Journal Article

FZJ-2024-01662

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Guided quantum walk

Schulz, S. (Corresponding author)FZJ* ; Willsch, D.FZJ* ; Michielsen, K.FZJ*

2024
APS College Park, MD

This record in other databases:    

Please use a persistent id in citations: doi:10.1103/PhysRevResearch.6.013312  doi:10.34734/FZJ-2024-01662

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.

---

Contributing Institute(s):

1. Jülich Supercomputing Center (JSC)

Research Program(s):

1. 5111 - Domain-Specific Simulation & Data Life Cycle Labs (SDLs) and Research Groups (POF4-511) (POF4-511)

Appears in the scientific report 2024

---

Database coverage:
; ; ; ; Article Processing Charges ; Clarivate Analytics Master Journal List ; DOAJ Seal ; Emerging Sources Citation Index ; Fees ; SCOPUS ; Web of Science Core Collection

---