# 2016 Talk Abstracts

## 1. The promise of variational quantum algorithms

Ryan Babbush, Martinis group (Google)

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

Recent work has shown that parameterize short quantum circuits can generate powerful variational ansätze for ground states of classically intractable fermionic models. This observation inspires hope that even without error correction, quantum computers may provide insight into problems of industrial importance such as quantum chemistry and superconductivity. As the number of qubits in superconducting devices keeps increasing, their dynamics are becoming prohibitively expensive to simulate classically. In anticipation of such a platform, we use devices with up to nine superconducting qubits to explore the viability of variational approaches. We discuss experiments showing surprising robustness to control errors, including the first quantum simulation of molecular energies to obtain chemical precision without precompilation. Nevertheless, with current gate fidelities it seems unlikely that variational approaches parameterize in terms of conventional logic gates will scale to the classically intractable regime. Instead, we propose to form variational ansätze at the level of hardware by parameterizing quantum circuits in terms of the experimentalist’s control knobs. We discuss an ongoing experiment to simulate Fermi-Hubbard models in this way. We conclude by asking how experiments can guide the design and analysis of quantum variational algorithms.

## 2. Informational completeness in bounded-rank quantum-state tomography

Charles Baldwin, Deutsch group (New Mexico)

(Session 3 : Thursday from 2:45 pm - 3:15 pm)

Quantum-state tomography is a demanding task, however, it can be made more efficient by applying prior information about the system. A common prior assumption is that the state being measured is pure, or close to pure, since most quantum information protocols require pure states. Measurements of pure states can be constructed to be more efficiently than measurements of an arbitrary state, and for these types of measurements, there exists two different notions of informational completeness. One notion, called strict-completeness, is more useful for practical applications since it is compatible with convex optimization and is robust to noise. We present a unified framework for both notions of completeness for a certain type of measurements. These are measurements that allow algebraic reconstruction of a few density matrix elements. The framework also aids in the construction of new strictly-complete measurements. Moreover, the results are easily generalized to the case when the prior information is the state has bounded rank.

## 3. Efficient tunnelling in quantum adiabatic optimization and its quantum Monte Carlo simulations

Lucas Brady, van Dam group (UC Santa Barbara)

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

We explore the behavior of Quantum Adiabatic Optimization (QAO) and path-integral Quantum Monte Carlo (QMC) methods while tunneling through potential barriers of varying size. We focus on n-qubit systems with a symmetric cost function where the annealing algorithms must tunnel through a barrier that has (width x height) proportional to (n^a x n^b). By tuning the exponents a and b it is possible to make a successful QAO algorithm take constant, polynomial, or exponential time in n. First we examine for which values of a and b these complexity transitions occur and numerically compare the run times of QAO with QMC which we find are correlated. Furthermore we find evidence that the time complexities of these two algorithms scale with each other in a way that suggests that QMC algorithms tunnel efficiently in the same setting as where QAO is efficient. See the linked manuscript for more details. Next, we look at the behavior of QAO in the polynomial scaling region of a and b. To do this, we compare our system to several similar toy models, and using these we rederive a folklore result by Goldstone that says that asymptotically the spectral gap scales as n^(1/2-a-b) for a+b>1/2 and 2a+b<1. We show numerically that our problem approaches the same asymptotic scaling limit as these toy problems, but in both cases, extremely large n are needed to realize the asymptotic limit.

## 4. Logical randomized benchmarking

Joshua Combes, (IQC, Waterloo and Perimeter)

(Session 9b : Friday from 4:00 pm - 4:30 pm)

Randomized Benchmarking is a characterization tool that is insensitive to state preparation and measurement errors. In many situations estimating the fidelity of a logical qubit from the physical fidelity can lead to over or under estimates. In this work we show how performing Randomized Benchmarking on a logical qubit can (i) help provide a more accurate assessment of the quality of the gates and physical channel, (ii) give estimates for the rates of correctable and uncorrectable errors.

## 5. Building a quantum computer using silicon quantum dots

Susan Coppersmith, (Wisconsin-Madison)

(Session 3 : Thursday from 1:30 pm - 2:15 pm)

This talk will discuss work at University of Wisconsin-Madison that aims to build a quantum computer using electrically-gated quantum dots in silicon. We have proposed and implemented a new "hybrid quantum dot qubit," which has an attractive combination of speed and fabrication simplicity [1]. Recent experimental and theoretical results demonstrating substantial progress towards high fidelity operation will be presented [2,3]. [1] Z. Shi, et al., Phys. Rev. Lett. 108, 140503 (2012). [2] D. Kim, et al., Nature 511, 70 (2014). [3] D. Kim, et al., npj Quant. Inf. 1, 15004 (2015). This work was supported in part by ARO (W911NF-12-0607), NSF (PHY-1104660), and ONR (N00014-15-1-0029).

## 6. Exploring the macroscopic quantum physics of motion with superfluid He-4

Laura De Lorenzo, Schwab group (IQIM, Caltech)

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

We demonstrate the utility of superfluid helium-4 as an extremely low loss optomechanical element. We form an optomechanical system with a cylindrical niobium superconducting TE011 resonator whose 40 cm^3 inner cylindrical cavity is filled with He-4. Coupling is realized via the variations in permittivity resulting from the density profile of the acoustic modes. Acoustic losses in helium-4 below 500 mK are governed by the intrinsic nonlinearity of sound, leading to an attenuation which drops as T^4, indicating the possibility of quality factors (Q) over 10^10 at 10 mK. In our lowest loss mode, we demonstrate this T^4 law at temperatures down to 50 mK, realizing an acoustic Q of 1.35*10^8 at 8.1 kHz. When coupled with a low phase noise microwave source, we expect this system to be utilized as a probe of macroscopic quantized motion, for precision measurements to search for fundamental physical length scales, and as a continuous gravitational wave detector. Our estimates suggest that a resonant superfluid acoustic system could exceed the sensitivity of current broad-band detectors for narrow-band sources such as pulsars.

