# 2018 Talk Abstracts

### Entangling trapped ions with a low-frequency magnetic field gradient

**Presenting Author**: David Allcock, National Institute of Standards and Technology, Boulder**Contributing Author(s)**: Raghavendra Srinivas, Shaun Burd, Daniel Slichter, Andrew Wilson, Dietrich Leibfried, David Wineland

Entangled states of trapped ions are typically generated using laser-induced spin-motion coupling. Spin-motion coupling with hyperfine qubits has also been demonstrated with microwave magnetic fields instead of lasers, thus eliminating photon scattering errors and offering potential benefits for scalability. These experiments have relied on either static magnetic field gradients or oscillating magnetic field gradients at GHz frequencies[1-4]. We present a method of spin-motion coupling using microwaves and a magnetic field gradient oscillating at MHz frequencies, related to the optical method discussed in [5]. We entangle the internal states of two trapped 25Mg+ ions in a cryogenic microfabricated surface-electrode trap and characterize the Bell-state fidelity. This implementation offers important technical advantages over both the static-gradient and GHz-gradient techniques. [1] Mintert and Wunderlich PRL 87, 257904 (2001) [2] Weidt et al. PRL 117, 220501 (2016) [3] Ospelkaus et al. Nature 476, 181 (2011) [4] Harty et al. PRL 117, 140501 (2016) [5] Ding et al. PRL 113, 073002 (2014)

### Correlators in continuous measurement of non-commuting qubit observables and their applications

**Presenting Author**: Juan Atalaya, University of California, Riverside**Contributing Author(s)**: Shay Hacohen-Gourgy, Leigh S. Martin, Leonid P. Pryadko, Irfan Siddiqi, and Alexander N. Korotkov

Read this article online: https://arxiv.org/abs/1710.05249, https://arxiv.org/abs/1702.08077

(Session 6: from 9:15am-9:45am)There has been a rapid experimental progress in continuous quantum measurement of superconducting qubits, including simultaneous measurement of non-commuting observables. In this talk, we focus on temporal correlations of the noisy measurement outputs and discuss the theory for the correlators, comparison with experiment, and applications in parameter estimation and quantum error correction. First, using the quantum Bayesian formalism, we derive analytics for the correlators in simultaneous measurement of two non-commuting observables of a qubit. The theory agrees with experiment very well. Moreover, the correlators can be used for an ultrasensitive estimation of residual Rabi oscillations. Next, we derive a general theoretical result for multi-time correlators in measurement of several non-commuting observables. Surprisingly, we find that for a unital evolution in the absence of phase backaction from measurement, the N-time correlators factorize into a product of two-time correlators for even N. For odd N, a similar factorization also includes the average signal at the earliest time. Experimental results for N=3 and N=4 with two non-commuting measurement channels show a good agreement with this prediction. Finally, we discuss application of the theoretical results for correlators in the error analysis for the 4-qubit Bacon-Shor code, operating with continuous measurement of non-commuting gauge operators.

### Low depth quantum simulation of electronic structure

**Presenting Author**: Ryan Babbush, Google**Contributing Author(s)**: Nathan Wiebe, Jarrod McClean, James McClain, Hartmut Neven, Garnet Chan

Read this article online: https://arxiv.org/abs/1706.00023

(Session 4: from 3:15pm-3:45pm)### The exciting and scary world of near term quantum computers

**Presenting Author**: Dave Bacon, Google

Quantum computing technology is entering a new era with multiple technologies set to build O(100) qubit devices with gate and measurement fidelities from two to three nines. These devices can, for artificial problems, thwart direct classical simulation (exciting!) but whether they can solve problems that are of practical importance is yet to be seen (scary!). In this talk I will discuss the challenges of these near term devices from the perspective of the Google's xmon superconducting qubit computers. Interesting challenges in computer architectures and programming languages emerge for these devices. I'll then discuss the prospects for different near term algorithms on these devices, attempting to inspire your brain to come up with new quantum algorithms for near term quantum computers.

### Evolution-time dependence in near-adiabatic quantum evolutions

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

We expand upon the standard quantum adiabatic theorem, examining the time-dependence of quantum evolution in the near-adiabatic limit. We examine a Hamiltonian that evolves along some fixed trajectory from H0 to H1 in a total evolution-time T, and our goal is to determine how the final state of the system depends on T. If the system is initially started in a non-degenerate ground state, the adiabatic theorem says that in the limit of large T, the system will stay in the ground state. We examine the near-adiabatic limit where the system evolves slowly enough that most but not all of the final state is in the ground state, and we find that the probability of leaving the ground state oscillates in T with a frequency determined by the integral of the spectral gap along the trajectory of the Hamiltonian, so long as the gap is big. If the gap becomes exceedingly small, the final probability is the sum of oscillatory behavior determined by the integrals of the gap before and after the small gap. We confirm these analytic predictions with numerical evidence from barrier tunneling problems in the context of quantum adiabatic optimization.

### Panel discussion: Progress of quantum information and SQuInT

**Presenting Author**: Kenneth Brown (Duke University), Isaac Chuang (MIT), Theresa Lynn (Harvey Mudd), Michael Nielsen, (Y Combinator Research),

### Combs and isotopic customization for trapped ion quantum computing

**Presenting Author**: Wesley C. Campbell, University of California, Los Angeles**Contributing Author(s)**: David Hucul, Anthony Ransford, Michael Ip, Justin Christensen, Conrad Roman, Xueping Long, Andrew M. Jayich, and Eric Hudson

Since ions bind their valence electrons tightly, the light needed to work with them is often in the UV part of the spectrum, where laser light is difficult to produce and manage. We have pursued two avenues in an attempt to address this problem. First, we will discuss how optical frequency combs may be employed to ease the creation of short-wavelength light. We find that, when illuminated by a comb, trapped ions can behave as a phonon laser whose gain saturation protects them from being boiled out of the trap by the hundreds of blue-detuned comb teeth present. Second, in collaboration with Eric Hudson's group at UCLA, we describe work with barium ions, the species with the longest-wavelength transitions among the obvious choices. We discuss why creating a particular radioactive isotope endows Ba+ with the atomic structure advantages of more-difficult species and position it as a flexible, easy to use, all purpose qubit.

