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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2024-03-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.6.013312 |
| _version_ | 1797210248437563392 |
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| author | Sebastian Schulz Dennis Willsch Kristel Michielsen |
| author_facet | Sebastian Schulz Dennis Willsch Kristel Michielsen |
| author_sort | Sebastian Schulz |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-24T10:07:35Z |
| format | Article |
| id | doaj.art-a2d1b73e957743eca172ca8362c3e887 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:07:35Z |
| publishDate | 2024-03-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-a2d1b73e957743eca172ca8362c3e8872024-04-12T17:40:44ZengAmerican Physical SocietyPhysical Review Research2643-15642024-03-016101331210.1103/PhysRevResearch.6.013312Guided quantum walkSebastian SchulzDennis WillschKristel MichielsenWe 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.http://doi.org/10.1103/PhysRevResearch.6.013312 |
| spellingShingle | Sebastian Schulz Dennis Willsch Kristel Michielsen Guided quantum walk Physical Review Research |
| title | Guided quantum walk |
| title_full | Guided quantum walk |
| title_fullStr | Guided quantum walk |
| title_full_unstemmed | Guided quantum walk |
| title_short | Guided quantum walk |
| title_sort | guided quantum walk |
| url | http://doi.org/10.1103/PhysRevResearch.6.013312 |
| work_keys_str_mv | AT sebastianschulz guidedquantumwalk AT denniswillsch guidedquantumwalk AT kristelmichielsen guidedquantumwalk |