## 7. Exploring small quantum error correcting codes with superconducting qubits

Jay Gambetta, (IBM)

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

I will review IBM's current approach towards quantum computing with superconducting qubits. The goal is to build a system using quantum error correction schemes based on rotated surface codes, which has a high error threshold, requires only nearest-neighbor qubit interactions, and uses simple syndrome extraction circuits. I will discuss our results on achieving high fidelity two- and single- quit gates, long coherence times, and our recent results on demonstrating small codes on square lattices of superconducting qubits.

## 8. A significant-loophole-free test of Bell's theorem with entangled photons

Marissa Giustina, Zeilinger group (Vienna)

(Session 2 : Thursday from 10:30 am - 11:00 am)

Local realism is the worldview in which physical properties of objects exist independently of measurement and where physical influences cannot travel faster than the speed of light. Bell's theorem states that this worldview is incompatible with the predictions of quantum mechanics, as is expressed in Bell's inequalities. Previous experiments convincingly supported the quantum predictions. Yet, every experiment requires assumptions that provide loopholes for a local realist explanation. Here we report a Bell test that closes the most significant of these loopholes simultaneously. Using a well-optimized source of entangled photons, rapid setting generation, and highly efficient superconducting detectors, we observe a violation of a Bell inequality with high statistical significance.

## 9. Data analysis for "A strong loophole-free test of local realism"

Scott Glancy, (NIST, Boulder)

(Session 2 : Thursday from 11:30 am - 12:00 pm)

Recent loophole-free tests of local realism have incorporated new analysis techniques to compute p-values (measures of statistical significance of the experiments). The new techniques do not require the support of assumptions upon which old techniques rely, they are effective for small data sets, and they accommodate imperfections in random number generators used to make measurement choices. In this talk I will describe the data analysis techniques used in the test of local realism performed at NIST. I will review the theory used to compute p-values, explain how it was implemented on our experiment's data, and compare our techniques to those used in the tests of local realism performed in Delft and Vienna.

## 10. Quantum simulation of spin-bath dynamics with trapped ions

Dylan Gorman, Häffner group (UC Berkeley)

(Session 9a : Friday from 4:00 pm - 4:30 pm)

Chains of trapped ions are an ideal platform for studying the dynamics of qubits coupled to bosonic environments. This kind of dynamics is of interest in many current problems in physics and biology such as charge transport, photosynthesis, and olfaction. In a chain of N trapped ions, an experimenter has access to an environment of the 3N vibrational modes of the chain, allowing for the simulation of very large vibrational environments with tunable spectral properties. In addition, the ions also serve as qubits, and both qubit-qubit and qubit-bath interactions can be engineered via quantum gates. Here, we discuss recent experimental progress investigating spin-bath dynamics in ion strings. We explore what happens as the spin-bath coupling is varied, as well as when the thermal occupation and quantum state of the environment is varied.

## 11. Enhanced emission of zero-phonon line photons from a single nitrogen-vacancy center in diamond

Michael Gould, Fu group (Washington)

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

We demonstrate efficient, resonantly enhanced collection of zero-phonon line (ZPL) photons from a single nitrogen-vacancy (NV) center in diamond. The near-surface NV center is optically coupled to an integrated gallium-phosphide-on-diamond (GaP-on-diamond) disk resonator, which is coupled to an output bus waveguide. We estimate a total collection rate of 3.2 x 10^5 ZPL photons into the bus waveguide. This corresponds to a quantum efficiency of approximately 4.5%, significantly higher than the 3% theoretical limit without the use of resonant enhancement. The device was fabricated on a GaP-on-diamond chip, alongside a large number of other integrated photonic devices. These include vertical grating couplers with average coupling efficiencies of 17%, low-loss single-mode waveguides and low-loss directional couplers. This work puts the platform in a strong position to enable fully integrated NV-NV entanglement generation, at rates several orders of magnitude larger than what has been demonstrated in literature.

## 12. Fisher symmetry and the geometry of quantum states

Jonathan A. Gross, Caves group (New Mexico)

(Session 9c : Friday from 4:30 pm - 5:00 pm)

The quantum Fisher information (QFI) is a valuable tool on account of the achievable lower bound it provides for single-parameter estimation. Due to the existence of incompatible quantum observables, however, the lower bound provided by the QFI cannot be saturated in the general multi-parameter case. A bound demonstrated by Gill and Massar (GM) captures some of the limitations that incompatibility imposes in the multi-parameter case. We further explore the structure of measurements allowed by quantum mechanics, identifying restrictions beyond those given by the QFI and GM bound. These additional restrictions give insight into the geometry of quantum state space and notions of measurement symmetry related to the QFI.

## 13. From a loophole-free Bell test to a quantum Internet

Ronald Hanson, (TU Delft)

(Session 1 : Thursday from 8:45 am - 9:30 am)

The realization of a highly connected network of qubit registers is a central challenge for quantum information processing and long-distance quantum communication. Diamond spins associated with NV centers are promising building blocks for such a network as they combine a coherent optical interface (similar to that of trapped atomic qubits) [1] with a local register of robust and well-controlled nuclear spin qubits [2]. We can now exploit these features simultaneously to achieve new functionalities such as unconditional remote quantum teleportation [3]. Here we present our latest progress towards scalable quantum networks, including the first loophole-free violation of Bell's inequalities [4]. References: [1] H. Bernien et al., Nature 497, 86 (2013). [2] T. H. Taminiau et al., Nature Nanotechnology 9, 171 (2014). [3] W. Pfaff et al., Science 345, 532 (2014). [4] B. Hensen et al., Nature 526, 682 (2015).

