Reflection-Based Adiabatic State Preparation

TL;DR

This paper introduces a quantum algorithm that combines reflection techniques with adiabatic evolution to efficiently prepare ground states, showing potential speed advantages over Grover's search for certain combinatorial problems.

Contribution

It presents a novel reflection-based adiabatic quantum algorithm for eigenstate preparation, demonstrating improved performance over Grover's search in solving NP-hard problems.

Findings

Algorithm can find solutions faster than Grover's search on average.

Numerical evidence supports efficiency in solving MAX-2SAT.

Applicable to combinatorial search problems.

Abstract

We propose a circuit-model quantum algorithm for eigenpath traversal that is based on a combination of concepts from Grover's search and adiabatic quantum computation. Our algorithm deploys a sequence of reflections determined from eigenspaces of instantaneous Hamiltonians defined along an adiabatic schedule in order to prepare a ground state of a target problem Hamiltonian. We provide numerical evidence suggesting that, for combinatorial search problems, our algorithm can find a solution faster, on average, than Grover's search. We demonstrate our findings by applying both algorithms to solving the NP-hard MAX-2SAT problem.