Designing fast quantum gates using optimal control with a reinforcement-learning ansatz

Abstract: Fast quantum gates are crucial not only for the contemporary era of noisy intermediate-scale quantum devices but also for the prospective development of practical fault-tolerant quantum computing. Leakage errors, which arise from data qubits jumping beyond the confines of the computational subspace, are the main challenges in realizing non-adiabatically driven, fast gates. In this work, we propose and illustrate the usefulness of reinforcement learning (RL) to generate fast two-qubit gates in practical multilevel superconducting qubits. In particular, we show that the RL controller offers great effectiveness in finding piecewise constant gate pulse sequences that act on two transmon data qubits coupled by a tunable coupler to generate a controlled-Z (CZ) gate with a gate time of 10 ns and an error rate of $\sim 4\times 10^{-3}$. Using a gradient-based method to solve the same optimization problem often does not achieve high fidelity for such fast gates. However, we show that using the gate pulses discovered by RL as an ansatz for the gradient-based controller can substantially enhance fidelity compared to using RL alone. While for a 10 ns pulse, this improvement is marginal, the combined RL + gradient approach decreases the gate errors below $10^{-4}$ for a gate of length 20 ns.