## 14. Nuclear-driven electron spin rotations in a coupled silicon quantum dot and single donor system

Patrick Harvey-Collard, Carroll group (Sandia)

(Session 4 : Thursday from 4:30 pm - 5:00 pm)

Single donors in silicon are very good qubits. However, a central challenge is to couple them to one another. To achieve this, many proposals rely on using a nearby quantum dot (QD) to mediate an interaction. In this talk, I will demonstrate the coherent coupling of electron spins between a single 31P donor and an enriched 28Si metal-oxide-semiconductor few-electron QD. I show that the electron-nuclear spin interaction can drive coherent rotations between singlet and triplet electron spin states. Moreover, the exchange interaction between the QD and donor electrons can be tuned electrically. The combination of single-nucleus-driven rotations and voltage-tunable exchange provides all elements for future all-electrical control of a spin qubit, and requires only a single dot and no additional magnetic field gradients. These results represent a key step in the realization of multi-donor qubit systems. It also generates exciting new possibilities for nuclear spin qubits. This work was performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science. 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. DOE's National Nuclear Security Administration under contract DE-AC04-94AL85000.

## 15. Quantum annealing for constrained optimization

Itay Hen, (Southern California)

(Session 9a : Friday from 6:00 pm - 6:30 pm)

Recent advances in quantum technology have led to the development and manufacturing of experimental programmable quantum annealers that could potentially solve certain quadratic unconstrained binary optimization problems faster than their classical analogues. The applicability of such devices for many theoretical and practical optimization problems, which are often constrained, is severely limited by the sparse, rigid layout of the devices' quantum bits. Traditionally, constraints are addressed by the addition of penalty terms to the Hamiltonian of the problem, which in turn requires prohibitively increasing physical resources while also restricting the dynamical range of the interactions. Here we propose a method for encoding constrained optimization problems on quantum annealers that eliminates the need for penalty terms and thereby removes many of the obstacles associated with the implementation of these. We argue the advantages of the proposed technique and illustrate its effectiveness. We then conclude by discussing the experimental feasibility of the suggested method as well as its potential to boost the encodability of other optimization problems.

## 16. Instantons in thermally-assisted tunneling and quantum Monte Carlo simulations

Zhang Jiang, (NASA Ames)

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

Despite the big body of literature in spin tunneling, it has only been studied, using path integrals, in systems with fixed total spin. We introduce a non-perturbative spin path-integral instanton calculus for systems where, due to thermal fluctuations, the total spin is not preserved. We demonstrate in a closed analytical form of the scaling equivalence between the transition rate of quantum Monte Carlo, and the quantum tunneling rate when the later is dominated by the most probable path (an instanton). Our analytical results are confirmed by detailed numerical studies.

## 17. Towards satellite-based quantum communication: field testing the QEYSSAT payload

Sarah Kaiser, Jennewein group (IQC, Waterloo)

(Session 9a : Friday from 5:30 pm - 6:00 pm)

Long-distance quantum communication systems are of interest for commercial and fundamental scientific projects. Currently, the link length of these systems is limited by optical fiber losses or free-space line of sight. Our goal is to use low earth orbit satellites as a relay, enabling distant locations to establish a link and exchange quantum systems, including those that were too far apart to link previously. In this talk, I will describe our progress towards a proposed quantum receiver satellite payload that has a passive polarization analyzer to detect photons sent from ground stations. We have designed and constructed prototypes of the QEYSSAT (Quantum EncrYption and Science SATellite) payload with commercial and government assistance. These prototypes comprise almost the entire system needed for a form-fit-function payload and ground station. I will present tests of our system in realistic scenarios representing the environments it will face. In particular, I will present the latest results of testing this system in an aircraft. Finally, I will also identify remaining challenges for practical long distance quantum communication.

## 18. Measuring entanglement entropy and local observables in a thermalizing many-body state

Adam Kaufman, Greiner group (Harvard)

(Session 6 : Friday from 9:15 am - 9:45 am)

Massive entanglement between the constituents of a many-body system is the defining feature of strongly correlated quantum systems. Recent theoretical developments point to the entropy of entanglement as a universal means to classify unusual quantum phases, such as spin liquids and topological phases. Despite its importance, there is no general scheme to experimentally verify entanglement in systems of interacting, delocalized particles. In this talk I will present an experimental scheme to probe entanglement in such itinerant systems through interference of two copies of a many-body state. Akin to Hong-Ou-Mandel interference of photons, this measurement performed with ultracold atoms in a quantum gas microscope probes the indistinguishability of quantum states. We directly measure quantum purity, second order Rényi entropy and mutual information for finite-sized Bose-Hubbard systems across the superfluid-insulator transition. More generally, our newly developed techniques can be used for detailed studies of disordered quantum systems or far-from-equilibrium dynamics. In recent experiments, we explore the evolution of quenched, isolated bosonic systems, where thermal ensembles appear to emerge from pure quantum states. We observe an approximate volume law scaling in the entanglement entropy and highlight its connection to the classical thermodynamic entropy, and we compare local measurements of the many-body state to the predictions of the eigenstate thermalization hypothesis.

