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arXiv:2010.03655 · Physical Review X

Reinforcement Learning for Many-Body Ground-State Preparation Inspired by Counterdiabatic Driving

Jiahao Yao, Lin Lin, Marin Bukov

Published Sep 30, 2021• 76 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevx.11.031070

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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.
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.
We propose a reinforcement learning (RL) scheme for feedback quantum control within the quantum approximate optimization algorithm (QAOA).We reformulate the QAOA variational minimization as a learning task, where an RL agent chooses the control parameters for the unitaries, given partial information on the system.Such an RL scheme finds a policy converging to the optimal adiabatic solution of the quantum Ising chain that can also be successfully transferred between systems with different sizes, even in the presence of disorder.This allows for immediate experimental verification of our proposal on more complicated models: the RL agent is trained on a small control system, simulated on classical hardware, and then tested on a larger physical sample.
Variational quantum eigensolvers have recently received increased attention, as they enable the use of quantum computing devices to find solutions to complex problems, such as the ground energy and ground state of strongly-correlated quantum many-body systems. In many applications, it is the optimization of both continuous and discrete parameters that poses a formidable challenge. Using reinforcement learning (RL), we present a hybrid policy gradient algorithm capable of simultaneously optimizing continuous and discrete degrees of freedom in an uncertainty-resilient way. The hybrid policy is modeled by a deep autoregressive neural network to capture causality. We employ the algorithm to prepare the ground state of the nonintegrable quantum Ising model in a unitary process, parametrized by a generalized quantum approximate optimization ansatz: the RL agent solves the discrete combinatorial problem of constructing the optimal sequences of unitaries out of a predefined set and, at the same time, it optimizes the continuous durations for which these unitaries are applied. We demonstrate the noise-robust features of the agent by considering three sources of uncertainty: classical and quantum measurement noise, and errors in the control unitary durations. Our work exhibits the beneficial synergy between reinforcement learning and quantum control.
Abstract Quantum many-body control is a central milestone en route to harnessing quantum technologies. However, the exponential growth of the Hilbert space dimension with the number of qubits makes it challenging to classically simulate quantum many-body systems and, consequently, to devise reliable and robust optimal control protocols. Here we present a framework for efficiently controlling quantum many-body systems based on reinforcement learning (RL). We tackle the quantum-control problem by leveraging matrix product states (1) for representing the many-body state and (2) as part of the trainable machine learning architecture for our RL agent. The framework is applied to prepare ground states of the quantum Ising chain, including states in the critical region. It allows us to control systems far larger than neural-network-only architectures permit, while retaining the advantages of deep learning algorithms, such as generalizability and trainable robustness to noise. In particular, we demonstrate that RL agents are capable of finding universal controls, of learning how to optimally steer previously unseen many-body states and of adapting control protocols on the fly when the quantum dynamics is subject to stochastic perturbations. Furthermore, we map our RL framework to a hybrid quantum–classical algorithm that can be performed on noisy intermediate-scale quantum devices and test it under the presence of experimentally relevant sources of noise.
We implement the reinforcement learning agent for a spin-1 atomic system to prepare spin squeezed state from given initial state. Proximal policy gradient (PPO) algorithm is used to deal with continuous external control field and final optimized protocol is given by a stochastic policy. In both mean-field system and two-body quantum system, RL agent finds the optimal policies. In many-body quantum system, it also gives polices that outperform purely greedy policy and optimized adiabatic passage. These polices given by RL agent have good physical interpretability in phase space and may help us to understand quantum dynamics. In fact, RL could be highly versatile in quantum optimal control problems.
Quantum computing exploits basic quantum phenomena such as state superposition and entanglement to perform computations. The Quantum Approximate Optimization Algorithm (QAOA) is arguably one of the leading quantum algorithms that can outperform classical state-of-the-art methods in the near term. QAOA is a hybrid quantum-classical algorithm that combines a parameterized quantum state evolution with a classical optimization routine to approximately solve combinatorial problems. The quality of the solution obtained by QAOA within a fixed budget of calls to the quantum computer depends on the performance of the classical optimization routine used to optimize the variational parameters. In this work, we propose an approach based on reinforcement learning (RL) to train a policy network that can be used to quickly find high-quality variational parameters for unseen combinatorial problem instances. The RL agent is trained on small problem instances which can be simulated on a classical computer, yet the learned RL policy is generalizable and can be used to efficiently solve larger instances. Extensive simulations using the IBM Qiskit Aer quantum circuit simulator demonstrate that our trained RL policy can reduce the optimality gap by a factor up to 8.61 compared with other off-the-shelf optimizers tested.