Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session X26: Quantum Optimal Control and Machine LearningFocus

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Sponsoring Units: DQI Chair: Daniel Egger, IBM Research  Zurich Room: BCEC 160B 
Friday, March 8, 2019 8:00AM  8:12AM 
X26.00001: Universal Quantum Control through Deep Reinforcement Learning Murphy Yuezhen Niu, Vadim Smelyanskiy, Sergio Boixo, Hartmut Neven We discover in this work that deep reinforcement learning (RL) techniques are capable of solving complex multiqubit quantum control problems robustly against control errors. We propose a control framework to jointly optimize over stochastic control errors and facilitates timedependent controls over all independent singlequbit Hamiltonians and twoqubit Hamiltonians, thus achieving full controllability for any twoqubit gate. As an essential ingredient, we derive an analytic leakage bound for a Hamiltonian control trajectory to account for both on and offresonant leakage errors. We utilize a continuousvariable policygradient RL agent consisting of twoneural networks to find highestreward/minimumcost analog controls for a variety of twoqubit unitary gates crucial for quantum simulation. We achieve up to a oneorderofmagnitude of improvement in gate time over the optimal gate synthesis approach based on the best known experimental gate parameters in superconducting qubits, an order of magnitude reduction in fidelity variance over solutions from both the noisefree RL counterpart and a baseline SGD method, and two orders of magnitude reduction in average infidelity over control solutions from the SGD method. 
Friday, March 8, 2019 8:12AM  8:24AM 
X26.00002: Reinforcement learning using AlphaZero to optimize entanglement sythesis in circuit QED Felix Motzoi, Mogens Dalgaard, Jens Jakob Sorenson, Jacob F Sherson We present an implementation of a reinforcement learning algorithm using deep neural networks and Monte Carlo tree search to demonstrate global optimization of the control landscape of superconducting qubits. Our findings show significant improvement in time and bestfound fidelity compared to long established localclimbing methods such as GRAPE. Our research suggests that for increasingly complex quantum control problems (as system sizes and architectures grow), sophisticated machine learning may become a preferable tool for calibrating and optimizing highperformance quantum computing experiments. 
Friday, March 8, 2019 8:24AM  9:00AM 
X26.00003: Applications of machine learning and related techniques to quantum control problems Invited Speaker: Sergio Boixo NISQ quantum computers require precise quantum control to achieve the necessary high fidelity operations. Machine learning offers tools that can be applied to this task. For example, reinforcement learning is a promising paradigm for universal quantum control. In the case of superconducting qubits, this requires explicit bounds on qubit leakage. To achieve high fidelity operations, quantum control parameters are fine tuned experimentally. Machine learning techniques can be applied in the optimization process. Cross entropy benchmarking is a technique to extract the experimental fidelity for generic operations with high precision, providing the cost function for the optimization loop. 
Friday, March 8, 2019 9:00AM  9:12AM 
X26.00004: Filtering noise through quantum control in highdimensional systems Michael Hush, Harrison Ball, Claire Edmunds, Dennis Lucarelli, Michael Jordan Biercuk Engineeringinspired filter functions are a powerful heuristic for the development of noiserobust quantum logic operations. We expand on existing singlequbit approaches and present a generalized, computationally efficient framework to calculate filter functions for operations performed on Ddimensional manifolds such as pairs of interacting qubits (including spectator levels), and qudits. We describe the computational approach and illustrate application in both systems. Filter function predictions for noise susceptibility in MolmerSorensen entangling gates are experimentally validated via experiments on trapped ions, showing good agreement with no free parameters. 
Friday, March 8, 2019 9:12AM  9:24AM 
X26.00005: Fast, highfidelity singlequbit gates in strongly coupled multiqubit systems Xiuhao Deng, Edwin Barnes, Sophia Economou Increasing the coupling strength between qubits can speed up multiqubit entangling gates, which is essential for implementing more complex algorithms on a quantum processor. However, there is a tradeoff: It becomes challenging to implement singlequbit gates in the strongcoupling regime because the relevant transition frequencies become strongly dependent on the states of other qubits. In a fixedfrequency processor, this leads to significant gate errors and fidelity loss if this effect is not taken into account. To avoid this issue, most works to date have focused on the weakly coupled regime where individual qubits retain their identity, albeit at the price of slow entangling operations. Even in the weakcoupling case though, errors due to interqubit coupling can still accumulate over the course of several gates applied in sequence. Here, we present a novel method to mitigate errors in singlequbit gates due to coupling to a second qubit that involves building the couplingdependent frequency shifts directly into the gate design. This is achieved through a combination of pulse shaping and pulse sequencing. Our techniques provide a way to speed up twoqubit entangling gates without sacrificing the speed and fidelity of singlequbit gates. 
Friday, March 8, 2019 9:24AM  9:36AM 
X26.00006: Optimal Control for Robust Atomic Fountain Interferometers Michael Goerz, Paul Kunz, Mark Kasevich, Vladimir Malinovsky Atomic fountain interferometers [1] provide precision measurements of gravitational fields with unprecedented sensitivity. This provides a wealth of possible applications, from fundamental science such as testing the equivalence principle, to nextgeneration inertial navigation systems. Fundamentally, the atom interferometer is implemented by laser pulses driving Braggtransitions between the momentum states of the atomic cloud. Signal contrast is limited by the ability to realize largemomentumtransfer atomic mirrors and beamsplitters with high fidelity and robustness with respect to laser amplitudes and initial velocity distribution of the atoms. Starting from a pulse scheme based on rapid adiabatic passage, we employ Krotov's method of numerical optimal control and ensemble optimization [2] to find shaped laser pulses that yield an increase in fidelity and robustness by roughly two orders of magnitude. 