## 19. Arbitrary Dicke-state control of symmetric Rydberg ensembles

Tyler Keating, Biedermann-Deutsch group (New Mexico/Sandia)

(Session 9a : Friday from 4:30 pm - 5:00 pm)

The Rydberg blockade is a versatile tool for quantum information in neutral atoms. While the blockade is, at its heart, a two-body effect, it can be naturally used to generate many-body entanglement by creating single, collective excitations across ensembles of atoms. Given a strong blockade, such an ensemble is isomorphic to the Jaynes-Cummings model (JCM): the presence/absence of a Rydberg excitation plays the role of a qubit, while the atoms' hyperfine ground states take the place of photons. By applying symmetric raman transitions to a blockaded ensemble, we can generate SU(2) rotations on the "photon number" degree of freedom; this gives a control Hamiltonian with no clear analogue in a cavity-based JCM. We show that such raman transitions, along with Rydberg excitation, make the system controllable within its symmetric subspace. Arbitrary, symmetric n-body states can therefore be produced, including highly entangled Dicke and cat states. Depending on the laser powers and detunings used, one can control either the complete (2n+1)-dimensional symmetric space or just the (n+1)-dimensional dressed-ground manifold. We discuss the advantages and disadvantages of each, and show simulated entanglement generation among 7 atoms in both regimes. For a wide range of parameters, the time required to generate maximal entanglement is independent of atom number, so this technique could be especially useful for rapidly entangling large ensembles.

## 20. A framework for approximating qubit unitaries

Vadym Kliuchnikov, QuArC (Microsoft)

(Session 7 : Friday from 11:30 am - 12:00 pm)

We present an algorithm for efficiently approximating of qubit unitaries over gate sets derived from totally definite quaternion algebras. It achieves ε-approximations using circuits of length O(log(1/ε)), which is asymptotically optimal. The algorithm achieves the same quality of approximation as previously-known algorithms for Clifford+T [arXiv:1212.6253], V-basis [arXiv:1303.1411] and Clifford+π/12 [arXiv:1409.3552], running on average in time polynomial in O(log(1/ε)) (conditional on a number-theoretic conjecture). Ours is the first such algorithm that works for a wide range of gate sets and provides insight into what should constitute a "good" gate set for a fault-tolerant quantum computer.

## 21. Quantum algorithms for topological data analysis

Seth Lloyd, (MIT)

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

This talk shows how quantum computers can supply an exponential speedup over classical computers to reveal the topology of data.

## 22. High-fidelity two-qubit quantum gates in a scalable surface ion trap

Peter Maunz, (Sandia)

(Session 8 : Friday from 1:30 pm - 2:15 pm)

Microfabricated ion traps are currently the most promising technology for scaling trapped ion quantum information processing systems to the size necessary to solve real-world problems. However, microfabricated surface traps usually have higher heating rates and a shallower trap depth than macroscopic three dimensional traps. In Sandia’s state of the art High Optical Access (HOA) trap, we have achieved heating rates at room temperature as low as 30 quanta/second (Ytterbium, 85µm from closest electrode) and have run measurements with a single ion for longer than 100 hours. Here, we present the realization of high-fidelity one- and two-qubit gates at room temperature in the HOA surface trap. We report on the first demonstration of single qubit gates above some fault-tolerance thresholds, as proven by analyzing the implemented quantum operations using Gate Set Tomography (GST) which yields a diamond distance to the target gate below 8(1) x 10^-5. Furthermore, we realize a Mølmer-Sørensen two-qubit gate and analyze the quantum operations in the symmetric subspace of the two-qubit Hilbert space using qutrit GST. For the two-qubit gate we achieve a process infidelity below 0.5%, the highest two-qubit fidelity reported to date in any scalable trap. These results demonstrate the viability of a scalable, state of the art system for quantum information processing using modern microfabricated surface ion traps.

## 23. Applying benchmarking protocols to encoded qubits with non-Markovian errors

Seth Merkel, (HRL)

(Session 3 : Thursday from 2:15 pm - 2:45 pm)

An essential goal for any quantum information processing platform is to develop the tools necessary to validate high-fidelity quantum gates. This effort has produced a suite of benchmarking and tomographic protocols that have been applied to a wide variety of physical implementations. All these protocols, however, were designed with strict error assumptions that can and will be violated by physical errors, especially as we push to lower and lower error rates. In this talk we look at randomized benchmarking with encoded states (from which leakage errors may occur) in the presence of non-Markovian noise and under the influence of sequence-length dependent filtering errors. These circumstances may apply to a variety of physical systems, but are particularly pertinent for 1/f charge noise and hyperfine leakage noise in electrically controlled quantum dot qubits. We demonstrate how these errors affect the outcome of randomized benchmarking, including the signatures of said errors and the confidence with which we can report an average gate fidelity.

## 24. Quantum computation using genuine two-dimensional symmetry-protected topological order

Jacob Miller, Miyake group (New Mexico)

(Session 9c : Friday from 5:30 pm - 6:00 pm)

We extend the connection between degenerate entanglement spectra present in symmetry-protected topological orders (SPTO's) of 1D spin chains and their use in measurement-based quantum computation (MQC) to the setting of 2D systems. We find surprisingly that the 2D cluster state, an archetypal resource state for MQC, is in a trivial 2D SPTO phase, and show, by a more fine-grained classification, that it does have nontrivial SPTO, but of the same nature as 1D spin chains. In contrast, we introduce a new ground state which possesses nontrivial SPTO entirely of a 2D nature, and show that it is universal for MQC. By utilizing genuine higher-dimensional SPTO, our results open up a research avenue to directly harness its greater quantum-gate complexity within the so-called Clifford hierarchy for the first time in MQC.

