A Monte Carlo Tree Search Framework for Quantum Circuit Transformation

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 executable, a circuit transformation process is necessary to transform it into a functionally equivalent one so that the connectivity constraints imposed by the QPU are satisfied. Due to the high branching factor and vast search space, almost all existing algorithms search very shallowly and thus, very often, can reach (at most) locally optimal solutions. We propose a Monte Carlo Tree Search framework to tackle this problem, which enables the search process to go deeper. In particular, we design, by taking both short- and long-term rewards into consideration, a scoring mechanism, and propose to use a fast random strategy for simulation. The thus designed search algorithm is polynomial in all relevant parameters and empirical results on extensive realistic circuits show that it can reduce, in average, the size of the output circuits by at least 30% when compared with the state-of-the-art algorithms on IBM Q20.