Speedup of the quantum adiabatic algorithm using delocalization catalysis
We propose a method to speed up the quantum adiabatic algorithm using catalysis by many-body delocalization. This is applied to random-field antiferromagnetic Ising spin models. The algorithm is catalyzed in such a way that the evolution approximates a Heisenberg model in the middle of its course, a...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2021-01-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.3.013092 |
| _version_ | 1797211165902766080 |
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| author | Chenfeng Cao Jian Xue Nic Shannon Robert Joynt |
| author_facet | Chenfeng Cao Jian Xue Nic Shannon Robert Joynt |
| author_sort | Chenfeng Cao |
| collection | DOAJ |
| description | We propose a method to speed up the quantum adiabatic algorithm using catalysis by many-body delocalization. This is applied to random-field antiferromagnetic Ising spin models. The algorithm is catalyzed in such a way that the evolution approximates a Heisenberg model in the middle of its course, and the model is in a delocalized phase. We show numerically that we can speed up the standard algorithm for finding the ground state of the random-field Ising model using this idea. We also demonstrate that the speedup is due to gap amplification, even though the underlying model is not frustration-free. The crossover to speedup occurs at roughly the value of the interaction which is known to be the critical one for the delocalization transition. We also calculate the participation ratio and entanglement entropy as a function of time: Their time dependencies indicate that the system is exploring more states and that they are more entangled than when there is no catalyst. Together, all these pieces of evidence demonstrate that the speedup is related to delocalization. Even though only relatively small systems can be investigated, the evidence suggests that the scaling of the method with system size is favorable. Our method is illustrated by experimental results from a small online IBM quantum computer, showing how to verify the method in future as such machines improve. The cost of the catalytic method compared with the standard algorithm is only a constant factor. |
| first_indexed | 2024-04-24T10:22:10Z |
| format | Article |
| id | doaj.art-f12d2e07cb3e4cb98a497873038c22fc |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:22:10Z |
| publishDate | 2021-01-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-f12d2e07cb3e4cb98a497873038c22fc2024-04-12T17:06:52ZengAmerican Physical SocietyPhysical Review Research2643-15642021-01-013101309210.1103/PhysRevResearch.3.013092Speedup of the quantum adiabatic algorithm using delocalization catalysisChenfeng CaoJian XueNic ShannonRobert JoyntWe propose a method to speed up the quantum adiabatic algorithm using catalysis by many-body delocalization. This is applied to random-field antiferromagnetic Ising spin models. The algorithm is catalyzed in such a way that the evolution approximates a Heisenberg model in the middle of its course, and the model is in a delocalized phase. We show numerically that we can speed up the standard algorithm for finding the ground state of the random-field Ising model using this idea. We also demonstrate that the speedup is due to gap amplification, even though the underlying model is not frustration-free. The crossover to speedup occurs at roughly the value of the interaction which is known to be the critical one for the delocalization transition. We also calculate the participation ratio and entanglement entropy as a function of time: Their time dependencies indicate that the system is exploring more states and that they are more entangled than when there is no catalyst. Together, all these pieces of evidence demonstrate that the speedup is related to delocalization. Even though only relatively small systems can be investigated, the evidence suggests that the scaling of the method with system size is favorable. Our method is illustrated by experimental results from a small online IBM quantum computer, showing how to verify the method in future as such machines improve. The cost of the catalytic method compared with the standard algorithm is only a constant factor.http://doi.org/10.1103/PhysRevResearch.3.013092 |
| spellingShingle | Chenfeng Cao Jian Xue Nic Shannon Robert Joynt Speedup of the quantum adiabatic algorithm using delocalization catalysis Physical Review Research |
| title | Speedup of the quantum adiabatic algorithm using delocalization catalysis |
| title_full | Speedup of the quantum adiabatic algorithm using delocalization catalysis |
| title_fullStr | Speedup of the quantum adiabatic algorithm using delocalization catalysis |
| title_full_unstemmed | Speedup of the quantum adiabatic algorithm using delocalization catalysis |
| title_short | Speedup of the quantum adiabatic algorithm using delocalization catalysis |
| title_sort | speedup of the quantum adiabatic algorithm using delocalization catalysis |
| url | http://doi.org/10.1103/PhysRevResearch.3.013092 |
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