## 25. Random number generation for loophole free Bell tests

Morgan Mitchell, (ICFO)

(Session 1 : Thursday from 9:30 am - 10:00 am)

The current generation of loophole-free Bell tests places stringent requirements on the methods for choosing "unpredictable" measurement settings, including very low excess predictability, generation in very short time windows, and statistical assurances very different from those typically used to characterize randomness sources, e.g. the NIST test suite. We show how these requirements have been met using a combination of ultra-fast phase-diffusion random number generators, purpose-built real-time randomness extraction, and novel statistical metrology. The approach produces bits traceable to spontaneous-emission events less than 28 ns in the past, with excess predictability (beyond the ideal 1/2) of less than 10e−4, both with strong metrological assurances. The approach has been employed in recent experiments closing the detection efficiency and communication loopholes, and addressing the freedom-of-choice loophole [Hensen et al. Nature 526, 682 (2015), Giustina et al. Phys. Rev. Lett. (Dec 2015), Shalm et al. Phys. Rev. Lett. (Dec 2015)]. We discuss the strategies for randomness generation in non-quantum theories and some significant deviations from "common wisdom" about randomness extraction that arise in the Bell test context.

## 26. Quantum speedup of backtracking and Monte Carlo algorithms

Ashley Montanaro, (University of Bristol)

(Session 7 : Friday from 10:15 am - 11:00 am)

In this talk I will describe how quantum computing can accelerate two standard types of classical algorithms: backtracking algorithms and Monte Carlo methods. Backtracking is a standard approach for solving constraint satisfaction problems (CSPs). Backtracking algorithms explore a tree whose vertices are partial solutions to a CSP in an attempt to find a complete solution. I will present a bounded-error quantum algorithm which finds a solution in time which is (almost) bounded by the square root of the size of the tree. In particular, this quantum algorithm can be used to speed up the DPLL algorithm, which is the basis of many of the most efficient SAT solvers used in practice. The quantum algorithm is based on the use of a quantum walk algorithm of Belovs to search in the backtracking tree. Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition functions. I will present a quantum algorithm which uses amplitude amplification to estimate the expected output value of an arbitrary randomised or quantum subroutine with bounded variance, and achieves a near-quadratic speedup over the best possible classical algorithm. Combining the algorithm with the use of quantum walks gives a quantum speedup of the fastest known classical algorithms with rigorous performance bounds for computing partition functions, which use multiple-stage Markov chain Monte Carlo techniques.

## 27. Our quantum future

John Preskill, (IQIM, Caltech)

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

The recent detection of gravitational waves by LIGO illustrates that amazing achievements are possible if we dream big dreams and work hard to fulfill them. What should we quantumists dream about? I don't know, but maybe this talk will stimulate you to think about it!

## 28. Interfering and entangling individual neutral atoms

Cindy Regal, (JILA, Colorado)

(Session 6 : Friday from 8:30 am - 9:15 am)

Ultracold gases of bosons and fermions present a unique opportunity in quantum science to investigate the relation between strongly-correlated quantum matter and quantum information concepts. Increasingly experiments have turned to developing single-atom imaging and control to elucidate these connections. In our work we show that it is now possible to harness Bose statistics by independently preparing single rubidium atoms cooled to their motional ground state. By using optical tweezers to dynamically bring the atoms together we can study tunnel-coupled bosons with a new level of control. We observe the Hong-Ou-Mandel (HOM) effect with massive particles when we arrange for atom tunneling to play the role of a balanced beamsplitter. In another experiment, we utilize spin-exchange between the atoms to create entanglement, and we then are able to verify the entanglement of the atoms after spatially separating them. I will discuss the implication of these experiments for the assembly and control of larger quantum systems.

## 29. Non-commuting two-local Hamiltonians for quantum error suppression

Eleanor Rieffel, (NASA Ames)

(Session 9b : Friday from 5:00 pm - 5:30 pm)

Physical constraints make it challenging to implement and control multi-body interactions. Designing quantum information processes with Hamiltonians consisting of only one- and two-local terms is a worthwhile challenge. A common approach to robust storage of quantum information is to encode in the ground subspace of a Hamiltonian. Even allowing particles with high Hilbert-space dimension, it is not possible to protect quantum information from single-site errors by encoding in the ground subspace of any Hamiltonian containing only commuting two-local terms [1]. We demonstrate how to get around this no-go result by encoding in the ground subspace of a Hamiltonian consisting of non-commuting two-local terms arising from the gauge operators of a subsystem code. Specifically, we show how to protect stored quantum information against single-qubit errors using a Hamiltonian consisting of sums of the gauge generators from Bacon-Shor codes [2] and generalized-Bacon-Shor code [3]. Thus, non-commuting two-local Hamiltonians have more error-suppressing power than commuting two-local Hamiltonians. Finally, we comment briefly on the robustness of the whole scheme. [1] I. Marvian and D. A. Lidar, PRL 113, 260504 (2014) [2] D. Bacon, PRA 73, 012340 (2006) [3] S. Bravyi, PRA 83, 012320 (2011)

## 30. Reversible circuit compilation with space constraints

Martin Roetteler, (Microsoft)

(Session 9c : Friday from 5:00 pm - 5:30 pm)

We develop a framework for resource efficient compilation of higher-level programs into lower-level reversible circuits. Our main focus is on optimizing the memory footprint of the resulting reversible networks. This is motivated by the limited availability of qubits for the foreseeable future. We apply three main techniques to keep the number of required qubits small when computing classical, irreversible computations by means of reversible networks: first, wherever possible we allow the compiler to make use of in-place functions to modify some of the variables. Second, an intermediate representation is introduced that allows to trace data dependencies within the program, allowing to clean up qubits early. This realizes an analog to “garbage collection” for reversible circuits. Third, we use the concept of so-called pebble games to transform irreversible programs into reversible programs under space constraints, allowing for data to be erased and recomputed if needed. We introduce REVS, a compiler for reversible circuits that can translate a subset of the functional programming language F# into Toffoli networks. We discuss a number of test cases that illustrate the advantages of our approach including reversible implementations of SHA-2 and other cryptographic hash-functions, reversible integer arithmetic, as well as a test-bench of combinational circuits used in classical circuit synthesis. Compared to Bennett's method, REVS can reduce space complexity by a factor of 4 or more, while having an only moderate increase in circuit size as well as in the time it takes to compile the reversible networks.

