Quantum Walk Inspired Dynamic Adiabatic Local Search

TL;DR

This paper addresses the challenge of translating continuous-time quantum walk algorithms into adiabatic quantum computing by modifying the Hamiltonian and exploring adaptive scheduling, demonstrating optimal running times through simulation.

Contribution

It introduces a modified catalyst Hamiltonian with a Z oracle to align CTQW and AQC paths and investigates adaptive scheduling to enhance adiabatic local search performance.

Findings

Modified Hamiltonian maintains optimal running time.

Adaptive scheduling improves adiabatic local search efficiency.

Simulation confirms theoretical improvements.

Abstract

We investigate the irreconcilability issue that raises in translating the search algorithm from the Continuous-Time Quantum Walk (CTQW) framework to the Adiabatic Quantum Computing (AQC) framework. For the AQC formulation to evolve along the same path as the CTQW requires a constant energy gap in the former Hamiltonian throughout the AQC schedule. To resolve the issue, we modify the CTQW-inspired AQC catalyst Hamiltonian with a $Z$ oracle operator. Through simulation we demonstrate that the total running time for the proposed approach remains optimal. Inspired by this solution, we further investigate adaptive scheduling for the catalyst Hamiltonian and its coefficient function in the adiabatic path to improve the adiabatic local search.