Vanishing performance of the parity-encoded quantum approximate optimization algorithm applied to spin-glass models
The parity mapping provides a geometrically local encoding of the Quantum Approximate Optimization Algorithm (QAOA), at the expense of having a quadratic qubit overhead for all-to-all connected problems. In this work, we benchmark the parity-encoded QAOA on spin-glass models. We address open questio...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2024-12-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2024-12-10-1554/pdf/ |
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| author | Elisabeth Wybo Martin Leib |
| author_facet | Elisabeth Wybo Martin Leib |
| author_sort | Elisabeth Wybo |
| collection | DOAJ |
| description | The parity mapping provides a geometrically local encoding of the Quantum Approximate Optimization Algorithm (QAOA), at the expense of having a quadratic qubit overhead for all-to-all connected problems. In this work, we benchmark the parity-encoded QAOA on spin-glass models. We address open questions in the scaling of this algorithm. In particular, we show that for fixed number of parity-encoded QAOA layers, the performance or the output energy, vanishes towards zero (the value achieved by random guessing) with problem size $N$ as $N^{-1/2}$. Our results suggest that the parity-encoded QAOA does not have a promising scaling compared to the standard version of QAOA. We perform tensor-network calculations to confirm our results, and comment on the concentration of optimal QAOA parameters over problem instances. |
| format | Article |
| id | doaj-art-e54cbfdca94a404facb0ee737876dca0 |
| institution | OA Journals |
| issn | 2521-327X |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj-art-e54cbfdca94a404facb0ee737876dca02025-08-20T01:59:16ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2024-12-018155410.22331/q-2024-12-10-155410.22331/q-2024-12-10-1554Vanishing performance of the parity-encoded quantum approximate optimization algorithm applied to spin-glass modelsElisabeth WyboMartin LeibThe parity mapping provides a geometrically local encoding of the Quantum Approximate Optimization Algorithm (QAOA), at the expense of having a quadratic qubit overhead for all-to-all connected problems. In this work, we benchmark the parity-encoded QAOA on spin-glass models. We address open questions in the scaling of this algorithm. In particular, we show that for fixed number of parity-encoded QAOA layers, the performance or the output energy, vanishes towards zero (the value achieved by random guessing) with problem size $N$ as $N^{-1/2}$. Our results suggest that the parity-encoded QAOA does not have a promising scaling compared to the standard version of QAOA. We perform tensor-network calculations to confirm our results, and comment on the concentration of optimal QAOA parameters over problem instances.https://quantum-journal.org/papers/q-2024-12-10-1554/pdf/ |
| spellingShingle | Elisabeth Wybo Martin Leib Vanishing performance of the parity-encoded quantum approximate optimization algorithm applied to spin-glass models Quantum |
| title | Vanishing performance of the parity-encoded quantum approximate optimization algorithm applied to spin-glass models |
| title_full | Vanishing performance of the parity-encoded quantum approximate optimization algorithm applied to spin-glass models |
| title_fullStr | Vanishing performance of the parity-encoded quantum approximate optimization algorithm applied to spin-glass models |
| title_full_unstemmed | Vanishing performance of the parity-encoded quantum approximate optimization algorithm applied to spin-glass models |
| title_short | Vanishing performance of the parity-encoded quantum approximate optimization algorithm applied to spin-glass models |
| title_sort | vanishing performance of the parity encoded quantum approximate optimization algorithm applied to spin glass models |
| url | https://quantum-journal.org/papers/q-2024-12-10-1554/pdf/ |
| work_keys_str_mv | AT elisabethwybo vanishingperformanceoftheparityencodedquantumapproximateoptimizationalgorithmappliedtospinglassmodels AT martinleib vanishingperformanceoftheparityencodedquantumapproximateoptimizationalgorithmappliedtospinglassmodels |