Modular Parity Quantum Approximate Optimization
The parity transformation encodes spin models in the low-energy subspace of a larger Hilbert space with constraints on a planar lattice. Applying the quantum approximate optimization algorithm (QAOA), the constraints can either be enforced explicitly, by energy penalties, or implicitly, by restricti...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2022-07-01
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| Series: | PRX Quantum |
| Online Access: | http://doi.org/10.1103/PRXQuantum.3.030304 |
| _version_ | 1818535876504846336 |
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| author | Kilian Ender Anette Messinger Michael Fellner Clemens Dlaska Wolfgang Lechner |
| author_facet | Kilian Ender Anette Messinger Michael Fellner Clemens Dlaska Wolfgang Lechner |
| author_sort | Kilian Ender |
| collection | DOAJ |
| description | The parity transformation encodes spin models in the low-energy subspace of a larger Hilbert space with constraints on a planar lattice. Applying the quantum approximate optimization algorithm (QAOA), the constraints can either be enforced explicitly, by energy penalties, or implicitly, by restricting the dynamics to the low-energy subspace via the driver Hamiltonian. While the explicit approach allows for parallelization with a system-size-independent circuit depth, we show that the implicit approach exhibits better QAOA performance. We propose a generalization of the two approaches in order to improve the QAOA performance while keeping the circuit parallelizable. Furthermore, we introduce a modular parallelization method that partitions the circuit into clusters of subcircuits with fixed maximal circuit depth, relevant for scaling up to large system sizes. |
| first_indexed | 2024-12-11T18:30:45Z |
| format | Article |
| id | doaj.art-8da432b487504948951ed6d71ba8d15d |
| institution | Directory Open Access Journal |
| issn | 2691-3399 |
| language | English |
| last_indexed | 2024-12-11T18:30:45Z |
| publishDate | 2022-07-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | PRX Quantum |
| spelling | doaj.art-8da432b487504948951ed6d71ba8d15d2022-12-22T00:54:55ZengAmerican Physical SocietyPRX Quantum2691-33992022-07-013303030410.1103/PRXQuantum.3.030304Modular Parity Quantum Approximate OptimizationKilian EnderAnette MessingerMichael FellnerClemens DlaskaWolfgang LechnerThe parity transformation encodes spin models in the low-energy subspace of a larger Hilbert space with constraints on a planar lattice. Applying the quantum approximate optimization algorithm (QAOA), the constraints can either be enforced explicitly, by energy penalties, or implicitly, by restricting the dynamics to the low-energy subspace via the driver Hamiltonian. While the explicit approach allows for parallelization with a system-size-independent circuit depth, we show that the implicit approach exhibits better QAOA performance. We propose a generalization of the two approaches in order to improve the QAOA performance while keeping the circuit parallelizable. Furthermore, we introduce a modular parallelization method that partitions the circuit into clusters of subcircuits with fixed maximal circuit depth, relevant for scaling up to large system sizes.http://doi.org/10.1103/PRXQuantum.3.030304 |
| spellingShingle | Kilian Ender Anette Messinger Michael Fellner Clemens Dlaska Wolfgang Lechner Modular Parity Quantum Approximate Optimization PRX Quantum |
| title | Modular Parity Quantum Approximate Optimization |
| title_full | Modular Parity Quantum Approximate Optimization |
| title_fullStr | Modular Parity Quantum Approximate Optimization |
| title_full_unstemmed | Modular Parity Quantum Approximate Optimization |
| title_short | Modular Parity Quantum Approximate Optimization |
| title_sort | modular parity quantum approximate optimization |
| url | http://doi.org/10.1103/PRXQuantum.3.030304 |
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