Vanishing performance of the parity-encoded quantum approximate optimization algorithm applied to spin-glass models
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913604974936064 |
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| author | Wybo, Elisabeth Leib, Martin |
| author_facet | Wybo, Elisabeth Leib, Martin |
| contents | 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 | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_02151 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Vanishing performance of the parity-encoded quantum approximate optimization algorithm applied to spin-glass models Wybo, Elisabeth Leib, Martin Quantum Physics 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. |
| title | Vanishing performance of the parity-encoded quantum approximate optimization algorithm applied to spin-glass models |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2311.02151 |