## 31. Spacetime replication of continuous variable quantum information

Grant Salton, Hayden group (Stanford)

(Session 9c : Friday from 6:00 pm - 6:30 pm)

The theory of relativity requires that no information travel faster than light, whereas the unitarity of quantum mechanics ensures that quantum information cannot be cloned. These conditions provide the basic constraints that appear in information replication tasks, which formalize aspects of the behavior of information in relativistic quantum mechanics. In this article, we provide continuous variable (CV) strategies for spacetime quantum information replication that are directly amenable to optical or mechanical implementation. We use a new class of homologically-constructed CV quantum error correcting codes to provide efficient solutions for the general case of information replication. As compared to schemes encoding qubits, our CV solution requires half as many shares per encoded system. We also provide an optimized five-mode strategy for replicating quantum information in a particular configuration of four spacetime regions designed not to be reducible to previously performed experiments. For this optimized strategy, we provide detailed encoding and decoding procedures using standard optical apparatus and calculate the recovery fidelity when finite squeezing is used. As such we provide a scheme for experimentally realizing quantum information replication using quantum optics.

## 32. Extending the lifetime of quantum information through error correction

Robert Schoelkopf, (Yale)

(Session 11 : Saturday from 10:45 am - 11:30 am)

In quantum error correction (QEC) one redundantly encodes an arbitrary bit of quantum information into a larger collection of quantum states, whose symmetry properties allow error syndrome measurements to project the state into a known error space without disturbing the qubit, and enable the recovery from errors via simple operations. Given the considerable overhead inherent in traditional proposals, realizing a QEC protocol at the "break-even" point, which extends the lifetime of information beyond the system's highest quality constituent, remains a difficult and outstanding challenge. Here we demonstrate a fully operational quantum error correction system, based on a logical encoding comprised of superpositions of cat states in a superconducting cavity. This system uses real-time classical feedback to encode, track the naturally occurring errors, decode, and correct, all without the need for post-selection. Using this hardware-efficient approach we reach, for the first time, the break-even point for QEC and preserve quantum information through active means.

## 33. Towards a model selection rule for quantum state tomography

Travis Scholten, Blume-Kohout group (Sandia)

(Session 9b : Friday from 6:00 pm - 6:30 pm)

Quantum tomography on continuous variable systems poses a challenge: the density matrix comprises infinitely many parameters, but only finite data is available. Allowing all those parameters to vary will incorporate excessive noise, producing a poor estimate. Fortunately, model selection techniques can be used to fix (or exclude) some parameters. Model selection has been used in tomography to determine the best rank for an estimate, characterize sources of entanglement, and detect drift in state preparation. But these methods rely implicitly or explicitly on the Wilks Theorem, which predicts the behavior of the loglikelihood ratio statistic (LLRS) used to choose between models. Until now, it was not known whether the Wilks Theorem is accurate for quantum state tomography. We investigated the behavior of the LLRS using Monte Carlo simulations, and found that Wilks' prediction fails dramatically. Instead, the distribution of the LLRS is heavily distorted by boundaries (in state space and between models). We construct a model for the behavior of the LLRS, derive an almost analytic prediction for its mean value, and compare it to numerical experiments. The new model improves on existing methods (e.g. the Wilks Theorem), but is still imperfect. We conclude that LLRS-based model selection techniques like Akaike’s AIC may not be reliable for quantum tomography.

## 34. Sub-cycle quantum optics: Direct sampling of vacuum fluctuations in experiment and theory

Denis Seletskiy, (Konstanz)

(Session 9a : Friday from 5:00 pm - 5:30 pm)

Study and manipulation of the ground state of the radiation field is one of the central subjects in quantum optics. In a typical approach of homodyne detection, the information is averaged over multiple cycles of light and amplification to finite intensity is necessary. We demonstrate direct detection of the vacuum fluctuations of the local electric field amplitude in free space via the linear Pockels effect. Broadband electro-optic sampling with gate pulses shorter than 6 femtoseconds enables quantum-statistic readout [1]. Distinction from the detector shot noise is achieved by modification of the sampled space-time volume, defined by an effective temporal duration and the spatial extent of the pulse in the electro-optic medium [1,2]. Ensuring an optimal detection bandwidth which matches the center frequency, here 70 THz, maximizes the vacuum amplitude since the ground-state energy approaches half a photon per optical cycle. The determined magnitude of the vacuum field [1] is in excellent agreement with paraxial theory [2]. Sub-cycle resolution of the oscillating noise in the field quadrature with substantial excursions below the bare vacuum level is predicted [2] and currently explored in the laboratory. Our collective findings open up a new avenue to quantum analysis and manipulation of light in the extreme time-domain limit ensuring sub-cycle access to the electric-field quadrature. [1] C. Riek et al, Science 350, 420 (2015). [2] A. S. Moskalenko et al., arXiv:1508.06953, accepted in PRL

## 35. A strong loophole-free test of local realism

Lynden K. Shalm, Nam group (NIST, Boulder)

(Session 2 : Thursday from 11:00 am - 11:30 am)

