum information over long distances may be achieved using quantum memory elements and quantum repeater protocols [Duan et al., Nature 414, 413 (2001)]. Transmission between nodes is best done with a photon as a flying qubit entangled with the memory. Typically, long-lived memories have had low repetition rates, whereas, here we propose a high entanglement rate Rydberg-based quantum repeater. Neutral atom memories can be long-lived, and collective effects in an ensemble allow the memory to be mapped onto a particular photon mode for efficient collection and transmission. Our quantum repeater nodes will use an ultra-cold ensemble of neutral 87Rb atoms and we are currently building this setup. Recently, a proposal for an ensemble-based Rydberg quantum repeater [Zhao et al., PRA 81, 052329 (2010)] highlighted the use of Rydberg excitations for deterministic entanglement generation and two qubit gates in a repeater network. We propose a simplified protocol for entanglement generation entanglement and show how this system can be used to perform teleportation between two nodes. We predict rates of successful teleportation as high as a kHz. This would represent a significant gain over recently realized teleportation experiments [Olmschenk et al., Science, 323, 486 (2009), Bao et al., PNAS, 203, 20347 (2012), and Pfaff et al., Science, 345, 532 (2014)] which have rates in the range of one every 4 to 12 minutes.

### 75. Inhomogeneous Quantum Control of Cold Atom Qudits

Hector Sosa Martinez, University of Arizona

view abstract +

Hector Sosa Martinez, Nathan Lysne, Poul Jessen (University of Arizona); Charlie Baldwin, Ivan Deutsch (University of New Mexico). Accurate and robust control over complex quantum systems (trapped atoms and ions, condensed matter devices, optical systems) plays a key role in quantum information science. The use of systems with large state spaces (qudits) may prove a useful resource for quantum information tasks if good laboratory tools for qudit manipulation and measurement can be developed. Over the past few years we have developed and experimentally implemented a protocol to perform high-fidelity unitary transformations in the 16 dimensional hyperfine ground manifold of Cesium-133 atoms, driving the system with phase modulated radio-frequency and microwave magnetic fields and using the tools of optimal control to find appropriate control waveforms. We have recently extended our protocol to investigate inhomogeneous quantum control. In particular, we aim to simultaneously perform different unitary transformations on qudits that see different light shifts from an optical addressing field. Experimental results show that it is possible to obtain high fidelities for such transformations in an 8 dimensional subspace, provided that the optical addressing field is well chosen and sufficient control time is allowed for the control waveform. Most recently, we have started to explore quantum state tomography based on a combination of unitary transformations and Stern-Gerlach analysis. Preliminary results shown that optimal tomography based on mutually-unbiased-bases (MUBs) can be implemented, and that reconstruction fidelities on the order of 99% can be achieved for arbitrarily chosen test states in a 16-dimensional Hilbert space. Ultimately, successful implementation of this kind of state tomography may prove very valuable, greatly reducing the required data for more complex procedures such as quantum process tomography.

### 76. Cavity-Optomechanics with cold atoms: Quantum mechanical oscillators coupled by a cavity-mediated optical spring

Nicolas Spethmann, University of California, Berkeley

view abstract +

Coherently interacting quantum oscillators lie at the heart of many applications in quantum information science. Oscillators comprised of the collective motion of many ultracold, neutral atoms are excellent model systems in the quantum regime. However, neutral atoms inherently exhibit only weak interactions, so that it is a challenge to create tuneable, long-range coupling. Such interactions can be induced employing photons in a cavity containing the ultracold atoms. Because of the decay of cavity photons, such a coupling necessarily leads to measurement back-action noise being imparted onto the oscillators. We demonstrate cavity-mediated coupling between two near-groundstate oscillators composed of ultracold Rb atoms trapped inside a high-finesse cavity. We observe coherent transfer of excitation between the oscillators. At the same time, we detect the motional noise of the oscillators to monotonically increase with coupling time due to back-action. We show that this back-action noise exhibits two-oscillator correlations, reflecting the properties of the coupled mode system during cavity-mediated interaction. Our results point to the potential, and also the challenge, of coupling quantum oscillators with light.

### 77. Leakage Suppression in theToric Code

Martin Suchara, IBM Research

view abstract +

Quantum codes excel at correcting local noise but fail to correct leakage faults that excite qubits to states outside the computational space. Aliferis and Terhal have shown that an accuracy threshold exists for leakage faults using gadgets called leakage reduction units (LRUs). However, these gadgets reduce the accuracy threshold and can increase overhead and experimental complexity, and these costs have not been thoroughly understood. Our work explores a variety of techniques for leakage-resilient, fault-tolerant error correction in the context of topological codes. Our contributions are threefold. First, we develop a leakage model that differs in critical details from earlier models. Second, we use Monte-Carlo simulations to survey several syndrome extraction circuits. Third, given the capability to perform three-outcome measurements, we present a dramatically improved syndrome processing algorithm. Our simulation results show that simple circuits with one extra CNOT per qubit and no additional ancillas reduce the accuracy threshold by less than a factor of 4 when leakage and depolarizing noise rates are comparable. This becomes a factor of 2 when the decoder uses 3-outcome measurements. Finally, when the physical error rate is less than 2 x 10^-4, placing LRUs after every gate may achieve the lowest logical error rates of all of the circuits we considered. We expect the closely related planar and rotated codes to exhibit the same accuracy thresholds and that the ideas may generalize naturally to other topological codes.