### Fault-tolerant quantum computation with few qubits

**Presenting Author**: Rui Chao, University of Southern California**Contributing Author(s)**: Ben Reichardt

Read this article online: https://arxiv.org/abs/1705.02329, https://arxiv.org/abs/1705.05365

(Session 9b: from 5:15pm-5:45pm)Reliable qubits are difficult to engineer, but standard fault-tolerance schemes use seven or more physical qubits to encode each logical qubit, with still more qubits required for error correction. The large overhead makes it hard to experiment with fault-tolerance schemes with multiple encoded qubits. We give space-efficient methods for fault-tolerant error correction and computation, which are promising to realize on near-term devices: 1. For many distance-three codes, two extra qubits are enough to perform fault-tolerant error correction. 2. For various small codes encoding multiple logical qubits, two ancilla qubits are also enough to apply arbitrary logical Clifford operations, and with another two ancillas we can even achieve universal computation. For example, with 19 qubits one can protect and compute universally on seven encoded qubits, fault tolerantly. Our main technique is to use circuit gadgets to catch bad faults. For space-efficient error correction, we add a “flag” ancilla to catch those faults that spread to multi-qubit data errors. For computation within a code block, multi-qubit faults are caught using flag gadgets, and are remedied before they can spread. These procedures could enable testing more sophisticated protected circuits in small-scale quantum devices, and could be used to reduce the overhead of general fault-tolerance schemes.

### Reliable numerical key rates for quantum key distribution

**Presenting Author**: Patrick Coles, Los Alamos National Laboratory**Contributing Author(s)**: Adam Winick, Norbert Luetkenhaus

Read this article online: https://arxiv.org/abs/1710.05511

(Session 2: from 11:00am-11:30am)The holy grail of quantum key distribution (QKD) theory is a robust, quantitative method to explore novel protocol ideas and to investigate the effects of device imperfections on the key rate. We argue that numerical methods are superior to analytical ones for this purpose. However, new challenges arise with numerical approaches, including the efficiency (i.e., possibly long computation times) and reliability of the calculation. In this work, we present a reliable, efficient, and tight numerical method for calculating key rates for finite-dimensional QKD protocols. We illustrate our approach by finding higher key rates than those previously reported in the literature for several interesting scenarios (e.g., the Trojan-horse attack and the phase-coherent BB84 protocol). Our method will ultimately improve our ability to automate key rate calculations and, hence, to develop a user-friendly software package that could be used widely by QKD researchers.

### Quasi-probabilities on a fermionic phase space

**Presenting Author**: Ninnat Dangniam, University of New Mexico CQuIC**Contributing Author(s)**: Christopher Jackson, Christopher Ferrie, Carlton Caves

Sometimes a classical simulation scheme of quantum processes given a restricted set of states and measurements can be naturally interpreted as a statistical simulation of positive quasi-probability distributions on a phase space. To explore the relation between classical simulatability and positivity of quasi-probabilities beyond the Wigner functions, we constructed quasi-probability representations on the compact phase space of fermionic Gaussian states (as opposed to coherent states in the usual Wigner phase space formulation) tailored to a classically simulatable problem of fermionic linear optics and found that fermionic Gaussian states possess negative quasi-probabilities. More generally, we showed that this construction due to Brif and Mann (Phys. Rev. A 59, 971 (1999)) is essentially unique given the group of quantum gates and an input state in the relevant representation.

### Robust quantum network architectures and topologies for entanglement distribution

**Presenting Author**: Siddhartha Das, Louisiana State University**Contributing Author(s)**: Sumeet Khatri, Jonathan P. Dowling

Read this article online: https://arxiv.org/pdf/1709.07404.pdf

(Session 9c: from 5:45pm-6:15pm)In this work [arXiv:1709.07404], we focus on two-dimensional quantum networks based on optical quantum technologies using dual-rail photonic qubits for the building of a fail-safe quantum internet. We lay out a quantum network architecture for entanglement distribution between distant parties using a Bravais lattice topology, with the technological constraint that quantum repeaters equipped with quantum memories are not easily accessible. We provide a robust protocol for simultaneous entanglement distribution between two distant groups of parties on this network. We also discuss a memory-based quantum network architecture that can be implemented on networks with an arbitrary topology. We examine networks with bow-tie lattice and Archimedean lattice topologies and use percolation theory to quantify the robustness of the networks. In particular, we provide figures of merit on the loss parameter of the optical medium that depend only on the topology of the network and quantify the robustness of the network against intermittent photon loss and intermittent failure of nodes. These figures of merit can be used to compare the robustness of different network topologies in order to determine the best topology in a given real-world scenario, which is critical in the realization of the quantum internet.

### New color centers in diamond for long distance quantum networks

**Presenting Author**: Nathalie de Leon, Princeton University

Color centers in diamond are promising candidates for quantum networks, as they can serve as solid state quantum memories with efficient optical transitions. Prior work has focused on the NV- center in diamond, which exhibits long spin coherence times and has narrow, spin-conserving optical transitions. However, the NV- center is prone to spectral diffusion, and over 97% of emission is in an incoherent phonon side band, severely limiting scalability. Alternatively, SiV- exhibits excellent optical properties, with 70% of its emission in the zero phonon line and a narrow inhomogeneous linewidth. However, SiV- suffers from significant interaction with phonons, with spin coherence times limited by an orbital relaxation time (T1) of around 40 ns at 5 K. Informed by the limitations of NV- and SiV-, we have developed new methods to control the diamond Fermi level to stabilize the neutral charge state of SiV, thus accessing a new spin configuration. SiV0 exhibits a spin T1 of around 1 minute at 4 K, coherence time (T2) approaching 1 second, over 90% of emission in the zero phonon line, and near-transform limited optical linewidths, making it a promising candidate for applications in quantum networks.