Quantum mechanics is a statistical theory. It cannot with certainty predict the outcome of all single events, but instead it predicts probabilities of outcomes. This probabilistic nature of quantum theory is at odds with the determinism inherent in Newtonian physics and relativity, where outcomes can be exactly predicted given sufficient knowledge of a system. In 1935, Einstein, Podolsky, and Rosen wrote “While we have thus shown that the wave function does not provide a complete description of the physical reality, we left open the question of whether or not such a description exists. We believe, however, that such a theory is possible.” It was hoped that quantum theory could be augmented with extra “hidden” variables that determine the outcomes of all possible measurements (a principle known as realism). In 1964, John Bell showed that for such a theory to agree with the predictions of quantum mechanics, hidden variables in one location can instantly change values because of events happening in distant locations. This seemingly violates the locality principle from relativity, which says that objects cannot signal one another faster than the speed of light. Using Bell’s theorem it is possible to test whether reality is governed by local realism. In this talk I will discuss our work at NIST testing Bell’s inequalities relying only on a minimal set of assumptions. We have developed a high-quality source of entangled photons, high-efficiency single-photon detectors, and fast random number generators that are space-like separated from one another. Our experiment closes and addresses all of the major loopholes that are known to exist in Bell tests. This Bell test machine we are building will be used to certify randomness that is useful in a number of cryptographic and security protocols.

## 36. Illuminating a path forward for silicon donor spin qubits

Stephanie Simmons, (Simon Fraser)

(Session 4 : Thursday from 3:45 pm - 4:30 pm)

When it comes to silicon donor-based quantum computation, the most pressing concern is the lack of reliable two-qubit interactions. Silicon donor qubits otherwise match or outperform many qubit rivals, by offering hours-long coherence times in the bulk and >99.9% simultaneous fidelities for single-qubit initialization, manipulation and readout. Moreover, they offer these attributes in a CMOS-compatible platform, which is ripe for future rapid commercialization. In this talk I will introduce an approach to measure and connect donor qubits photonically. This approach should be robust to device environments with variable strains and electric fields, and will allow for CMOS-compatible, bulk-like, spatially separated donor qubit placement, parity measurements, and 4.2K operation. I will present preliminary data in support of this approach, including 4.2K optical readout in Earth's magnetic field, where long T1/T2 times have been measured.

## 37. A Trotter-Suzuki approximation for Lie groups with applications to Hamiltonian simulation

Rolando Somma, (Los Alamos National Laboratory)

(Session 7 : Friday from 11:00 am - 11:30 am )

We present a product formula to approximate the exponential of a skew-Hermitian operator that is a sum of elements of a Lie algebra. The number of terms in the product depends on the structure factors of the algebra. When the dimension of the algebra is small but the elements have large or unbounded norm, or when the norm of nested commutators is significantly less than the product of the norms, our formula results in a significant improvement upon well-known product formulas in the literature. We apply these results to construct product formulas useful for the quantum simulation of continuous-variable, bosonic physical systems. In these cases, we show that the number of terms in the product can be sublinear or even subpolynomial in the dimension of the relevant local Hilbert spaces, where such a dimension is determined by the energy scale of the problem. Our results emphasize the power of quantum computing for the simulation of various quantum systems.

## 38. Optimal strategies for quantum state and process tomography: efficiency versus robustness

Hector Sosa Martinez, Jessen group (Arizona)

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

To build useful quantum hardware one needs good ways to characterize its behavior. In principle quantum tomography (QT) is an ideal tool, capable of providing complete information about an unknown state (QST) or process (QPT). In practice, the protocols used for QT are resource intensive and scale poorly with system size. Even for modest sized Hilbert spaces corresponding to only a few qubits, this puts a premium on schemes that are as efficient as possible. Theoretical work on QST has identified sets of POVM elements that are optimal under varying assumptions, in each case prescribing a minimal number of measurements of a given structure. Laboratory exploration of these POVM constructions has, however, been constrained by the ability to control SPAM errors and generate accurate test states and processes in all but the simplest quantum systems. Here we present the findings from a comprehensive experimental study comparing 6 different POVM constructions and 4 different state estimators, using as our testbed the d = 16 dimensional hyperfine manifold in the 6S1/2 electronic ground state of the 133Cs atom. Our results show a clear trade-off between efficiency and robustness to experimental error, with mutually unbiased bases achieving the best compromise in our system and reaching a QST fidelity of ~98% in d = 16. We have further used a minimal set of intelligently chosen probe states to implement QPT, testing the scheme on randomly chosen unitary processes in Hilbert spaces of varying dimension, and reaching a QPT fidelity of ~90% in d = 16.

## 39. Recent progress on trapped-ion quantum information processing at NIST

Ting Rei Tan, Wineland group (NIST, Boulder)

(Session 8 : Friday from 2:15 pm - 2:45 pm)

Recent experiments on quantum information processing using hyperfine/Zeeman states of trapped 9Be+ and 25Mg+ ions are described. With an improved laser setup including better laser beam quality provided by robust UV optical fibers, two-qubit gate fidelity F 0.999 is achieved. We also realize two-qubit “hybrid” Mølmer-Sørensen, CNOT, and SWAP gates between a 9Be+ - 25Mg+ ion pair. We demonstrate two qubit entanglement (F > 0.99) with an implementation of “quantum Zeno dynamics” subspace engineering technique, which relaxes certain technical requirements. We also summarize progress on (1) spin-squeezing of ~ 100 ions in a Penning trap, (2) all-microwave quantum gates in a surface-electrode trap, (3) cryogenic trap operations, and (4) studies of “anomalous” heating. *Supported by IARPA, ONR, and the NIST Quantum Information Program

## 40. A DC-SQUID force sensor: an atomtronic proposal

Eddy Timmermans, (Los Alamos)

