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.
翻译:我们引入了一种二进制、放松的梯度、信任区域优化脉动序列以控制量子计算机的单通量 量子计算机(SFQ) 。 脉动序列的优化目标是实现单一门变换。 每个脉冲都有固定的振幅和持续时间。 我们将这一过程模拟为二进制的最佳控制问题, 受Schr\"{o}丁杰方程式的限制, 其中二进制变量显示每个脉冲是否在开关。 我们引入了一种一进制信任区域方法, 利用一种放松的梯度来确定最佳脉动序列, 最大限度地减少门不忠, 同时抑制泄漏到更高的能量水平。 提议的算法具有计算复杂性$$_ car O}( p\log( p) $, 其中美元是脉冲序列中的数。 我们为H 和 X门提供了数字结果, 在那里, 优化的脉动序列使门的忠度高于99.9 $, $\ approx 25 信任区域值。