Quantum Walk Inspired Dynamic Adiabatic Local Search

Abstract

We investigate the irreconcilability issue that raises from translating the search algorithm from the Continuous-Time Quantum Walk (CTQW) framework to the Adiabatic Quantum Computing (AQC) framework. One major issue is the constant energy gap in the translated Hamiltonian throughout the AQC schedule. To resolve the issue in the initial investigation, we choose only Z operator as the catalyst Hamiltonian and show that this modification keeps the running time optimal. Inspired by this irreconcilability issue and our solution, we further investigate to find the proper timing for releasing the chosen catalyst Hamiltonian and the suitable coefficient function of the catalyst Hamiltonian in the AQC schedule to improve the Adiabatic local search.Comment: 9 pages, 8 figure