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arXiv:2011.11987 · Physical Review Letters

Faster State Preparation across Quantum Phase Transition Assisted by Reinforcement Learning

Shuai-Feng Guo, Feng Chen, Qi Liu, Ming Xue, Junjie Chen, Jiahao Cao, Tian-Wei Mao, Meng Khoon Tey, Li You

Published Feb 9, 2021• 43 citations
arXivHTMLPDF

Abstract

An energy gap develops near quantum critical point of quantum phase transition in a finite many-body (MB) system, facilitating the ground state transformation by adiabatic parameter change. In real application scenarios, however, the efficacy for such a protocol is compromised by the need to balance finite system lifetime with adiabaticity, as exemplified in a recent experiment that prepares three-mode balanced Dicke state near deterministically [Y.-Q. Zou et al., Proc. Natl. Acad. Sci. U.S.A. 115, 6381 (2018)PNASA60027-842410.1073/pnas.1715105115]. Instead of tracking the instantaneous ground state as unanimously required for most adiabatic crossing, this work reports a faster sweeping policy taking advantage of excited level dynamics. It is obtained based on deep reinforcement learning (DRL) from a multistep training scheme we develop. In the absence of loss, a fidelity ≥99% between prepared and the target Dicke state is achieved over a small fraction of the adiabatically required time. When loss is included, training is carried out according to an operational benchmark, the interferometric sensitivity of the prepared state instead of fidelity, leading to better sensitivity in about half of the previously reported time. Implemented in a Bose-Einstein condensate of ∼10^{4} ^{87}Rb atoms, the balanced three-mode Dicke state exhibiting an improved number squeezing of 13.02±0.20 dB is observed within 766 ms, highlighting the potential of DRL for quantum dynamics control and quantum state preparation in interacting MB systems.

