Error-robust controls in quantum algorithms

Mirko Legnini, Julian Berberich

The Feedback-based Algorithm for Quantum Optimization (FALQON) is a Lyapunov inspired quantum algorithm proposed to tackle combinatorial optimization problems. In this paper, we examine the robustness of FALQON against coherent control errors, a class of multiplicative errors that affect the control input. We show that the algorithm is asymptotically robust with respect to systematic errors, and we derive robustness bounds for independent errors. Finally, we propose a robust version of FALQON which minimizes a regularized Lyapunov function. Our theoretical results are supported through simulations.

Alicia B Magann

Alicia B Magann

Haijin Ding, Re-Bing Wu

High-precision manipulation of multiqubit quantum systems requires strictly clocked and synchronized multichannel control signals. However, practical arbitrary wave-form generators always suffer from random signal jitters and channel latencies that induce nonignorable state or gate operation errors. In this paper, we analyze the average gate error caused by clock noises, from which an estimation formula is derived for quantifying the control robustness against clock noises. This measure is then employed for finding robust controls via a homotopic optimization algorithm. We also introduce our recently proposed stochastic optimization algorithm, b-grape, for training robust controls via randomly generated clock-noise samples. Numerical simulations on a two-qubit example demonstrate that both algorithms can greatly improve the control robustness against clock noises. The homotopic algorithm converges much faster than the b-grape algorithm, but the latter can achieve higher control robustness.

Yulong Dong, Xiang Meng, Lin Lin +2 more

Quantum variational algorithms have garnered significant interest recently, due to their feasibility of being implemented and tested on noisy intermediate scale quantum (NISQ) devices. We examine the robustness of the quantum approximate optimization algorithm (QAOA), which can be used to solve certain quantum control problems, state preparation problems, and combinatorial optimization problems. We demonstrate that the error of QAOA simulation can be significantly reduced by robust control optimization techniques, specifically, by sequential convex programming (SCP), to ensure error suppression in situations where the source of the error is known but not necessarily its magnitude. We show that robust optimization improves both the objective landscape of QAOA as well as overall circuit fidelity in the presence of coherent errors and errors in initial state preparation.

将光 坂東, 翼 市川, 近藤 康 +1 more