Bounding first-order quantum phase transitions in adiabatic quantum computing
In the context of adiabatic quantum computation (AQC), it has been argued that first-order quantum phase transitions (QPTs) due to localization phenomena cause AQC to fail by exponentially decreasing the minimal spectral gap of the Hamiltonian along the annealing path as a function of the qubit numb...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2023-12-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.5.043236 |
| _version_ | 1797210320105635840 |
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| author | Matthias Werner Artur García-Sáez Marta P. Estarellas |
| author_facet | Matthias Werner Artur García-Sáez Marta P. Estarellas |
| author_sort | Matthias Werner |
| collection | DOAJ |
| description | In the context of adiabatic quantum computation (AQC), it has been argued that first-order quantum phase transitions (QPTs) due to localization phenomena cause AQC to fail by exponentially decreasing the minimal spectral gap of the Hamiltonian along the annealing path as a function of the qubit number. The vanishing of the spectral gap is often linked to the localization of the ground state in a local minimum, requiring the system to tunnel into the global minimum at a later stage of the annealing. Recent methods have been proposed to avoid this phenomenon by carefully designing the involved Hamiltonians. However, it remains a challenge to formulate a comprehensive theory of the effect of the various parameters and the conditions under which QPTs make the AQC algorithm fail. Equipped with concepts from graph theory, in this work we link graph quantities associated with the Hamiltonians along the annealing path with the occurrence of QPTs. These links allow us to derive bounds on the location of the minimal spectral gap along the annealing path, augmenting the toolbox for the analysis of strategies to improve the runtime of AQC algorithms. |
| first_indexed | 2024-04-24T10:08:43Z |
| format | Article |
| id | doaj.art-8d2827c7cb2c4343915e6f04093a02d7 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:08:43Z |
| publishDate | 2023-12-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-8d2827c7cb2c4343915e6f04093a02d72024-04-12T17:36:57ZengAmerican Physical SocietyPhysical Review Research2643-15642023-12-015404323610.1103/PhysRevResearch.5.043236Bounding first-order quantum phase transitions in adiabatic quantum computingMatthias WernerArtur García-SáezMarta P. EstarellasIn the context of adiabatic quantum computation (AQC), it has been argued that first-order quantum phase transitions (QPTs) due to localization phenomena cause AQC to fail by exponentially decreasing the minimal spectral gap of the Hamiltonian along the annealing path as a function of the qubit number. The vanishing of the spectral gap is often linked to the localization of the ground state in a local minimum, requiring the system to tunnel into the global minimum at a later stage of the annealing. Recent methods have been proposed to avoid this phenomenon by carefully designing the involved Hamiltonians. However, it remains a challenge to formulate a comprehensive theory of the effect of the various parameters and the conditions under which QPTs make the AQC algorithm fail. Equipped with concepts from graph theory, in this work we link graph quantities associated with the Hamiltonians along the annealing path with the occurrence of QPTs. These links allow us to derive bounds on the location of the minimal spectral gap along the annealing path, augmenting the toolbox for the analysis of strategies to improve the runtime of AQC algorithms.http://doi.org/10.1103/PhysRevResearch.5.043236 |
| spellingShingle | Matthias Werner Artur García-Sáez Marta P. Estarellas Bounding first-order quantum phase transitions in adiabatic quantum computing Physical Review Research |
| title | Bounding first-order quantum phase transitions in adiabatic quantum computing |
| title_full | Bounding first-order quantum phase transitions in adiabatic quantum computing |
| title_fullStr | Bounding first-order quantum phase transitions in adiabatic quantum computing |
| title_full_unstemmed | Bounding first-order quantum phase transitions in adiabatic quantum computing |
| title_short | Bounding first-order quantum phase transitions in adiabatic quantum computing |
| title_sort | bounding first order quantum phase transitions in adiabatic quantum computing |
| url | http://doi.org/10.1103/PhysRevResearch.5.043236 |
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