DOI
10.1103/physrevlett.126.060401

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An energy gap develops near quantum critical point of quantum phase transition in a finite many-body (MB) system, facilitating the ground state transformation by adiabatic parameter change. In real application scenarios, however, the efficacy for such a protocol is compromised by the need to balance finite system lifetime with adiabaticity, as exemplified in a recent experiment that prepares three-mode balanced Dicke state near deterministically [Y.-Q. Zou et al., Proc. Natl. Acad. Sci. U.S.A. 115, 6381 (2018)PNASA60027-842410.1073/pnas.1715105115]. Instead of tracking the instantaneous ground state as unanimously required for most adiabatic crossing, this work reports a faster sweeping policy taking advantage of excited level dynamics. It is obtained based on deep reinforcement learning (DRL) from a multistep training scheme we develop. In the absence of loss, a fidelity ≥99% between prepared and the target Dicke state is achieved over a small fraction of the adiabatically required time. When loss is included, training is carried out according to an operational benchmark, the interferometric sensitivity of the prepared state instead of fidelity, leading to better sensitivity in about half of the previously reported time. Implemented in a Bose-Einstein condensate of ∼10^{4} ^{87}Rb atoms, the balanced three-mode Dicke state exhibiting an improved number squeezing of 13.02±0.20 dB is observed within 766 ms, highlighting the potential of DRL for quantum dynamics control and quantum state preparation in interacting MB systems.
The fast and efficient preparation of quantum critical states is a challenging yet crucial task for various quantum technologies. This difficulty is most particularly for systems near a quantum phase transition, where the closure of the energy gap fundamentally limits the timescale of adiabatic processes and thus precludes rapid state preparation. We propose a framework using deep reinforcement learning (DRL) to rapidly prepare quantum critical states, with broad extendibility to light-matter interaction systems. Specifically, a DRL agent optimizes a set of time-dependent control Hamiltonians to drive the system from an initial noncritical state to a target critical state within a finite time and over experimentally accessible parameter ranges. As a concrete application, we focus on the quantum Rabi model. The DRL-optimized time-dependent control Hamiltonian yield a final state with high-fidelity (>0.999>0.999>0.999) to the target critical state. The protocol can be readily extended to other quantum critical systems described by light-matter interaction models, such as quantum Dicke model. This investigation provides a powerful new framework for preparing and manipulating quantum critical states.
The fast and efficient preparation of quantum critical states is a challenging yet crucial task for various quantum technologies. This difficulty is most particularly for systems near a quantum phase transition, where the closure of the energy gap fundamentally limits the timescale of adiabatic processes and thus precludes rapid state preparation. We propose a framework using deep reinforcement learning (DRL) to rapidly prepare quantum critical states, with broad extendibility to light-matter interaction systems. Specifically, a DRL agent optimizes a set of time-dependent control Hamiltonians to drive the system from an initial noncritical state to a target critical state within a finite time and over experimentally accessible parameter ranges. As a concrete application, we focus on the quantum Rabi model. The DRL-optimized time-dependent control Hamiltonian yields a final state with high fidelity ( > 0.999 ) to the target critical state. The protocol can be readily extended to other quantum critical systems described by light-matter interaction models, such as quantum Dicke model. This investigation provides a powerful framework for preparing and manipulating quantum critical states.
Finding optimal control strategies to suppress quantum thermalization for arbitrarily initial states, the so-called quantum nonergodicity control, is important for quantum information science and technologies. Previous control methods relied largely on theoretical model of the target quantum system, but invertible model approximations and inaccuracies can lead to control failures. We develop a model-free and deep reinforcement-learning (DRL) framework for quantum nonergodicity control. It is a machine-learning method with the unique focus on balancing exploration and exploitation strategies to maximize the cumulative rewards so as to preserve the initial memory in the time-dependent nonergodic metrics over a long stretch of time. We use the paradigmatic one-dimensional tilted Fermi-Hubbard system to demonstrate that the DRL agent can efficiently learn the quantum many-body system solely through the interactions with the environment. The optimal policy obtained by the DRL provides broader control scenarios for managing nonergodicity in the phase diagram as compared to, e.g., the specific protocol for Wannier-Stark localization. The continuous control protocols and observations are experimentally feasible. The model-free nature of DRL and its versatile search space for control functions render promising nonergodicity control in more complex quantum many-body systems.
The computation of electronic excited states and real-time quantum dynamics of many-fermion systems is among the most promising applications of near-term quantum computing. In this work, we generalize the reinforcement learning contracted quantum eigensolver (RL-CQE), previously developed for ground-state problems, to electronic excited states and real-time quantum dynamics, in which a deep Q-network agent adaptively selects the two-body operators at each iteration, yielding more compact ansätze and improved robustness with respect to critical hyperparameters. A key feature of the algorithm is a scalable state representation based on the ACSE residuals, whose dimension grows with the one-particle basis but remains independent of the number of targeted excited states. We also verify the equivalence of sign-free qubit operators in the excited-state setting, extending a result previously established for ground-state problems. Our RL-CQE for time evolution derives from a constant-scaling ansatz that represents the wave function with a fixed number of unitary transformations independent of simulation time ttt, enabled by the shared unitary structure of the purified ensemble treatment of excited states. Benchmarks on chemical systems demonstrate chemical accuracy with minimal operator counts across a range of bond lengths.
The Quantum Approximate Optimization Ansatz (QAOA) is a prominent example of variational quantum algorithms. We propose a generalized QAOA ansatz called CD-QAOA, which is inspired by the counter-diabatic (CD) driving procedure, designed for quantum many-body systems, and optimized using a reinforcement learning (RL) approach. The resulting hybrid control algorithm proves versatile in preparing the ground state of quantum-chaotic many-body spin chains, by minimizing the energy. We show that using terms occurring in the adiabatic gauge potential as additional control unitaries, it is possible to achieve fast high-fidelity many-body control away from the adiabatic regime. While each unitary retains the conventional QAOA-intrinsic continuous control degree of freedom such as the time duration, we take into account the order of the multiple available unitaries appearing in the control sequence as an additional discrete optimization problem. Endowing the policy gradient algorithm with an autoregressive deep learning architecture to capture causality, we train the RL agent to construct optimal sequences of unitaries. The algorithm has no access to the quantum state, and we find that the protocol learned on small systems may generalize to larger systems. By scanning a range of protocol durations, we present numerical evidence for a finite quantum speed limit in the nonintegrable mixed-field spin-1/2 Ising model, and for the suitability of the ansatz to prepare ground states of the spin-1 Heisenberg chain in the long-range and topologically ordered parameter regimes. This work paves the way to incorporate recent success from deep learning for the purpose of quantum many-body control.
The quantum alternating operator ansatz (QAOA) is a prominent example of variational quantum algorithms.We propose a generalized QAOA called CD-QAOA, which is inspired by the counterdiabatic driving procedure, designed for quantum many-body systems and optimized using a reinforcement learning (RL) approach.The resulting hybrid control algorithm proves versatile in preparing the ground state of quantum-chaotic many-body spin chains by minimizing the energy.We show that using terms occurring in the adiabatic gauge potential as generators of additional control unitaries, it is possible to achieve fast highfidelity many-body control away from the adiabatic regime.While each unitary retains the conventional QAOA-intrinsic continuous control degree of freedom such as the time duration, we consider the order of the multiple available unitaries appearing in the control sequence as an additional discrete optimization problem.Endowing the policy gradient algorithm with an autoregressive deep learning architecture to capture causality, we train the RL agent to construct optimal sequences of unitaries.The algorithm has no access to the quantum state, and we find that the protocol learned on small systems may generalize to larger systems.By scanning a range of protocol durations, we present numerical evidence for a finite quantum speed limit in the nonintegrable mixed-field spin-1=2 Ising and Lipkin-Meshkov-Glick models, and for the suitability to prepare ground states of the spin-1 Heisenberg chain in the long-range and topologically ordered parameter regimes.This work paves the way to incorporate recent success from deep learning for the purpose of quantum many-body control.