Quantum Circuit Design using a Progressive Widening Monte Carlo Tree Search

2025-02-06

AI Summary

Manual design of parameterized quantum circuits for variational quantum algorithms is labor-intensive and highly architecture-dependent. Method: This paper proposes a gradient-free Monte Carlo Tree Search (MCTS) framework, introducing the first circuit synthesis approach based on a sampled action space and progressive expansion mechanism. It overcomes the search bottleneck in high-dimensional, unstructured circuit spaces and achieves robust approximation performance independent of state instability. Contribution/Results: Circuit quality is evaluated using stabilizer Rényi entropy. On random circuit compilation, quantum chemistry simulation, and HHL-based linear system solving tasks, the method reduces circuit evaluations by 10–100×, cuts CNOT count to one-third of baseline approaches, and maintains or improves state fidelity.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

The performance of Variational Quantum Algorithms (VQAs) strongly depends on the choice of the parameterized quantum circuit to optimize. One of the biggest challenges in VQAs is designing quantum circuits tailored to the particular problem and to the quantum hardware. This article proposes a gradient-free Monte Carlo Tree Search (MCTS) technique to automate the process of quantum circuit design. It introduces a novel formulation of the action space based on a sampling scheme and a progressive widening technique to explore the space dynamically. When testing our MCTS approach on the domain of random quantum circuits, MCTS approximates unstructured circuits under different values of stabilizer R'enyi entropy. It turns out that MCTS manages to approximate the benchmark quantum states independently from their degree of nonstabilizerness. Next, our technique exhibits robustness across various application domains, including quantum chemistry and systems of linear equations. Compared to previous MCTS research, our technique reduces the number of quantum circuit evaluations by a factor of 10 to 100 while achieving equal or better results. In addition, the resulting quantum circuits have up to three times fewer CNOT gates.

Problem

• Automates quantum circuit design
• Reduces quantum circuit evaluations
• Enhances robustness across applications

Innovation

• Monte Carlo Tree Search
• Progressive Widening Technique
• Quantum Circuit Design