### A robust, single-shot measurement for binary phase-shift keyed coherent state discrimination

**Presenting Author**: Matthew DiMario, University of New Mexico CQuIC**Contributing Author(s)**: Francisco Becerra

The discrimination of binary phase-shift keyed (BPSK) coherent states is an integral part of many classical and quantum communication schemes. While complex measurement strategies employing feedback can far surpass the Quantum Noise Limit (QNL) set by a Homodyne measurement, there is also a need for non-adaptive strategies that can be scaled to high bandwidths and incorporated into current and future communication methods. Moreover, all measurement strategies are subject to non-ideal conditions and must be able to overcome realistic noise and imperfections in real-world communication channels while keeping their sensitivity performance. We investigate and experimentally demonstrate a robust, high-sensitivity discrimination strategy for BPSK coherent states that is based on a single, optimized displacement operation in phase space followed by photon counting. Robustness of the discrimination strategy comes from the information gained through a photon number resolving (PNR(m)) measurement, corresponding to projections onto Fock states up to a threshold of “m” photons, which characterizes the finite number resolution of realistic detectors. Optimal single shot measurements are compatible with high-bandwidth communication while being able to achieve sensitivities below the QNL under realistic conditions. Our experimental demonstration with a realistic detector and finite photon number resolution, allows the measurement to continually outperform the QNL, adjusted for our detection

### The Fermi-Hubbard model for universal quantum computation

**Presenting Author**: David Feder, University of Calgary**Contributing Author(s)**: Jiawei Ji

Quantum circuits based only on matchgates are able to perform non-trivial (but not universal) quantum algorithms. Because matchgates can be mapped to non-interacting fermions, these circuits can be efficiently simulated on a classical computer. One can perform universal quantum computation by adding any non-matchgate parity-preserving gate, implying that interacting fermions could be natural candidates for universal quantum computation within the circuit model. Most work to date has focused on Majorana fermions, which are difficult to realize in the laboratory. We instead explore both spinless (spin-polarized) and spin-1/2 fermions within the context of matchgate circuits, investigating interactions within a family of Fermi-Hubbard Hamiltonians, to obtain experimentally realizable conditions under which interacting fermions are able to perform universal quantum computation.

### Detecting metrologically useful asymmetry and entanglement by a few local measurements

**Presenting Author**: Davide Girolami, Los Alamos National Laboratory**Contributing Author(s)**: Chao Zhang, Benjamin Yadin, Zhi-Bo Hou, Huan Cao, Bi-Heng Liu, Yun-Feng Huang, Reevu Maity, Vlatko Vedral, Chuan-Feng Li, Guang-Can Guo

Important properties of a quantum system are not directly measurable, but they can be disclosed by how fast the system changes under controlled perturbations. In particular, asymmetry and entanglement can be verified by reconstructing the state of a quantum system. Yet, this usually requires experimental and computational resources which increase exponentially with the system size. Here we show how to detect metrologically useful asymmetry and entanglement by a limited number of measurements. This is achieved by studying how they affect the speed of evolution of a system under a unitary transformation. We show that the speed of multiqubit systems can be evaluated by measuring a set of local observables, providing exponential advantage with respect to state tomography. Indeed, the presented method requires neither the knowledge of the state and the parameter-encoding Hamiltonian nor global measurements performed on all the constituent subsystems. We implement the detection scheme in an all-optical experiment. References: Phys. Rev. Lett. 113, 170401 (2014); Phys. Rev. A 96, 042327 (2017).

### Schroedinger's cat meets Maxwell's demon: Quantum error correction (that works)

**Presenting Author**: Steven Girvin, Yale University

Successful quantum error correction requires construction of a quantum "Maxwell's demon" which can remove the entropy generated by errors in the N physical qubits comprising a logical qubit, without learning (and therefore destroying) the quantum information stored in the logical qubit. Because N physical qubits have an error rate N times larger than a single physical qubit, the Maxwell demon must be sufficiently fast and accurate to overcome this factor of N just to reach the 'break-even' point where the lifetime of the quantum information begins to be enhanced. Experiments at Yale have successfully demonstrated quantum error correction that reaches the break-even point for the first time. In addition, recent experiments have demonstrated entanglement between logically encoded qubits. Paradoxically, these successes were achieved by storing the quantum information in objects that are normally considered quite fragile, namely 'Schoedinger cat' states of photons. Elementary: [1] Wiring up quantum systems, R.J. Schoelkopf and S.M. Girvin, Nature 451, 664 (2008). [2] Superconducting Circuits for Quantum Information: An Outlook, M.H. Devoret and R.J. Schoelkopf, Science 339, 1169 (2013). Advanced: [3] Deterministically encoding quantum information in 100-photon Schoedinger cat states, Vlastakis, B., et al. Science 342, 607 (2013). [4] A Schroedinger Cat Living in Two Boxes, Chen Wang, et al., Science 352, 1087 (2016). [5] Extending the lifetime of a quantum bit with error correction in superconducting circuits, Nissim Ofek, et al., Nature 536, 441445 (2016). [6] A CNOT gate between multiphoton qubits encoded in two cavities, Serge Rosenblum, et al., arXiv:1709.05425.