Friday, March 8, 2019 9:36AM  9:48AM 
X26.00007: Hamiltonian Amplification Christian Arenz, Denys Bondar, Daniel Burgarth, Cecilia Cormick, Herschel A Rabitz Speedingup quantum dynamics is of paramount importance for quantum technology. However, in finite dimensions and without full knowledge of the dynamics, it is easily shown to be impossible. In sharp contrast we show that many continuous variable systems can be spedup without such knowledge, given that the structure of the underlying Hamiltonian is known. We call the resultant procedure Hamiltonian amplification. The method relies on the application of local squeezing operations allowing to amplify even unknown or noisy couplings and frequencies by acting on individual modes. We discuss the performance, physical realisations, robustness and implications of Hamiltonian amplification. Furthermore, we show how to combine amplification with dynamical decoupling to achieve amplifiers that are free from environmental noise. Finally, a significant reduction in gate times of cavity resonator qubits illustrates one potential use of Hamiltonian amplification. 
Friday, March 8, 2019 9:48AM  10:00AM 
X26.00008: Enhanced superconducting qubit gates via accelerated adiabatic evolution Hugo Ribeiro, Aashish Clerk Qubit gates based on adiabatic evolution are in principle attractive, as they exhibit inbuilt robustness: they are in principle insensitive to the amplitude, duration and phase of control pulses used to realize the gate. However, the requirement of adiabaticity makes them extremely slow, and hence impractical in many settings. Here, we show how counterdiabatic driving techniques can be used to design one and two qubit gates that have many of the advantages of purely adiabatic gates, but are at the same time fast. We focus on approaches based on accelerated STIRAP (stimulated Raman adiabatic passage) [1, 2], and on specific implementations in various superconducting circuit architectures (both for transmon style qubits, and for fluxonium style qubits). 
Friday, March 8, 2019 10:00AM  10:12AM 
X26.00009: Optimized Single Flux Quantum Pulse Trains for Highfidelity Qubit Control Kangbo Li, Robert F McDermott, Maxim Vavilov The hardware overhead associated with microwave control is a major obstacle to scaleup of superconducting quantum computing. An alternative approach to qubit control involves irradiation of the qubits with trains of Single Flux Quantum (SFQ) pulses, pulses of voltage whose time integral is precisely quantized to the magnetic flux quantum. SFQ pulses can be generated and delivered to the qubit via a proximal classical Josephson digital circuit, offering the possibility of a streamlined, lowfootprint classical coprocessor for monitoring errors and feeding back to the qubit array. In this talk, we describe an approach for the derivation and validation of complex SFQ pulse sequences in which classical bits are clocked to the qubit at a frequency that is a factor of a few higher than the qubit oscillation frequency, allowing for variable pulsetopulse timing in the qubit control sequence. Optimized sequences allow fast, coherent rotations in the qubit 01 subspace while suppressing leakage out of the computational manifold. We present simulation results and demonstrate that the performance of optimized SFQ control sequences is comparable to that of microwavebased sequences, with significantly reduced hardware requirements. 
Friday, March 8, 2019 10:12AM  10:24AM 
X26.00010: Minimal Time Robust Control for Superconducting Qubit Devices Eran Ginossar, Joseph Allen, Robert Kosut Fault tolerant quantum computing requires quantum gates with high delity. Given limitations 
Friday, March 8, 2019 10:24AM  10:36AM 
X26.00011: Error robust quantum logic for superconducting circuits Harrison Ball, Per J Liebermann, Michael Hush, Michael Jordan Biercuk Superconducting quantum computers differ substantially in the physical implementation of quantum logic operations, and therefore exhibit divergent error processes across hardware systems. In this talk we describe error modeling identifying dominant error channels in superconducting circuits implementing both parametrically activated and crossresonance twoqubit gates. We use these insights to derive new classes of errorrobust controls which combine modulation of both fields mediating the entangling operation and unitary operations applied to individual qubits. We present both analytic and numerically optimized solutions which are designed to reduce sensitivity to timevarying noise in critical system parameters by orders of magnitude. 
Friday, March 8, 2019 10:36AM  10:48AM 
X26.00012: Geometric formalism for constructing arbitrary singlequbit dynamically corrected gates Junkai Zeng, Edwin Barnes Implementing highfidelity quantum control and reducing the effect of the coupling between a quantum system and environmental noise is a major challenge in developing quantum information technologies. In recent work, a geometrical pulseshaping method was introduced to facilitate the design of timeoptimized pulses that implement gates while suppressing quasistatic noise errors. This method works for resonant pulses that implement a subset of singlequbit gates corresponding to rotations of the qubit about an axis that is orthogonal to the noise fluctuation term in the qubit Hamiltonian. Here, we show that these earlier findings are a special case of a larger geometrical structure hidden within the timedependent Schroedinger equation. In this framework, any noisesuppressing singlequbit gate corresponds to a closed threedimensional space curve, where the driving fields that implement the robust gates can be extracted from the curvature and torsion of the space curves. This provides a systematic approach to obtain all possible driving fields that implement an arbitrary dynamically corrected gate in the presence of quasistatic noise. We show that similar geometrical structures exist for quantum systems of arbitrary Hilbert space dimension. 
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