Classical certification of quantum gates under the dimension assumption
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913985975025664 |
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| author | Nöller, Jan Miklin, Nikolai Kliesch, Martin Gachechiladze, Mariami |
| author_facet | Nöller, Jan Miklin, Nikolai Kliesch, Martin Gachechiladze, Mariami |
| contents | The rapid advancement of quantum hardware necessitates the development of reliable methods to certify its correct functioning. However, existing certification tests fall short, as they either suffer from systematic errors or do not guarantee that only a correctly functioning quantum device can pass the test. We introduce a certification method for quantum gates tailored for a practical server-user scenario, where a classical user tests the results of exact quantum computations performed by a quantum server. This method is free from the systematic state preparation and measurement (SPAM) errors. For single-qubit gates, including those that form a universal set for single-qubit quantum computation, we demonstrate that our approach offers soundness guarantees based solely on the dimension assumption. Additionally, for a highly-relevant phase gate - which corresponds experimentally to a $π/2$-pulse - we prove that the method's sample complexity scales as $\mathrm{O}(\varepsilon^{-1})$ relative to the average gate infidelity $\varepsilon$. By combining the SPAM-error-free and sound notion of certification with practical applicability, our approach paves the way for promising research into efficient and reliable certification methods for full-scale quantum computation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17006 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classical certification of quantum gates under the dimension assumption Nöller, Jan Miklin, Nikolai Kliesch, Martin Gachechiladze, Mariami Quantum Physics The rapid advancement of quantum hardware necessitates the development of reliable methods to certify its correct functioning. However, existing certification tests fall short, as they either suffer from systematic errors or do not guarantee that only a correctly functioning quantum device can pass the test. We introduce a certification method for quantum gates tailored for a practical server-user scenario, where a classical user tests the results of exact quantum computations performed by a quantum server. This method is free from the systematic state preparation and measurement (SPAM) errors. For single-qubit gates, including those that form a universal set for single-qubit quantum computation, we demonstrate that our approach offers soundness guarantees based solely on the dimension assumption. Additionally, for a highly-relevant phase gate - which corresponds experimentally to a $π/2$-pulse - we prove that the method's sample complexity scales as $\mathrm{O}(\varepsilon^{-1})$ relative to the average gate infidelity $\varepsilon$. By combining the SPAM-error-free and sound notion of certification with practical applicability, our approach paves the way for promising research into efficient and reliable certification methods for full-scale quantum computation. |
| title | Classical certification of quantum gates under the dimension assumption |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2401.17006 |