Open-System Adiabatic Quantum Search under Dephasing

Abstract:Adiabatic quantum algorithms must evolve slowly enough to suppress non-adiabatic transitions while remaining fast enough to be practical. In open systems, this trade-off is reshaped by decoherence. For Hamiltonians subject to dephasing Lindbladians, Avron et al. [Phys. Rev. A 82, 040304(R) (2010)] showed that a unique timetable exists that maximizes the fidelity with a target state. This optimal schedule is characterized by a constant tunneling rate along the adiabatic path. In this work, we revisit their analysis and apply it to the adiabatic Grover search framework, obtaining closed-form expressions for the optimal evolution schedule, the minimum runtime, and the resulting achievable fidelity. Moreover, by invoking an energy-time uncertainty argument, we identify a critical dephasing threshold beyond which further noise-assisted acceleration is prohibited, showing that the apparent advantage of strong dephasing is a Zeno-type stabilization mechanism rather than a conventional algorithmic speedup over unitary Grover search.

arXiv:2603.28506 [quant-ph]

(or arXiv:2603.28506v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2603.28506 Focus to learn more arXiv-issued DOI via DataCite

Phys. Rev. A 114, 042411 (2026)

https://doi.org/10.1103/9q9k-92cf Focus to learn more DOI(s) linking to related resources

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