Optimal synthesis into fixed XX interactions

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 CX1/2 and CX1/3 alongside the standard gate CX, near to the optimal limit of ≈36.9% obtained by including all fractional applications CXα, € 2 [0, 1].