### 78. Study of anomalous electric field noise in planar ion traps

Ishan Talukdar, University of California, Berkeley

view abstract +

Decoherence caused by electric field noise is a major hurdle in ion trap quantum computing. We study the characteristics of this noise by trapping individual Calcium ions 50 micrometers above a Cu-coated Al-surface. For quantum information applications, the phase coherence of the ion motion is of particular importance. We study the phase coherence, and assuming an inverse scaling of the noise with the frequency infer a lower cutoff for anomalous electric field noise. In addition, we also study the polarization of electric field noise. We show that the most natural technical noise models lead to a strong polarization of the noise whereas anomalous electric field noise originating from either patches or small dipoles is only weakly polarized. Using a single ion trapped 100 micrometers above a Gold surface, we find that the noise is about a factor of 4 larger normal to the surface than horizontally. This observation is consistent with similar contributions from surface and technical noise.

### 79. Universal Quantum Computation by Scattering in the Fermi-Hubbard Model

Nathaniel Thomas, Stanford University

view abstract +

The Hubbard model may be the simplest model of particles interacting on a lattice, but simulation of its dynamics remains beyond the reach of current numerical methods. We show that general quantum computations can be encoded into the physics of wave packets propagating through a planar graph, with scattering interactions governed by the fermionic Hubbard model. Therefore, simulating the model on planar graphs is as hard as simulating quantum computation. We give two different arguments, demonstrating that the simulation is difficult both for wave packets prepared as excitations of the fermionic vacuum, and for hole wave packets at filling fraction one-half in the limit of strong coupling. In the latter case, which is described by the t-J model, there is only reflection and no transmission in the scattering events, as would be the case for classical hard spheres. In that sense, the construction provides a quantum mechanical analog of the Fredkin-Toffoli billiard ball computer.

### 80. Squeezing characterization and on-chip integration of Josephson parametric amplifiers

David Toyli, Quantum Nanoelectronics Laboratory, UC Berkeley

view abstract +

In recent years, superconducting parametric amplifiers (paramps) have become essential tools for low-noise measurement of superconducting qubits and the generation of squeezed microwave states. Here we describe two experiments aimed at understanding the performance limitations of conventional paramp designs and exploring novel device architectures for qubit readout. In the first experiment we systematically image the squeezed output fields of lumped-element Josephson parametric amplifiers (JPAs) using homodyne detection techniques. These experiments provide insights on the impact of commonly-neglected nonlinear terms in the paramp Hamiltonian on JPA noise properties. Moreover, these results highlight the importance of weak device nonlinearities for the generation of highly squeezed states. In the second experiment we perform dispersive measurement of a transmon qubit with an on-chip parametric amplifier. We observe that the backaction of the amplifier on the qubit depends on the relative phase of the amplifier pump and qubit measurement tones, suggesting a means to perform low-noise qubit measurement without lossy isolators between the qubit and paramp. We discuss the potential application of this system for weak, continuous measurement of superconducting qubits. Authors: David Toyli, Andrew Eddins, Aditya Venkatramani, Eli Levenson-Falk, and Irfan Siddiqi (Quantum Nanoelectronics Laboratory, UC Berkley); Samuel Boutin and Alexandre Blais (Departement de Physique, Universite de Sherbrooke); and Benjamin Levitan, Saeed Khan, Nicolas Didier, and Aashish Clerk (Department of Physics, McGill University). This work is supported by the ARO and ONR.

### 81. Relativistic Quantum Metrology

Jim van Meter, National Institute of Standards and Technology

view abstract +

Utilizing a generally covariant formalism developed by Brunetti, Fredenhagen, and Verch for handling quantum fields in a locally perturbed, classical spacetime background, Downes, Milburn, and Caves recently introduced the idea of applying the Cramer-Rao bound to optimizing gravitational parameter estimation. This results in a Heisenberg-like uncertainty relation between quantum field observables and classical gravitational quantities. Building on their work I show how this general method can be adapted to global spacetime parameters and discuss various applications, from cosmological observations to gravimeters to accelerometers. In particular, I derive a bound on the accuracy of laser-interferometric gravitational wave observatories.