### Dynamical control techniques with superconducting qubits

**Presenting Author**: Simon Gustavsson, Massachusetts Institute of Technology**Contributing Author(s)**: Fei Yan, Gianluigi Catelani, Jonas Bylander, Jeffrey Birenbaum, David Hover, Danna Rosenberg, Gabriel Samach, Steven J. Weber, Jonilyn L. Yoder, John Clarke, Andrew J. Kerman, Fumiki Yoshihara, Yasunobu Nakamura, Terry P. Orlando, William D. Oliver

Read this article online: http://science.sciencemag.org/content/354/6319/1573?ijkey=aS%2520B1OEKGNuLt2&keytype=ref&siteid=sci, https://www.nature.com/articles/ncomms12964

(Session 11: from 10:15am-11:00am)Dynamical error suppression techniques are commonly used to improve coherence in quantum systems. They reduce dephasing errors by applying control pulses designed to reverse erroneous coherent evolution driven by environmental noise. However, such methods cannot correct for irreversible processes such as energy relaxation (T1). Here, we investigate a complementary, stochastic approach to reducing errors: instead of deterministically reversing the unwanted qubit evolution, we use control pulses to shape the noise environment dynamically. In the context of superconducting qubits, we implement a pumping sequence to reduce the number of unpaired electrons - quasiparticles - in close proximity to the device. We report a 70% reduction in the quasiparticle density, resulting in a threefold enhancement in qubit relaxation times, and a comparable reduction in coherence variability. In a separate experiment, we investigate qubit dephasing (T2) due to photon shot noise in a flux qubit transversally coupled to a coplanar microwave resonator. We have made the first quantitative spectroscopy of this noise for both thermal (i.e., radiation from higher temperature stages) and coherent photons (residual photons from the readout and control pulses), and we uniquely identify thermal shot noise as the dominant source of dephasing. Furthermore, by improving the filtering, we are able to reduce the residual photon population to 0.0004, resulting in T2 echo times approaching 100 us.

### Singular loops and their non-Abelian geometric phases in ultracold spin-1 atoms

**Presenting Author**: Bharath H. M., Georgia Institute of Technology**Contributing Author(s)**: Matthew Boguslawski, Maryrose Barrios, Lin Xin, Michael Chapman

Read this article online: https://arxiv.org/abs/1702.08564

(Session 13: from 4:45pm-5:15pm)We use coherent control of ultracold Rubidium atoms in a dipole trap to experimentally explore the recently introduced non-Abelian geometric phases of singular loops inside the Bloch ball [1]. Non-Abelian and non-adiabatic variants of Berry's geometric phase have been pivotal in the recent advances in fault-tolerant quantum computation gates, while Berry's phase itself is at the heart of the study of topological phases of matter. In [1], geometric phase was generalized to loops on or inside the Bloch ball and was formulated as an SO(3) operator, carried by the spin-fluctuation tensor of a spin-1 system . The special class of loops inside the Bloch ball passing through the center, which we refer to as singular loops, are significant in two ways. First, their geometric phase is non-Abelian and second, their geometrical properties are qualitatively different from the nearby non-singular loops, making them akin to critical points of a quantum phase transition. [1] H. M. Bharath, “Non-Abelian geometric phases carried by the spin fluctuation tensor”, arXiv:1702.08564

### Advantages of versatile neural-network decoders for topological codes

**Presenting Author**: Tomas Jochym-O'Connor, California Institute of Technology**Contributing Author(s)**: Nishad Maskara, Aleksander Kubica

Decoding of generic stabilizer codes is a computationally hard problem, even given simple noise models. While the task is simplified for codes with some structure, such as topological codes with geometrically-local stabilizer generators, finding optimal decoders remains challenging. In our work, we analyze the versatility and performance of neural network decoders. We rephrase the decoding problem as a classification task, which is well-suited for machine learning. We show versatility of the approach by studying two-dimensional variants of the toric and color codes and different error models, bit- and phase-flip, as well as nearest-neighbor depolarizing noise models. The resulting decoders have improved performance and thresholds over previously known methods. We believe that neural decoding will play a key role in error correction for near-term experiments where unknown noise sources could severely affect the performance of the code.

### Experimental measurement of leakage-error in exchange-only SiGe quantum dot qubits by extending randomized benchmarking

**Presenting Author**: Aaron Jones, HRL Laboratories

Randomized benchmarking is a common method for quantifying qubit gate error, but has questionable validity or reliability for some physically relevant error sources. The focus of this talk will be leakage out of the computational subspace of a decoherence-free subsystem, which can introduce additional benchmarking decay and unreliable error estimates. Though techniques have been developed to characterize leakage, it is not clear how best to use that information to inform computational error rates. Here we develop an extension to the randomized benchmarking protocol that estimates both computational and leakage errors by means of preparing and tracking different final states of the benchmarking sequence. Using this protocol, we experimentally measure the leakage error per gate in an exchange-only SiGe triple quantum dot at rates well below that of state-preparation-and-measurement (SPAM) error and pulse error from electrical noise. These leakage rates are in close agreement with a noise model with electrical and hyperfine-induced magnetic noise terms.

### Engineered hopping integrals in exciton-polariton quantum simulators

**Presenting Author**: Na Young Kim, University of Waterloo**Contributing Author(s)**: Haining Pan, K. Winkler, C. Schneider, S. Hoefling

Microcavity exciton-polaritons are hybrid quantum quasi-particles as an admixture of cavity photons and quantum-well excitons. We engineer exciton-polariton-lattice systems, where we seek the beauty of non- zero momentum boson order arising from the intrinsic open-dissipative nature of the condensate as well as the topology of lattices. In this work, we quantify the hopping integrals of the lowest-band exciton-polaritons in terms of two physical parameters: nearest-neighbor site distance, d (3, 4,5 and 7 𝜇m), and detuning values Δ ( - 19 ~ 9 meV) in engineered two-dimensional honeycomb lattices. The artificial lattices are formed by an etching-overgrowth technique to module the cavity layer thickness to induce a photon confinement. The lattice potential depths vary 3-5 meV at different Δ values, and we construct the band structures of the exciton- polaritons via a low-power angle-resolved photoluminescence spectroscopy. The hopping integrals of nearest- neighbor and next-nearest neighbor sites in the lowest bands are extracted from the measured band structures by the tight-binding Hamiltonian fittings.

