Automated Calibration of Two-Qubit Gates with Robust Phase Estimation

Robust phase estimation (RPE) is a technique for rapidly learning the rotation angle (or phase) of a quantum gate, in a way that is Heisenberg-limited in accuracy, robust against moderate decoherence effects, and requires only a few tens of circuits. While RPE has heretofore been used for high-accuracy single-qubit gate characterization, we show how RPE may be used to learn all phases present in a two-qubit entangling gate. We use two-qubit RPE as the core of a closed-loop calibration routine for minimizing the coherent errors on a controlled-Z gate on a superconducting transmon qubit platform. With this automated calibration routine we are able to achieve a controlled-Z over-rotation error at about 10^-3 radians on the Advanced Quantum Testbed superconducting transmon platform.