### 82. A Heisenberg Limit for Quantum Region Estimation

Michael Walter, Stanford University

view abstract +

The laws of quantum mechanics place fundamental limits on the accuracy of measurements and therefore on the estimation of physical parameters by a quantum system. In joint work with Joe Renes (ETHZ), we have proved lower bounds on the size of confidence regions reported by any region estimator for a given ensemble of probe states and probability of success. Our bounds are derived from a previously unnoticed connection between the size of confidence regions and the error probabilities of a corresponding binary hypothesis test. In group-covariant scenarios, we find that there is an ultimate bound for any estimation scheme which depends only on the representation-theoretic data of the probe system, and we evaluate its asymptotics in the limit of many systems, establishing a general "Heisenberg limit" for region estimation. We apply our results to several scenarios, in particular to phase estimation, where our bounds strengthen the well-known Heisenberg and shot-noise scaling.

### 83. Degenerate Perturbation Theory as a Tool for Quantum Search

Tom Wong, University of Latvia

view abstract +

Degenerate perturbation theory is a "textbook tool" for quantum mechanics, famously used to derive the spectra of atoms in the presence of an external electric field (i.e., the Stark effect). In this talk, we show that it can also be used to analyze quantum computing algorithms, specifically quantum search on graphs. Using it, we show two intuitions to be false, that global symmetry and high connectivity are not necessary for fast quantum search.

### 84. Trying to efficiently distill non-stabilizer states from a minimum number of magic states

Raymond Wong, University of California, Santa Barbara

view abstract +

We look at the problem of efficiently constructing generic non-stabilizer states using only magic states and stabilizer operations. Specifically, we investigate how well stabilizer circuits and H type magic states can be used to produce "meridian qubits" of the kind cos(a)|0> + sin(a)|1>. In previous work Duclos-Cianci and Svore [Phys. Rev. A 88, 042325 (2013)] presented protocols for constructing such meridian states using stabilizer circuits of four qubits and they showed how they can be used to produce a dense subset of them. Here we present a class of protocols that uses sequences of two qubit stabilizer circuits that are more efficient than those of [Duclos-Cianci and Svore] and that produces the same dense subset. Our result uses a classification of the 11,520 possible two qubit stabilizer circuits into four distinct categories.

### 85. Towards Raman Motional Gates in Mixed Species Ion Chains

John Wright, University of Washington

view abstract +

Mixed species ion chains can potentially help resolve engineering challenges in scalable trapped ion quantum computation. Using a fiber laser to address a narrow quadrupole transition in Barium ions, we have taken initial measurements of temperatures for different configurations of cooled Barium ions and uncooled Ytterbium ions. As predicted by theory, ion-ion couplings between different species are strongly suppressed when using radial modes because of the mass difference. Further, when only one species is cooled the decoupled modes have very high average motional occupation numbers. Taking these measurements into account, we consider strategies for implementing Raman motional gates between the two ion species as part of a next generation quantum computing architecture.

### 86. Design and characterization of niobium lumped Josephson parametric amplifiers

Dirk Wright, University of California, Berkeley

view abstract +

Providing large gain with near quantum-limited noise performance, superconducting parametric amplifiers (paramps) have proven themselves invaluable tools for fast, high-fidelity measurement in circuit QED, and have recently been proposed for use in the Axion Dark Matter Experiment (ADMX) at the University of Washington. Here we demonstrate a series of single-ended, niobium lumped Josephson parametric amplifiers optimized for such dark matter detection experiments. In contrast to conventional aluminum circuits, the niobium paramps enable device characterization at liquid helium temperatures, an important check for ADMX. Moreover, the single-ended design eliminates the need for ring hybrids that become prohibitively large at the low frequencies (~1 GHz) relevant for dark matter detection. The amplifiers are tunable over the L or C bands and achieve 20 dB gain with an instantaneous bandwidth ~10 MHz. We discuss circuit design, device housing, and measured amplifier performance over a range of temperatures and under different pumping configurations. Authors: Dirk Wright, Reinhard Lolowang, Nicholas Frattini, Andrew Eddins, Chris Macklin, Irfan Siddiqi (Quantum Nanoelectronics Laboratory, UC Berkeley) David Hover, Vlad Bolkhovsky, and William D. Oliver (MIT Lincoln Labs). This research is supported by the Army Research Office.

### 87. Ion heating rate measurement in a microfabricated surface trap

Zichao Zhou, University of Washington

view abstract +

Trapped atomic ion ensemble is an attractive choice for quantum information processing and quantum simulations. Microfabricated surface traps, with their controllable pseudopotential, are recognized as one of the promising systems to build the quantum computer. Recently, Barium ions have been trapped in a newly designed surface trap (High Optical Access Version 2.0) built by Sandia National Lab. We have measured the dark lifetime about 4s and laser cooled lifetimes over an hour in our preliminary experiments.