Reinforcement Learning for Parameterized Quantum State Preparation: A Comparative Study

TL;DR

This study applies reinforcement learning to optimize parameterized quantum circuits for state preparation, comparing one-stage and two-stage training methods, and evaluates their effectiveness on small to medium-sized quantum systems.

Contribution

It introduces a reinforcement learning framework for continuous quantum state preparation and compares two training regimes, providing insights into their performance and scalability.

Findings

PPO outperforms A2C in this setting.

Both methods achieve high success rates for basis and Bell states.

Scalability limits are observed beyond 4 qubits.

Abstract

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 \(R_x\), \(R_y\), and \(R_z\). 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 \(\lambda\) 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 \(5\times10^{-4}\) with a self-fidelity-error threshold of 0.01; two-stage: learning rate approximately \(10^{-4}\)). Both approaches reliably reconstruct computational basis states (between 83\% and 99\% success) and Bell states (between 61\% and 77\% success). However, scalability saturates for \(\lambda\) of approximately three to four and does not extend to ten-qubit targets even at \(\lambda=2\). 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.