Quantum circuit synthesis via a random combinatorial search

TL;DR

This paper introduces a random search method for quantum circuit synthesis, demonstrating that near-optimal circuits can be efficiently found by exploring a large space of quantum gate sequences, especially when considering alternative two-qubit gates.

Contribution

The paper presents a novel random search approach for quantum circuit synthesis and analyzes the impact of different two-qubit gates on circuit size and efficiency.

Findings

The fraction of perfect-fidelity circuits increases rapidly beyond the minimum circuit size.

Using the B gate reduces the minimum quantum circuit size for two-qubit operations.

A 15 CNOT-gate decomposition of the 4-qubit Toffoli gate was achieved.

Abstract

We use a random search technique to find quantum gate sequences that implement perfect quantum state preparation or unitary operator synthesis with arbitrary targets. This approach is based on the recent discovery that there is a large multiplicity of quantum circuits that achieve unit fidelity in performing a given target operation, even at the minimum number of single-qubit and two-qubit gates needed to achieve unit fidelity. We show that the fraction of perfect-fidelity quantum circuits increases rapidly as soon as the circuit size exceeds the minimum circuit size required for achieving unit fidelity. This result implies that near-optimal quantum circuits for a variety of quantum information processing tasks can be identified relatively easily by trying only a few randomly chosen quantum circuits and optimizing their parameters. In addition to analyzing the case where the CNOT gate is the elementary two-qubit gate, we consider the possibility of using alternative two-qubit gates. In particular, we analyze the case where the two-qubit gate is the B gate, which is known to reduce the minimum quantum circuit size for two-qubit operations. We apply the random search method to the problem of decomposing the 4-qubit Toffoli gate and find a 15 CNOT-gate decomposition.