On the role of coherence for quantum computational advantage
Fuente:
arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866916997475860480 |
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| author | Thomas, Hugo Emeriau, Pierre-Emmanuel Mezher, Rawad Kashefi, Elham Ollivier, Harold Chabaud, Ulysse |
| author_facet | Thomas, Hugo Emeriau, Pierre-Emmanuel Mezher, Rawad Kashefi, Elham Ollivier, Harold Chabaud, Ulysse |
| contents | Quantifying the resources available to a quantum computer appears to be necessary to separate quantum from classical computation. Among them, entanglement, nonstabilizerness and coherence are arguably of great significance. We introduce path coherence as a measure of the coherent paths interferences arising in a quantum computation. Leveraging the sum-over-paths formalism, we obtain a classical algorithm for estimating quantum transition amplitudes, the complexity of which scales with path coherence. As path coherence relates to the hardness of classical estimation of quantum transition amplitudes, it provides a new perspective on the role of coherence in quantum computational advantage. Beyond their fundamental significance, our results have practical applications for simulating large classes of quantum computations with classical computers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07024 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the role of coherence for quantum computational advantage Thomas, Hugo Emeriau, Pierre-Emmanuel Mezher, Rawad Kashefi, Elham Ollivier, Harold Chabaud, Ulysse Quantum Physics Quantifying the resources available to a quantum computer appears to be necessary to separate quantum from classical computation. Among them, entanglement, nonstabilizerness and coherence are arguably of great significance. We introduce path coherence as a measure of the coherent paths interferences arising in a quantum computation. Leveraging the sum-over-paths formalism, we obtain a classical algorithm for estimating quantum transition amplitudes, the complexity of which scales with path coherence. As path coherence relates to the hardness of classical estimation of quantum transition amplitudes, it provides a new perspective on the role of coherence in quantum computational advantage. Beyond their fundamental significance, our results have practical applications for simulating large classes of quantum computations with classical computers. |
| title | On the role of coherence for quantum computational advantage |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2410.07024 |