### Robust entanglement renormalization on a noisy quantum computer

**Presenting Author**: Isaac Kim, Stanford University**Contributing Author(s)**: Brian Swingle

Read this article online: https://arxiv.org/abs/1711.07500

(Session 12: from 2:15pm-2:45pm)### Quantum vs. classical proofs

**Presenting Author**: Shelby Kimmel, Middlebury College

QMA is the quantum generalization of the complexity class NP. QMA contains important and physically relevant problems, such as whether a local Hamiltonian admits a low energy ground state. In QMA, the goal is to verify a proof using a quantum verifier, where the proof is given as a quantum state. It is an open question whether the complexity class loses power if the proof is restricted to be a classical bit-string rather than a quantum state. I will describe work with Bill Fefferman in which we find a class of permutation-oracle-based problems where a quantum proof can be used for verification, but any classical proof is insufficient. This builds off of work by Aaronson and Kuperberg, who first described such a separation using oracles derived from Haar random states.

### State insensitive trapping for ground and Rydberg atoms

**Presenting Author**: Jacob Lampen, University of Michigan**Contributing Author(s)**: Huy Nguyen, Matthew Winchester, Lin Li, Paul Berman, Alex Kuzmich

. The enhanced ground Rydberg coherence times open new opportunities for precise creation and manipulation of entangled many-atom states and for interfacing these states with quantum optical fields.

### Optimized two-qubit gates in a long, linear ion crystal using continuous frequency modulation

**Presenting Author**: Pak Hong Leung, Duke University**Contributing Author(s)**: Kevin Landsman, Caroline Figgatt, Norbert Linke, Kenneth Brown, Christopher Monroe

Read this article online: https://arxiv.org/abs/1708.08039

(Session 8: from 2:45-3:15pm)High-fidelity two-qubit gates in a multi-ion crystal has become one of the greatest challenges in ion trap quantum computation. As we scale up the number of ions, it becomes increasingly difficult to disentangle the qubits from multiple motional modes. We propose using a continuous frequency-modulated driving force to achieve such a purpose, and present simulational and experimental results of optimized two-qubit gates with a five-ion chain. To predict the mechanics of even longer ion chains, we perform simulation of motional modes with 20 ions or more as we approach the continuum limit, where we may model the chain as a linear charge density.

### Advances in optimal Hamiltonian simulation

**Presenting Author**: Guang Hao Low, Microsoft Research**Contributing Author(s)**: Isaac Chuang

Read this article online: https://arxiv.org/abs/1610.06546, https://arxiv.org/abs/1707.05391

(Session 4: from 3:45pm-4:15pm)### A CPHASE gate between Rydberg‐dressed neutral atoms

**Presenting Author**: Michael Martin, Sandia National Laboratories**Contributing Author(s)**: Jongmin Lee, Yuan- Yu Jau, Ivan Deutsch, Grant Biedermann

Neutral atom‐based qubits are highly scalable and controllable. With optical excitation of high‐lying, strongly interacting Rydberg states, one can achieve on‐demand, laser‐controlled interactions for quantum logic operations. We present studies of entangling operations within a two‐atom system employing individually trapped ultra‐cold cesium atoms that interact via single‐photon laser coupling to a Rydberg level [1], where the Rydberg‐dressed many‐body Hamiltonian permits pairwise and beyond-pairwise interaction regimes. We describe a detailed study of a two‐atom controlled‐phase (CPHASE) gate that is insensitive to the detrimental effects of atomic motion and light shifts, and that should enable high-quality entangling operations between atom pairs or within larger ensembles. We also present work towards larger‐scale systems employing reconfigurable traps formed via digital holography, with the goal of scaling the successes of the two‐atom system. [1] Y.‐Y. Jau et al., “Entangling atomic spins with a Rydberg‐dressed spin‐flip blockade,” Nat. Phys. 12, 71‐74 (2016). This work was supported by the Laboratory Directed Research and Development program at Sandia National Laboratories.

### Bounding the quantum process fidelity with a minimal set of input states

**Presenting Author**: Karl Mayer, National Institute of Standards and Technology, Boulder**Contributing Author(s)**: Emanuel Knill

We investigate the problem of bounding the quantum process fidelity given bounds on the fidelities between target states and the action of a process on a set of pure input states. We formulate the problem as a semidefinite program and prove convexity of the minimum process fidelity as a function of the errors on the output states. We characterize the conditions required to uniquely determine a process in the case of no errors, and derive a lower bound on its fidelity in the limit of small errors for any set of input states satisfying these conditions. Finally, we introduce a set of d+1 pure states in d dimensions which form a minimal symmetric POVM. We prove that for this set of input states the minimum fidelity scales linearly with the average output state error, providing an efficient method for estimating the process fidelity without the use of full process tomography.

### Michelson-Morley analogue for electrons using trapped ions to test Lorentz symmetry

**Presenting Author**: Eli Megidish, University of California Berkeley**Contributing Author(s)**: Joe Broz, Nicole Greene, Hartmut Haeffner

Probing for local Lorentz violation is important in the search for physics beyond the standard model. Lorentz violations in the electro- magnetic sector can be probed by performing an electron analogue of the Michelson-Morley experiment. We split an electron wave packet inside a Calcium ion into two parts with different orientations and recombine them back to probe for any phase differences. As the earth rotates, the absolute spatial orientation of the two wave packets change, and anisotropies in the electron dispersion will modify the phase of the interference signal. To reduce noise, we prepare a highly entangled state in calcium ions insusceptible to common magnetic field noise. Our experiment demonstrates the potential use of quantum entanglement to enhance the sensitivity of precision measurements.