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

In atomtronics cold atom physicists laser-guide ultra-cold atoms in closed flow patterns that resemble the current of an electronic circuit. The control of and measurement on such flows can realize novel sensing protocols. Following a superfluid helium proposal, the recently reported Bose-Einstein condensate (BEC) superfluid quantum interference devices (SQUIDs) can, in principle, measure rotations. The reported BEC-SQUID - a single loop BEC with movable effective potential barriers that act as Josephson constrictions - realized the two arm geometry of interferometers and demonstrated the Josephson constricted critical current of conventional superconducting SQUIDs. However, these atomtronic devices did not support the flow-through current that feeds into and out of the superfluid SQUID loop of direct current (DC) SQUIDs. We propose an atomtronic BEC-SQUID design that is based on a two-loop geometry, in which the two loops share a leg: One loop of finite winding number controls the BEC current that feeds into a second loop of two Josephson constricted arms. We propose to meet the challenge of measuring the current of a neutral, superfluid particle flow by controlling the length of the control loop at fixed winding number. The control loop length at which the steady flow of the SQUID loop ceases to be superfluid is the critical length. We develop the direct current superfluid circuit analysis that predicts the critical length. We show that the effect of a weak external force on the dispersion of the coherent BEC wave can be described by an effective index of refraction. The weak external force alters the critical length and determining the critical length can measure the force on a micron scale distance and possibly at high resolution.

## 41. Towards a new class of trapped ion experiments with ion rings

Erik Urban, Häffner group, (UC Berkeley)

(Session 8 : Friday from 2:45 pm - 3:15 pm)

We present the design and implementation of a novel surface ion trap allowing for trapping of ions in a ring configuration. A ring topology introduces a number of new features that are not present in conventional, linear ion traps, such as extremely low trap frequencies, periodic boundary conditions, and the ability to rotate. These new features open the possibility to conduct a new class of experiments previously inaccessible to ion traps. Towards this goal, we trap up to 25 ions 400 μm above the plane of a trap surface in a ring geometry with a diameter of 90 μm. The large trapping height relative to the ion-ion spacing gives us the the ability to control electric fields at the trapping point with only a few compensation electrodes. This control allows us to pin the ions either into a localized crystal on one side of the ring or to fully delocalize them over the full extent of the ring, demonstrating any symmetry breaking in our ring is on energy scales below the Doppler limit of 0.5 mK. We present studies of the trap frequencies in a pinned configuration and its transition to a depinned, rotating state.

## 42. Detecting memory effects in QIP architectures

Andrzej Veitia, van Enk group (Oregon)

(Session 9b : Friday from 4:30 pm - 5:00 pm)

We present a method to test for temporal correlations between quantum gates. Our protocol can also detect strong memory effects, i.e., non-Markovianity. Moreover, our method is insensitive to state preparation and measurement errors (SPAM).

## 43. Efficient Bayesian phase estimation

Nathan Wiebe, QuArC (Microsoft)

(Session 9b : Friday from 5:30 pm - 6:00 pm)

We provide a new efficient adaptive algorithm for performing phase estimation that does not require that the user infer the bits of the eigenphase in reverse order; rather it directly infers the phase and estimates the uncertainty in the phase directly from experimental data. Our method is highly flexible, recovers from failures, can be run in the presence of substantial decoherence and other experimental imperfections, can learn instantaneous eigenphases for time dependent systems and is as fast or faster than existing algorithms. Finally, we show a new method for performing phase and amplitude estimation in small quantum systems that makes these methods practical for characterizing small quantum systems using present day hardware.

## 44. Recoverability in quantum information theory

Mark Wilde, (Louisiana)

(Session 9c : Friday from 4:00 pm - 4:30 pm)

The fact that the quantum relative entropy is non-increasing with respect to quantum physical evolutions lies at the core of many optimality theorems in quantum information theory and has applications in other areas of physics. In this work, we establish improvements of this entropy inequality in the form of physically meaningful remainder terms. One of the main results can be summarized informally as follows: if the decrease in quantum relative entropy between two quantum states after a quantum physical evolution is relatively small, then it is possible to perform a recovery operation, such that one can perfectly recover one state while approximately recovering the other. This can be interpreted as quantifying how well one can reverse a quantum physical evolution. Furthermore, the recovery operation has an explicit form and is universal, in the sense that it depends only on the channel and the state which can be perfectly recovered. Our proof method relies on complex interpolation and the recently introduced Renyi generalization of a relative entropy difference. The theorem has a number of applications in quantum information theory, which have to do with providing physically meaningful improvements to many known entropy inequalities. This submission is based on the following two papers: [1] Mark M. Wilde. "Recoverability in quantum information theory," Proceedings of the Royal Society A, vol. 471, no. 2182, page 20150338 October 2015 [2] Marius Junge, Renato Renner, David Sutter, Mark M. Wilde, Andreas Winter. "Universal recovery from a decrease of quantum relative entropy", arXiv:1509.07127.

## 45. Broadband nanophotonic quantum interface with a cavity-protected rare-earth ensemble

Tian Zhong, Faraon Group (IQIM, Caltech)

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

Ensembles of solid-state optical emitters are at the core of hybrid quantum interfaces between spins, optical, and microwave photons. To transfer information at quantum level, decoherence resulting from ensemble inhomogeneous broadening is currently suppressed using optical spin rephrasing techniques based on spectral hole burning, which require long preparation steps and reduce the interface bandwidth. We demonstrate that a solid-state ensemble of neodymium rare-earth ions strongly coupled to a photonic crystal resonator exhibits polaritons with strongly suppressed decoherence via the cavity protection phenomenon. Without using preparation steps, frequency qubits are stored and retrieved from the two polaritons with 98.7% fidelity and 50GHz bandwidth. The polaritons are supperadiant modes with emission rates >10^6 greater than uncoupled rare-earth ions, which enable ultra-fast (20 ps) control of the neodymium ensemble. Combined with long-lived spin-wave storage in rare-earth crystals, these results enable always-ready, on-demand, high-bandwidth quantum memories.