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We describe an optimal procedure, as well as its efficient softwareimplementation, for exact and approximate synthesis of two-qubit unitaryoperations into any prescribed discrete family of XX-type interactions andlocal gates. This arises from the analysis and manipulation of certainpolyhedral subsets of the space of canonical gates. Using this, we analyzewhich small sets of XX-type interactions cause the greatest improvement inexpected infidelity under experimentally-motivated error models. For the exactcircuit synthesis of Haar-randomly selected two-qubit operations, we find animprovement in estimated infidelity by ~31.4% when including alongside CX itssquare- and cube-roots, near to the optimal limit of ~36.9% obtained byincluding all fractional applications of CX.

Optimal synthesis into fixed XX interactions