### Entanglement constraints in various symmetric subspaces

**Presenting Author**: Alexander Meill, University of California San Diego**Contributing Author(s)**: David Meyer

Read this article online: https://arxiv.org/abs/1702.07295

(Session 9c: from 4:45pm-5:15pm)We simplify the search for constraints on multi-partite entanglement by restricting the calculations to Hilbert spaces of 3-5 qubits which exhibit relevant symmetries. In 3 qubits we describe the space of achievable local unitary polynomial invariants among states which are fully symmetric under party relabeling. In 4 and 5 qubits we discuss pairwise concurrence relations in states which are invariant under cyclic permutation of the party labels.

### Improved quantum algorithms using linear combination of unitaries

**Presenting Author**: Anirban Narayan Chowdhury, University of New Mexico CQuIC**Contributing Author(s)**: Yigit Subasi, Rolando Diego Somma

The technique of implementing a linear combination of unitary (LCU) operators has led to significant improvements in the complexities of quantum algorithms for diverse problems such as Hamiltonian simulation and solving linear systems of equations. Here we combine LCU with a version of amplitude amplification to tackle two tasks that arise in the context of quantum algorithms for optimization problems - namely Gibbs state preparation, and that of implementing a reflection about eigenstates of a unitary operator. In both cases, we obtain improvements in resource requirements over earlier protocols that used quantum phase estimation (PE). The LCU approach for Gibbs state preparation has complexity that scales exponentially better in inverse precision and, for a certain class of Hamiltonians, polynomially better in terms of other parameters. We use similar ideas to approximate a reflection about an eigenstate of a given unitary using an LCU. Our implementation requires exponentially fewer ancilla qubits in terms of a precision parameter than a PE based approach, and has gate complexity that is comparable. Our analysis also improves upon the gate complexity of the PE-reflection by using an approximate quantum Fourier transform. Our results are useful as they reduce the resources needed by a large variety of existing quantum algorithms. We also prove a lower bound on the query complexity of implementing reflections.

### Exchange interactions in a strontium superradiant laser

**Presenting Author**: Matthew Norcia, University of Colorado JILA**Contributing Author(s)**: Robert Lewis-Swan, Julia Cline, Bihui Zhu, Ana Maria Rey, James Thompson

Read this article online: https://arxiv.org/pdf/1711.03673.pdf

(Session 13: from 3:45pm-4:15pm)I will present a characterization of collective atomic interactions mediated by the exchange of cavity photons via the 1 mHz linewidth optical clock transition in an ensemble of superradiantly emitting strontium atoms. These interactions are of a form known to generate useful entanglement through one-axis twisting dynamics and to cause a suppression of decoherence through the generation of a many-body energy gap. In addition, they are key to understanding the sensitivity of superradiant frequency references to cavity detuning. We observe signatures of these effects through precision frequency measurements of the emitted superradiant light.

### Classifying and diagnosing crosstalk in quantum information processors

**Presenting Author**: Kenneth Rudinger, Sandia National Laboratories**Contributing Author(s)**: Mohan Sarovar, Dylan Langharst, Tim Proctor, Kevin Young, Erik Nielsen, Robin Blume-Kohout

Quantum information processor technology continues to progress, as illustrated by the construction and operation of devices with as many as sixteen qubits. While high-fidelity one- and two-qubit operations have been exhibited on such devices, there are a variety of errors that must be further mitigated prior to executing quantum error correction or meaningful quantum algorithms. One such error source is that of crosstalk, the process by which one or more qubits is affected by the state of, or operations on, neighboring qubits. In this talk we present a comprehensive taxonomy of crosstalk, and provide architecture-agnostic methods for detecting and characterizing such noise processes. Using experimental data taken from superconducting qubit systems, we show these protocols can be used to successfully diagnose multiple forms of crosstalk. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

### Approximate operator algebra quantum error correction (decoding the hologram in AdS/CFT)

**Presenting Author**: Grant Salton, Stanford University**Contributing Author(s)**: Jordan Cotler, Patrick Hayden, Brian Swingle, Michael Walter

Read this article online: https://arxiv.org/abs/1704.05839

(Session 9b: from 5:45pm-6:15pm)Quantum error correction -- originally invented for quantum computing -- has proven itself useful in a variety of non-computational physical systems, as the ideas of QEC are broadly applicable. In this talk, I'll mention a few examples of error correction in the wild, including the recent discovery that the AdS/CFT correspondence implements quantum error correction. We will then study the hypothesis that any local bulk operator in AdS can be reconstructed using only a causally disconnected subregion of the CFT. This hypothesis has been proven under the assumption that error correction in AdS/CFT is exact, but this assumption is not expected to be true. Fortunately, recent advances in the theory of approximate quantum error correction have emerged. We will review these results on recoverability and approximate quantum error correction, as well as AdS/CFT and the so-called entanglement wedge reconstruction hypothesis. We will then prove the entanglement wedge hypothesis robustly and find an explicit formula for reconstructed bulk operators. If time permits, we will explore a generalization of the theory of universal recovery channels to the case of finite-dimensional von Neumann algebras.

