Quantum-Walk-Inspired Dynamic Adiabatic Local Search

Round 1

Reviewer 1 Report

Quantum adiabatic computing (AQC) is designed by Hamiltonians : an initial and a target Hamiltonians are interpolated by a time parameter. It may be accelerated by an additional Hamiltonian, which is called a catalyst Hamiltonian in the manuscript. In the manuscript, the authors modify continuous time quantum walk to AQC catalyst Hamiltonian from XZ to Z operators. Then, the authors demonstrated through numerical simulations that the ruling time with the modified catalyst Hamiltonian remains optimal. 

The results are interesting, I found, and is also useful for future development. 

It’d be nice to add a reference, along the QAOA and quantum search: 

Quantum amplitude-amplification operators Phys. Rev. A 104, 062438 (2021). 

The manuscript is also well presented, and I would like to recommend the manuscript for publication. 

Reviewer 2 Report

This manuscript explores modifications of adiabatic quantum computing Hamiltonians that are inspired from consideration of continuous time quantum computing ones. Modifications are the replacement of the original catalyst Hamiltonian by an oracle operator but keeping the coefficient function the same, and secondly replacing the coefficient function. Search simulation experiments are presented which show the superiority of the two modifications over the original adiabatic one. Furthermore, different coefficient functions in the adiabatic local search experiment are tested to reduce the sluggish period in the search path. The tested coefficient functions show improvement and outperform the adiabatic local search. 

The manuscript is well-written and presented. I recommend publication.   

Minor spelling errors. After Eq. (7)  '.... of the eigenstate...'. After Eq. (13) 'explicitly'. After Eq. (17) '..functions that reach their maximum....'.