Quantum Circuit Transformation: A Monte Carlo Tree Search Framework

TL;DR

This paper introduces a Monte Carlo Tree Search framework for quantum circuit transformation that significantly reduces overhead costs, improving the fidelity of quantum circuits on NISQ devices by exploring deeper search strategies.

Contribution

It proposes a novel MCTS-based framework for quantum circuit transformation, enabling deeper search and more optimal solutions compared to existing shallow-search algorithms.

Findings

Reduces circuit size overhead by 66% on average

Decreases circuit depth overhead by 84% on average

Outperforms tket compiler on realistic circuits and IBM Q Tokyo

Abstract

In Noisy Intermediate-Scale Quantum (NISQ) era, quantum processing units (QPUs) suffer from, among others, highly limited connectivity between physical qubits. To make a quantum circuit effectively executable, a circuit transformation process is necessary to transform it, with overhead cost the smaller the better, into a functionally equivalent one so that the connectivity constraints imposed by the QPU are satisfied. While several algorithms have been proposed for this goal, the overhead costs are often very high, which degenerates the fidelity of the obtained circuits sharply. One major reason for this lies in that, due to the high branching factor and vast search space, almost all these algorithms only search very shallowly and thus, very often, only (at most) locally optimal solutions can be reached. In this paper, we propose a Monte Carlo Tree Search (MCTS) framework to tackle the circuit transformation problem, which enables the search process to go much deeper. The general framework supports implementations aiming to reduce either the size or depth of the output circuit through introducing SWAP or remote CNOT gates. The algorithms, called MCTS-Size and MCTS-Depth, are polynomial in all relevant parameters. Empirical results on extensive realistic circuits and IBM Q Tokyo show that the MCTS-based algorithms can reduce the size (depth, resp.) overhead by, on average, 66% (84%, resp.) when compared with tket, an industrial level compiler.