Optimal synthesis into fixed XX interactions

TL;DR

This paper presents an optimal and efficient method for synthesizing two-qubit unitaries into fixed XX interactions, improving fidelity in quantum circuit implementations under realistic error models.

Contribution

It introduces a novel optimal synthesis procedure for XX-type interactions and analyzes their impact on fidelity improvements in quantum circuits.

Findings

Achieves approximately 31.4% reduction in infidelity with specific XX interactions.

Provides an efficient software implementation for exact and approximate synthesis.

Identifies the potential for near-optimal fidelity improvements using fractional applications of CX.

Abstract

We describe an optimal procedure, as well as its efficient software implementation, for exact and approximate synthesis of two-qubit unitary operations into any prescribed discrete family of XX-type interactions and local gates. This arises from the analysis and manipulation of certain polyhedral subsets of the space of canonical gates. Using this, we analyze which small sets of XX-type interactions cause the greatest improvement in expected infidelity under experimentally-motivated error models. For the exact circuit synthesis of Haar-randomly selected two-qubit operations, we find an improvement in estimated infidelity by ~31.4% when including alongside CX its square- and cube-roots, near to the optimal limit of ~36.9% obtained by including all fractional applications of CX.