Improving the speed of variational quantum algorithms for quantum error correction
We consider the problem of devising suitable quantum error correction (QEC) procedures for a generic quantum noise acting on a quantum circuit. In general, there is no analytic universal procedure to obtain the encoding and correction unitary gates, and the problem is even harder if the noise is unk...
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| Format: | Article |
| Language: | English |
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American Physical Society
2024
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| Online Access: | https://hdl.handle.net/1721.1/153922 |
| _version_ | 1824458056058011648 |
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| author | Zoratti, Fabio De Palma, Giacomo Kiani, Bobak Nguyen, Quynh T. Marvian, Milad Lloyd, Seth Giovannetti, Vittorio |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Zoratti, Fabio De Palma, Giacomo Kiani, Bobak Nguyen, Quynh T. Marvian, Milad Lloyd, Seth Giovannetti, Vittorio |
| author_sort | Zoratti, Fabio |
| collection | MIT |
| description | We consider the problem of devising suitable quantum error correction (QEC) procedures for a generic quantum noise acting on a quantum circuit. In general, there is no analytic universal procedure to obtain the encoding and correction unitary gates, and the problem is even harder if the noise is unknown and has to be reconstructed. The existing procedures rely on variational quantum algorithms (VQAs) and are very difficult to train since the size of the gradient of the cost function decays exponentially with the number of qubits. We address this problem using a cost function based on the quantum Wasserstein distance of order 1 (QW1). At variance with other quantum distances typically adopted in quantum information processing, QW1 lacks the unitary invariance property which makes it a suitable tool to avoid getting trapped in local minima. Focusing on a simple noise model for which an exact QEC solution is known and can be used as a theoretical benchmark, we run a series of numerical tests that show how, guiding the VQA search through the QW1, can indeed significantly increase both the probability of a successful training and the fidelity of the recovered state, with respect to the results one obtains when using conventional approaches. |
| first_indexed | 2024-09-23T11:08:33Z |
| format | Article |
| id | mit-1721.1/153922 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2025-02-19T04:19:49Z |
| publishDate | 2024 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1539222024-12-21T05:47:49Z Improving the speed of variational quantum algorithms for quantum error correction Zoratti, Fabio De Palma, Giacomo Kiani, Bobak Nguyen, Quynh T. Marvian, Milad Lloyd, Seth Giovannetti, Vittorio Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Department of Mechanical Engineering We consider the problem of devising suitable quantum error correction (QEC) procedures for a generic quantum noise acting on a quantum circuit. In general, there is no analytic universal procedure to obtain the encoding and correction unitary gates, and the problem is even harder if the noise is unknown and has to be reconstructed. The existing procedures rely on variational quantum algorithms (VQAs) and are very difficult to train since the size of the gradient of the cost function decays exponentially with the number of qubits. We address this problem using a cost function based on the quantum Wasserstein distance of order 1 (QW1). At variance with other quantum distances typically adopted in quantum information processing, QW1 lacks the unitary invariance property which makes it a suitable tool to avoid getting trapped in local minima. Focusing on a simple noise model for which an exact QEC solution is known and can be used as a theoretical benchmark, we run a series of numerical tests that show how, guiding the VQA search through the QW1, can indeed significantly increase both the probability of a successful training and the fidelity of the recovered state, with respect to the results one obtains when using conventional approaches. 2024-03-22T21:09:41Z 2024-03-22T21:09:41Z 2023-08-18 2024-03-22T20:30:20Z Article http://purl.org/eprint/type/JournalArticle 2469-9926 2469-9934 https://hdl.handle.net/1721.1/153922 Zoratti, Fabio, De Palma, Giacomo, Kiani, Bobak, Nguyen, Quynh T., Marvian, Milad et al. 2023. "Improving the speed of variational quantum algorithms for quantum error correction." Physical Review A, 108 (2). en 10.1103/physreva.108.022611 Physical Review A Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Physical Society American Physical Society |
| spellingShingle | Zoratti, Fabio De Palma, Giacomo Kiani, Bobak Nguyen, Quynh T. Marvian, Milad Lloyd, Seth Giovannetti, Vittorio Improving the speed of variational quantum algorithms for quantum error correction |
| title | Improving the speed of variational quantum algorithms for quantum error correction |
| title_full | Improving the speed of variational quantum algorithms for quantum error correction |
| title_fullStr | Improving the speed of variational quantum algorithms for quantum error correction |
| title_full_unstemmed | Improving the speed of variational quantum algorithms for quantum error correction |
| title_short | Improving the speed of variational quantum algorithms for quantum error correction |
| title_sort | improving the speed of variational quantum algorithms for quantum error correction |
| url | https://hdl.handle.net/1721.1/153922 |
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