Open-System Adiabatic Quantum Search under Dephasing

TL;DR

This paper analyzes the impact of dephasing noise on adiabatic quantum search algorithms, deriving optimal schedules and identifying noise thresholds that limit acceleration.

Contribution

It revisits and extends previous work by providing closed-form solutions for optimal evolution and fidelity in dephasing environments, applying them to Grover search.

Findings

Derived closed-form expressions for optimal schedules and minimum runtime.

Identified a critical dephasing threshold beyond which acceleration is impossible.

Established physical limits for noise-assisted adiabatic quantum search.

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.