A Rubik's Cube inspired approach to Clifford synthesis

TL;DR

This paper introduces a machine learning-based method inspired by Rubik's Cube solving to decompose Clifford elements into gates, offering more flexible and potentially more efficient synthesis tailored to specific quantum devices.

Contribution

It presents a novel, flexible machine learning approach for Clifford synthesis that can incorporate various gate sets and device constraints, improving efficiency over existing methods.

Findings

Often produces fewer gates than existing algorithms

Flexible in accommodating different gate sets and device topologies

Probabilistic approach with computational intensity

Abstract

The problem of decomposing an arbitrary Clifford element into a sequence of Clifford gates is known as Clifford synthesis. Drawing inspiration from similarities between this and the famous Rubik's Cube problem, we develop a machine learning approach for Clifford synthesis based on learning an approximation to the distance to the identity. This approach is probabilistic and computationally intensive. However, when a decomposition is successfully found, it often involves fewer gates than existing synthesis algorithms. Additionally, our approach is much more flexible than existing algorithms in that arbitrary gate sets, device topologies, and gate fidelities may incorporated, thus allowing for the approach to be tailored to a specific device.