Optimal synthesis into fixed XX interactions

Understand

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.