Robustly decorrelating errors with mixed quantum gates

Coherent errors in quantum operations are ubiquitous. Whether arising from spurious environmental couplings or errors in control fields, such errors can accumulate rapidly and degrade the performance of a quantum circuit significantly more than an average gate fidelity may indicate. As Hastings [1] and Campbell [2] have recently shown, by replacing the deterministic implementation of a quantum gate with a randomized ensemble of implementations, on can dramatically suppress coherent errors. Our work begins by reformulating the results of Hastings and Campbell as a quantum optimal control problem. We then discuss a family of convex programs designed to improve the performance, implementability, and robustness of the resulting mixed quantum gates. Finally, we implement these mixed quantum gates on a superconducting qubit and discuss randomized benchmarking results consistent with a marked reduction in the coherent error. [1] M. B. Hastings, Quantum Information & Computation 17, 488 (2017). [2] E. Campbell, Physical Review A 95, 042306 (2017).