### Frequency control of single quantum emitters in integrated photonic circuits

**Presenting Author**: Emma Schmidgall, University of Washington**Contributing Author(s)**: Srivatsa Chakravarthi, Michael Gould, Ian Christen, Karine Hestroffer, Fariba Hatami, Kai-Mei Fu

An entangled graph state of qubits is a valuable resource for both universal quantum computation and quantum communication. To date, entanglement generation rates are too low to realize these multi-qubit networks due to photon emission into unwanted spatial and spectral modes. The integration of crystal defect-based qubits with photonic circuits can significantly enhance photon collection efficiency, albeit at the cost of degrading the defect's optical properties, such as an increase in inhomogeneous emission energies (linewidth broadening of GHz vs a few tens of MHz) and decreased spectral stability (spectral diffusion of tens of GHz vs a few hundred MHz). Compensating for this static and dynamic spread in emission energies is of critical importance for scalable on-chip graph state generation. We demonstrate the ability to tune the emission energy of photonic device-coupled near-surface NV centers over a large (200 GHz) tuning range with applied bias voltage. This is larger than the inhomogeneity of implanted NV centers suggesting a viable route for indistinguishable photons from separate emitters. However, measurements on many single waveguide-coupled NV centers highlight the variability in response to an applied bias voltage. Despite this variability, we are able to apply real-time voltage feedback control to partially stabilize the emission energy of a device-coupled NV center.

### Renyi relative entropies of quantum Gaussian states

**Presenting Author**: Kaushik Seshadreesan, University of Arizona**Contributing Author(s)**: Ludovico Lami and Mark M. Wilde

Read this article online: https://arxiv.org/pdf/1706.09885.pdf

(Session 2: from 11:30am-12:00pm)The quantum Rényi relative entropies play a prominent role in quantum information theory, finding applications in characterizing error exponents and strong converse exponents for quantum hypothesis testing and quantum communication theory. On a different thread, quantum Gaussian states have been intensely investigated theoretically, motivated by the fact that they are more readily accessible in the laboratory than are other, more exotic quantum states. In this talk, we discuss the derivation of formulas for the quantum Rényi relative entropies of quantum Gaussian states. We consider both the traditional (Petz) Rényi relative entropy as well as the more recent sandwiched Rényi relative entropy, finding formulas that are expressed solely in terms of the mean vectors and covariance matrices of the underlying quantum Gaussian states. Our development handles the hitherto elusive case for the Petz-Rényi relative entropy when the Rényi parameter is larger than one. Finally, we also derive a formula for the max-relative entropy of two quantum Gaussian states, and we discuss some applications of the formulas derived here.

### Realizing the optimal tomography through a sequence of collective weak measurements

**Presenting Author**: Ezad Shojaee, University of New Mexico**Contributing Author(s)**: Christopher S. Jackson, Carlos A. Riofrio, Amir Kalev, Ivan H. Deutsch

Abstract: In their seminal 1995 paper, Massar and Popescu proved that, given N-copies of an unknown pure qubit, the best strategy to reconstruct its state (without any adaptive feedback) is to do a collective measurement on the ensemble [1]. The optimal fidelity with which one can reconstruct the state of a pure qubit is (N+1)/(N+2) averaged over all unknown states and measurement outcomes. This can be achieved through a POVM whose measurement outcomes are spin coherent states of the collective spin J=N/2. In this work, we prove that we can realize this optimal measurement through a sequence of weak measurements of the collective spin along random directions on the sphere. Numerical evidence supports this result, and shows that we saturate the optimal fidelity for quantum state tomography averaged over all unknown states. We discuss the connection between this protocol and tomography via continuous weak measurement in the presence of time-dependent control [2]. [1] S. Massar and S. Popescu, Phys. Rev. Lett. 74, 1259 (1995). [2] A. Silberfarb, P. S. Jessen, and I. H. Deutsch Phys. Rev. Lett. 95, 030402 (2005); C. A. Riofrio, P. S. Jessen, and I. H. Deutsch, J. Phys. B: At. Mol. Opt. Phys. 44, 154007 (2011).

### Detecting continuous gravitational waves with superfluid helium

**Presenting Author**: Swati Singh, Williams College**Contributing Author(s)**: Laura DeLorenzo, Igor Pikovski and Keith Schwab

Read this article online: http://iopscience.iop.org/article/10.1088/1367-2630/aa78cb

(Session 9a: from 4:15pm-4:45pm)are detectable. Measuring such strains is possible by implementing state of the art microwave transducer technology. We show that the proposed system can compete with interferometric detectors and potentially surpass the gravitational strain limits set by them for certain pulsar sources within a few months of integration time.

### Progress on the quantum channel capacity problems

**Presenting Author**: Graeme Smith, University of Colorado Boulder

I will review what we know about the communication capacities of quantum channels, and give a flavor for why this problem is so challenging. I will also present some recent progress that allows us to tame low-noise channels, and gain new insights into high-noise channels.

### Control and measurement of single-photon pulses

**Presenting Author**: Brian Smith, University of Oregon

The ability to manipulate the spectral-temporal waveform of optical pulses in the classical domain has enabled a wide range of applications from ultrafast spectroscopy to high-speed communications. Extending these concepts to quantum light has the potential to enable breakthroughs in optical quantum science and technology. However, filtering and amplifying often employed in classical pulse shaping techniques are incompatible with non-classical light. Controlling and efficiently measuring the pulsed mode structure of quantum light requires efficient means to achieve deterministic, unitary manipulation that preserves fragile quantum coherences. Here an approach to deterministically modify the pulse-mode structure of quantum states of light within an integrated optical platform is presented. The method is based upon application of both spectral and temporal phase modulation to the wave packet. These techniques lay the ground for future quantum wavelength- and time-division multiplexing applications and facilitate interfacing of different physical platforms where quantum information can be stored and manipulated.

