BINARY OPTIMAL CONTROL OF SINGLE-FLUX-QUANTUM PULSE SEQUENCES

We introduce a binary, relaxed gradient, trust-region method for optimizing pulse sequences for single flux quanta control of a quantum computer. The pulse sequences are optimized with the goal of realizing unitary gate transformations. Each pulse has a fixed amplitude and duration. We model this process as a binary optimal control problem, constrained by Schrodinger's equation, where the binary variables indicate whether each pulse is on or off. We introduce a first-order trust-region method, which takes advantage of a relaxed gradient to determine an optimal pulse sequence that minimizes the gate infidelity, while also suppressing leakage to higher energy levels. The proposed algorithm has a computational complexity of O (p log(p)), where p is the number of pulses in the sequence. We present numerical results for the H and X gates, where the optimized pulse sequences give gate fidelities better than 99:9%, in approximate to 25 trust-region iterations.