Quantum Circuit Design using a Progressive Widening Enhanced Monte Carlo Tree Search

TL;DR

This paper introduces a gradient-free Monte Carlo Tree Search method with progressive widening for automated quantum circuit design, improving efficiency and circuit simplicity across multiple quantum computing applications.

Contribution

It presents a novel MCTS-based approach with a new action space formulation and progressive widening, reducing evaluations and circuit complexity in quantum circuit design.

Findings

MCTS approximates quantum states independently of nonstabilizerness.

Technique reduces quantum circuit evaluations by 10 to 100 times.

Circuits generated have up to three times fewer CNOT gates.

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. This article proposes a gradient-free Monte Carlo Tree Search (MCTS) technique to automate the process of quantum circuit design. Our proposed technique 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 up to 100 while achieving equal or better results. In addition, the resulting quantum circuits exhibit up to three times fewer CNOT gates, which is important for implementation on noisy quantum hardware.