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  • Open Access

Open-system adiabatic quantum search under dephasing

Afaf El Kalai1,2,*, Peter J. Eder2,3,†, and Christian B. Mendl3,4,‡

  • *Contact author: afaf.el-kalai@tum.de
  • †Contact author: peter-josef.eder@siemens.com
  • ‡Contact author: christian.mendl@tum.de
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Phys. Rev. A 114, 042411 – Published 7 October, 2026

DOI: https://doi.org/10.1103/9q9k-92cf

Abstract

Adiabatic quantum algorithms must evolve slowly enough to suppress nonadiabatic 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 the unitary Grover search.

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Phys. Rev. A 114, 042411– Published 7 October, 2026
  • Received 7 April 2026
  • Accepted 14 September 2026
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