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 (2017 Quantum Inf. Comput. 17 488) and Campbell (2017 Phys. Rev. A 95 042306) have recently shown, by replacing the deterministic implementation of a quantum gate with a randomized ensemble of implementations, one 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 able to solve this problem, as well as a set of secondary objectives 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.

量子运算中的相干错误无处不在。无论是由虚假的环境耦合还是控制场中的错误引起的，这些错误都会迅速累积，并大大降低量子电路的性能，这比平均门保真度所表明的要大得多。作为 Hastings (2017 Quantum Inf. Comput. 17 488) 和 Campbell (2017 Phys. Rev. A 95 )042306）最近表明，通过用随机实现的集合替换量子门的确定性实现，可以显着抑制相干误差。我们的工作首先将 Hastings 和 Campbell 的结果重新表述为一个量子最优控制问题。然后，我们讨论了一系列能够解决这个问题的凸程序，以及一组旨在提高所得混合量子门的性能、可实现性和鲁棒性的次要目标。最后，我们在超导量子位上实现这些混合量子门，并讨论与相干误差显着降低一致的随机基准测试结果。