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| Main Authors: | , , , , , , , , , , , , , , , , , , , , |
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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2408.16914 |
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| _version_ | 1866929479188742144 |
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| author | Miller, Daniel Levi, Kyano Postler, Lukas Steiner, Alex Bittel, Lennart White, Gregory A. L. Tang, Yifan Kuehnke, Eric J. Mele, Antonio A. Khatri, Sumeet Leone, Lorenzo Carrasco, Jose Marciniak, Christian D. Pogorelov, Ivan Guevara-Bertsch, Milena Freund, Robert Blatt, Rainer Schindler, Philipp Monz, Thomas Ringbauer, Martin Eisert, Jens |
| author_facet | Miller, Daniel Levi, Kyano Postler, Lukas Steiner, Alex Bittel, Lennart White, Gregory A. L. Tang, Yifan Kuehnke, Eric J. Mele, Antonio A. Khatri, Sumeet Leone, Lorenzo Carrasco, Jose Marciniak, Christian D. Pogorelov, Ivan Guevara-Bertsch, Milena Freund, Robert Blatt, Rainer Schindler, Philipp Monz, Thomas Ringbauer, Martin Eisert, Jens |
| contents | Throughout its history, the theory of quantum error correction has heavily benefited from translating classical concepts into the quantum setting. In particular, classical notions of weight enumerators, which relate to the performance of an error-correcting code, and MacWilliams' identity, which helps to compute enumerators, have been generalized to the quantum case. In this work, we establish a distinct relationship between the theoretical machinery of quantum weight enumerators and a seemingly unrelated physics experiment: we prove that Rains' quantum shadow enumerators - a powerful mathematical tool - arise as probabilities of observing fixed numbers of triplets in a Bell sampling experiment. This insight allows us to develop here a rigorous framework for the direct measurement of quantum weight enumerators, thus enabling experimental and theoretical studies of the entanglement structure of any quantum error-correcting code or state under investigation. On top of that, we derive concrete sample complexity bounds and physically-motivated robustness guarantees against unavoidable experimental imperfections. Finally, we experimentally demonstrate the possibility of directly measuring weight enumerators on a trapped-ion quantum computer. Our experimental findings are in good agreement with theoretical predictions and illuminate how entanglement theory and quantum error correction can cross-fertilize each other once Bell sampling experiments are combined with the theoretical machinery of quantum weight enumerators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_16914 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Experimental measurement and a physical interpretation of quantum shadow enumerators Miller, Daniel Levi, Kyano Postler, Lukas Steiner, Alex Bittel, Lennart White, Gregory A. L. Tang, Yifan Kuehnke, Eric J. Mele, Antonio A. Khatri, Sumeet Leone, Lorenzo Carrasco, Jose Marciniak, Christian D. Pogorelov, Ivan Guevara-Bertsch, Milena Freund, Robert Blatt, Rainer Schindler, Philipp Monz, Thomas Ringbauer, Martin Eisert, Jens Quantum Physics Throughout its history, the theory of quantum error correction has heavily benefited from translating classical concepts into the quantum setting. In particular, classical notions of weight enumerators, which relate to the performance of an error-correcting code, and MacWilliams' identity, which helps to compute enumerators, have been generalized to the quantum case. In this work, we establish a distinct relationship between the theoretical machinery of quantum weight enumerators and a seemingly unrelated physics experiment: we prove that Rains' quantum shadow enumerators - a powerful mathematical tool - arise as probabilities of observing fixed numbers of triplets in a Bell sampling experiment. This insight allows us to develop here a rigorous framework for the direct measurement of quantum weight enumerators, thus enabling experimental and theoretical studies of the entanglement structure of any quantum error-correcting code or state under investigation. On top of that, we derive concrete sample complexity bounds and physically-motivated robustness guarantees against unavoidable experimental imperfections. Finally, we experimentally demonstrate the possibility of directly measuring weight enumerators on a trapped-ion quantum computer. Our experimental findings are in good agreement with theoretical predictions and illuminate how entanglement theory and quantum error correction can cross-fertilize each other once Bell sampling experiments are combined with the theoretical machinery of quantum weight enumerators. |
| title | Experimental measurement and a physical interpretation of quantum shadow enumerators |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2408.16914 |