Binary Optimal Control Of Single-Flux-Quantum Pulse Sequences

Abstract

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¨odinger’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 fidelity’s better than 99 . 9%, in ≈ 25 trust-region iterations. , the trust-region convergence history of the objective functions J 1 , J 2 , and J 1 + C 1 J 2 . These plots illustrate that the number of iterations required to find a local minimizing binary solution is modest. For θ = π 300 , we find a minimal solution in around 25 iterations. In the case of θ = π 100 , around 20 iterations are needed. Since the number of control pulses in this case are p = 1600, there are 2 1600 ≈ 4 . 44 × 10 481 feasible solutions to the binary optimal control problem. In spite of the enormous size of the solution space, our method quickly finds quality solutions for both tip angles, with significant reduction in the infidelity term. We also observe that the leakage