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Conference proceedings/Conference proceedings - IEEE International Conference on Systems, Man, and Cybernetics

Quantum State Generation Via Deep Reinforcement Learning

Shaojun Wu, Shan Jin, Xiaoting Wang

Published Oct 1, 2023• 1 citation
Publisher

Abstract

The quantum state generation problem is a major research goal of quantum control and quantum variational algorithms, which use iterative optimization methods to evolve the initial state to the target state. The Twin Delayed Deep Deterministic Policy (TD3) algorithm in reinforcement learning achieves high learning efficiency and better stability in continuous control tasks. Here, using the TD3, we propose a new quantum state preparation method that does not require case-by-case optimization, to find a suitable evolution path to obtain the desired state. Specifically, we input the initial state into the trained actor-network, which can output the parameters of the unitary gates step by step, thus gradually evolving the initial state to the fixed quantum state. According to the reversibility of the unitary transformation, we can obtain a sequence of unitary gates to evolve the fixed state to the desired state. To verify the effectiveness of the algorithm, we perform simulations for one-qubit, two-qubit, and four-qubit cases, and the results show that the trained actor-network can provide appropriate unitary transformations to obtain the fixed state.

DOI
10.1109/smc53992.2023.10394265

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The quantum state generation problem is a major research goal of quantum control and quantum variational algorithms, which use iterative optimization methods to evolve the initial state to the target state. The Twin Delayed Deep Deterministic Policy (TD3) algorithm in reinforcement learning achieves high learning efficiency and better stability in continuous control tasks. Here, using the TD3, we propose a new quantum state preparation method that does not require case-by-case optimization, to find a suitable evolution path to obtain the desired state. Specifically, we input the initial state into the trained actor-network, which can output the parameters of the unitary gates step by step, thus gradually evolving the initial state to the fixed quantum state. According to the reversibility of the unitary transformation, we can obtain a sequence of unitary gates to evolve the fixed state to the desired state. To verify the effectiveness of the algorithm, we perform simulations for one-qubit, two-qubit, and four-qubit cases, and the results show that the trained actor-network can provide appropriate unitary transformations to obtain the fixed state.
This paper investigates quantum gate control problems using the deep reinforcement learning algorithm, i.e., a model-free machine learning method. We implement the twin delayed deep deterministic policy gradient (TD3) algorithm to search for piece-wise constant control pulses for quantum gates through the trail interaction with the quantum system. Simulation results on four typical gates, including three one-qubit gates and a two-qubit CNOT gate, demonstrate that deep reinforcement learning exhibits improved performance for quantum gate control tasks. By setting punishment for steps in the reward function, DRL can automatically find a shorter control sequence than the traditional gradient-based algorithm (e.g., GRAPE algorithm) and the evolutionary algorithm (e.g., DE algorithm) while maintaining high control precision.
Quantum computers promise significant computational advantages over classical computers for specific tasks. However, one of the challenges in the noisy intermediate-scale quantum (NISQ) era is the efficient compilation of quantum states and gates, which is crucial for the implementation of quantum algorithms. Given the high dimensionality of quantum systems, this compilation task is non-trivial. Reinforcement learning (RL) is a machine learning subfield focused on developing algorithms for decision-making in dynamic environments. An agent learns by interacting with its environment, how to act to optimize its performance on a certain task. Recently, the integration of deep learning has given rise to deep reinforcement learning (DRL), where deep neural networks approximate functions like value or policy, allowing agents to tackle high-dimensional and complex tasks with greater efficiency and success. Recently, deep reinforcement learning (DRL) has been proposed as a method to automate quantum compiling. In this thesis, we explore the application of RL for quantum state and unitary matrix synthesis, focusing on the use of two reinforcement learning algorithms Deep Q-Networks (DQN) and Proximal Policy Optimization (PPO). Our results indicate that DRL shows promise in generalizing the task of quantum unitary synthesis and quantum state preparation. However, the current state-of-the-art is still limited to working in the no-volume law entangled part of the Hilbert space.
Quantum reinforcement learning (QRL) is a promising paradigm for near-term quantum devices. While existing QRL methods have shown success in discrete action spaces, extending these techniques to continuous domains is challenging due to the curse of dimensionality introduced by discretization. To overcome this limitation, we introduce a quantum Deep Deterministic Policy Gradient (DDPG) algorithm that efficiently addresses both classical and quantum sequential decision problems in continuous action spaces. Moreover, our approach facilitates single-shot quantum state generation: a one-time optimization produces a model that outputs the control sequence required to drive a fixed initial state to any desired target state. In contrast, conventional quantum control methods demand separate optimization for each target state. We demonstrate the effectiveness of our method through simulations and discuss its potential applications in quantum control.
Abstract Accurate and efficient preparation of quantum state is a core issue in building a quantum computer. In this paper, we investigate how to prepare a certain single- or two-qubit target state from arbitrary initial states in semiconductor double quantum dots with only a few discrete control pulses by leveraging the deep reinforcement learning. Our method is based on the training of the network over numerous preparing tasks. The results show that once the network is well trained, it works for any initial states in the continuous Hilbert space. Thus repeated training for new preparation tasks is avoided. Our scheme outperforms the traditional optimization approaches based on gradient with both the higher efficiency and the preparation quality in discrete control space. Moreover, we find that the control trajectories designed by our scheme are robust against stochastic fluctuations within certain thresholds, such as the charge and nuclear noises.
We extend directed quantum circuit synthesis (DQCS) with reinforcement learning from purely discrete gate selection to parameterized quantum state preparation with continuous single-qubit rotations RxR_xRx​, RyR_yRy​, and RzR_zRz​. We compare two training regimes: a one-stage agent that jointly selects the gate type, the affected qubit(s), and the rotation angle; and a two-stage variant that first proposes a discrete circuit and subsequently optimizes the rotation angles with Adam using parameter-shift gradients. Using Gymnasium and PennyLane, we evaluate Proximal Policy Optimization (PPO) and Advantage Actor--Critic (A2C) on systems comprising two to ten qubits and on targets of increasing complexity with λλλ ranging from one to five. Whereas A2C does not learn effective policies in this setting, PPO succeeds under stable hyperparameters (one-stage: learning rate approximately 5×10−45\times10^{-4}5×10−4 with a self-fidelity-error threshold of 0.01; two-stage: learning rate approximately 10−410^{-4}10−4). Both approaches reliably reconstruct computational basis states (between 83\% and 99\% success) and Bell states (between 61\% and 77\% success). However, scalability saturates for λλλ of approximately three to four and does not extend to ten-qubit targets even at λ=2λ=2λ=2. The two-stage method offers only marginal accuracy gains while requiring around three times the runtime. For practicality under a fixed compute budget, we therefore recommend the one-stage PPO policy, provide explicit synthesized circuits, and contrast with a classical variational baseline to outline avenues for improved scalability.
State preparation is currently the only means to provide input data for quantum algorithm, but finding the shortest possible sequence of gates to prepare a given state is not trivial. We approach this problem using reinforcement learning (RL), first on an agent that is trained to only prepare a single fixed quantum state. Despite the overhead of training a whole network to just produce one single data point, gradient-based backpropagation appears competitive to genetic algorithms in this scenario and single state preparation thus seems a worthwhile task. In a second case we then train a single network to prepare arbitrary quantum states to some degree of success, despite a complete lack of structure in the training data set. In both cases we find that training is severely improved by using QR decomposition to automatically map the agents' outputs to unitary operators to solve the problem of sparse rewards that usually makes this task challenging.