Analysis and Optimization of Tunable-Coupler-Based Controlled-Phase Gates

The use of tunable coupling elements in superconducting qubit architectures enables fast two-qubit gates, while minimizing crosstalk during idling time and single-qubit pulses. In particular, controlled-phase (CPHASE) gates based on flux-tunable couplers have been realized with fidelities above 99%. To further improve the fidelity of CPHASE gates we employ optimal control principles and efficient numerical simulations, including decoherence effects that limit fidelities for long pulses. We analyze the system dynamics for different pulse parametrizations and find pulse shapes that harness destructive interference of the leakage amplitudes between the first and second half of the pulse. This recovers intermediate population losses during the pulse and minimizes final leakage. In simulations with experimentally realistic decay times, gate fidelities above 99.9% are obtained for a wide range of device parameters using 20ns long pulses with not more than six parameters.