Open-System Adiabatic Quantum Search under Dephasing

• URL: http://arxiv.org/abs/2603.28506v1
• Date: Mon, 30 Mar 2026 14:42:03 GMT
• Title: Open-System Adiabatic Quantum Search under Dephasing
• Abstract summary: Adiabatic quantum algorithms must evolve slowly enough to suppress non-adiabatic transitions while remaining fast enough to be practical.<n>In open systems, this trade-off is reshaped by decoherence.<n>For Hamiltonians subject to dephasing Lindbladians, Avron et al. showed that a unique timetable exists that maximizes the fidelity with a target state.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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. [1] 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, thereby defining the physically realizable boundaries for dephasing-based adiabatic quantum search protocols.

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