  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 Schr\"{o}dinger'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.
