Guided quantum walk

Physical Review Research, vol. 6

Abstract

We utilize the theory of local amplitude transfer (LAT) to gain insights into quantum walks (QWs) and quantum annealing (QA) beyond the adiabatic theorem. By representing the eigenspace of the problem Hamiltonian as a hypercube graph, we demonstrate that probability amplitude traverses the search space through a series of local Rabi oscillations. We argue that the amplitude movement can be systematically guided towards the ground state using a time-dependent hopping rate based solely on the problem's energy spectrum. Building upon these insights, we extend the concept of multistage QW by introducing the guided quantum walk (GQW) as a bridge between QW-like and QA-like procedures. We assess the performance of the GQW on exact cover, traveling salesperson, and garden optimization problems with 9 to 30 qubits. Our results provide evidence for the existence of optimal annealing schedules, beyond the requirement of adiabatic time evolutions. These schedules might be capable of solving large-scale combinatorial optimization problems within evolution times that scale linearly in the problem size. Published by the American Physical Society 2024

Authors 3

1. Sebastian Schulz

   Forschungszentrum Jülich · Jülich Supercomputing Centre

   Affiliation as printed

   Jülich Supercomputing Centre, Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany

2. Dennis Willsch

   Forschungszentrum Jülich · Jülich Supercomputing Centre

   Affiliation as printed

   Jülich Supercomputing Centre, Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany

3. Kristel F. L. Michielsen Aachen

   RWTH Aachen University · Forschungszentrum Jülich · Jülich Supercomputing Centre

   Affiliation as printed

   AIDAS, 52425 Jülich, Germany

   Jülich Supercomputing Centre, Institute for Advanced Simulation, Forschungszentrum Jülich, 52425 Jülich, Germany

   RWTH Aachen University, 52056 Aachen, Germany