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 (SFQ) 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 an binary optimal control problem, constrained by Schrödinger'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 ${\cal O}(p\log(p)$, 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 fidelity's better than $99.9\%$, in $\approx 25$ trust-region iterations.