This title appears in the Scientific Report :
2024
Please use the identifier:
http://dx.doi.org/10.34734/FZJ-2024-01662 in citations.
Please use the identifier: http://dx.doi.org/10.1103/PhysRevResearch.6.013312 in citations.
Guided quantum walk
Guided quantum walk
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 sp...
Saved in:
Personal Name(s): | Schulz, Sebastian (Corresponding author) |
---|---|
Willsch, Dennis / Michielsen, Kristel | |
Contributing Institute: |
Jülich Supercomputing Center; JSC |
Published in: | Physical review research, 6 (2024) 1, S. 013312 |
Imprint: |
College Park, MD
APS
2024
|
DOI: |
10.34734/FZJ-2024-01662 |
DOI: |
10.1103/PhysRevResearch.6.013312 |
Document Type: |
Journal Article |
Research Program: |
Domain-Specific Simulation & Data Life Cycle Labs (SDLs) and Research Groups |
Link: |
Get full text OpenAccess OpenAccess |
Publikationsportal JuSER |
Please use the identifier: http://dx.doi.org/10.1103/PhysRevResearch.6.013312 in citations.
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. |