### Generating non-classical states of motion using spontaneous emission

**Presenting Author**: Jason Twamley, Macquarie University**Contributing Author(s)**: Ben Baragiola (Royal Melbourne Institute for Technology)

The generation of non-classical states of motion of matter is interesting both from a fundamental quantum science viewpoint but also permits such non-classical quantum states as potential resources for various quantum tasks such as quantum teleportation, sensing, communication and computation. In this work, using the SLH formalism, we explore systems of two-level emitters which are initially excited and are motionally trapped and optically coupled to a 1D waveguide either directly or via optical cavities. The emitter suffers a motional recoil upon the emission of a photon and this entangles the motion of the emitter with the emitted photon pulse. We find that for an emitter either directly coupled to a 1D waveguide, or coupled within a Fabry-Perot type cavity defined within the waveguide, the emitter is left in a mixed motional state which is typically classical (i.e. possesses a Wigner function which is positive). Interestingly, we find situations, e.g. emitter in front of a mirror, where the emitter is left in a mixed but highly non-classical motional state. We hypothesize that such non-classicality can only be achieved if the atom can re-interact with the emitted photon field. We also discover subtleties in the application of the SLH formalism to situations where the photon field can become trapped in the optical network.

### Investigations of the quantum alternating operator ansatz or optimization problems with constraints

**Presenting Author**: Zhihui Wang, NASA - Ames Research Center**Contributing Author(s)**: Eleanor Rieffel, Stuart Hadfield, Bryan O'Gorman, Nicholas C Rubin, Zhang Jiang, Davide Venturelli

Read this article online: https://arxiv.org/pdf/1709.03489.pdf

(Session 10: from 9:15am-9:45am)The emerging prototype universal quantum processors enables implementation of a wider variety of algorithms. Of particular interest are quantum heuristics, which have the potential to significantly expand the breadth of quantum computing applications. Here, we investigate the Quantum Alternating Operator Ansatz [1], an extension of the framework defined by Farhi et al. [2], that supports optimization problems with constraints and more efficient implementations. We present both theoretical and empirical results that demonstrate that choosing mixing unitaries that maintain the quantum evolution in the feasible subspace achieves better performance than adding penalties to a cost function to enforce the constraints. We discuss design criteria for mixing operators [1], mappings of a variety of specific problems [1], and compilations to near-term hardware [3]. [1] Stuart Hadfield, Zhihui Wang, Bryan O'Gorman, Eleanor G. Rieffel, Davide Venturelli, Rupak Biswas, From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz, arXiv:1709.03489 [2] Edward Farhi, Jeffrey Goldstone, and Sam Gutmann. A Quantum Approximate Optimization Algorithm Applied to a Bounded Occurrence Constraint Problem. arXiv:1412.6062 [3] Davide Venturelli, Minh Do, Eleanor G. Rieffel, Jeremy Frank, Compiling Quantum Circuits to Realistic Hardware Architectures using Temporal Planners, arXiv:1705.08927

### Optimizing quantum optimization algorithms via faster quantum gradient computation

**Presenting Author**: Nathan Wiebe, Microsoft Research**Contributing Author(s)**: Andres Gilyen, Srinivasan Arunachalam

Read this article online: https://arxiv.org/abs/1711.00465

(Session 4: from 4:15pm-4:45pm)We consider a generic framework of optimization algorithms based on gradient descent. We develop a quantum algorithm that calculates the gradient of a multi-variate real-valued function by evaluating it at only a logarithmic number of points in superposition. Our algorithm is an improved version of Jordan's gradient calculation algorithm, providing an approximation of the gradient of the function with quadratically better dependence on the evaluation accuracy of the function, for a class of smooth functions. Furthermore, we show that most functions arising from quantum optimization algorithms satisfy the necessary smoothness conditions; our new algorithm thereby provides a quadratic improvement in the complexity of their gradient calculation step. We also show that in a continuous phase query model, our gradient calculation algorithm has optimal query complexity up to poly-logarithmic factors, for a particular class of smooth functions. One of the main technical challenges in applying our gradient calculation procedure for optimization algorithms is the necessity of interconversion between a probability oracle (which is common in quantum optimization procedures) and phase oracle (which is common in quantum query algorithms) of the objective function. We provide efficient subroutines to perform this delicate interconversion between the two type of oracles incurring only a logarithmic overhead, which might be of independent interest.

### NIST ions at SQuInT

**Presenting Author**: David Wineland, NIST, Boulder/University of Oregon

The trapped ion group at NIST has enjoyed a long and rewarding association with SQuInT and its precursor meetings organized by Ivan Deutsch and colleagues. SQuInT's lifetime coincides closely with the rapid growth of interest in Quantum Information (QI) that followed the introduction of Shor's algorithm. These days, there are approximately fifty trapped-ion groups around the world that contribute to QI and many more groups pursuing QI in other physical platforms. I will highlight some of the developments of the NIST ions, but these are only representative of the progress being made by many groups around the world.

### Reaching the quantum Cramér-Rao bound of transmission measurements

**Presenting Author**: Timothy Woodworth, University of Oklahoma**Contributing Author(s)**: Carla Hermann-Avigliano, Kam Wai Clifford Chan, Alberto Marino

The quantum Cramér-Rao bound (QCRB) is commonly used to quantify the lower bound for the uncertainty in the estimation of a given parameter. Here, we calculate the QCRB for transmission measurements of an optical system probed by a beam of light. Estimating the transmission of an optical element is important as it is required for the calibration of optimal states for interferometers, characterization of high efficiency photodetectors, or as part of other measurements, such as those in plasmonic sensors or in ellipsometry. We use a beam splitter model for the losses introduced by the optical system to calculate the QCRB for different input states. We compare the bound for a coherent state, a two-mode squeezed-state (TMSS), and a Fock state. We prove that the Fock state gives the lowest possible uncertainty in estimating the transmission for any state and demonstrate that the TMSS approaches this ultimate bound for large levels of squeezing. Finally, we show that a simple measurement strategy for the TMSS, namely an intensity difference measurement, is able to saturate the QCRB. We then perform experiments to show this.