The Prevalence of Straight Shots in Control Space for Reaching Optimal Quantum Performance

Abstract:Gradient-based algorithms are often applied to identify an optimal control for maximizing a quantum objective functional by following a steepest ascent path to the top of the control landscape. In contrast, this paper explores straight shots through control space where movement along such a path corresponds to a less demanding monotonic complete climb up the landscape for the optimal objective value. Existing studies of control landscapes have revealed the presence of straight shots, but identifying them required computationally intensive stochastic methods. In this paper, we introduce a non-stochastic straight-shot search algorithm (STSA) that identifies a large class of straight shots. We apply STSA to numerically generate more than 10,000 distinct straight-shot optimization paths and analyze their statistical distribution for each of the objectives of (i) state-to-state transitions, (ii) general observables, and (iii) unitary transformation generation. The results show a decrease in the nearest-neighbor distances among straight shots as the sample size increases, suggesting their prevalence in control space. We further conjecture that the starting locations of the straight-shot pathways on a landscape level set may form connected neighborhoods, motivating future investigation into their underlying topological structure. The present paper focuses on the use of STSA for locating massive numbers of straight solutions. However, the STSA is not a high-efficiency algorithm in its present form, but the discovered prevalence of control straight shots leaves open future advances to accelerate the discovery of straight shots as optimal controls.

arXiv:2610.28852 [quant-ph]

(or arXiv:2610.28852v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.28852 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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