Finite-rate sparse quantum codes aplenty
We introduce a methodology for generating random multi-qubit stabilizer codes based on solving a constraint satisfaction problem (CSP) on random bipartite graphs. This framework allows us to enforce stabilizer commutation, $X/Z$ balancing, finite rate, sparsity, and maximum-degree constraints simult...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2023-04-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2023-04-20-985/pdf/ |
| _version_ | 1797843488983744512 |
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| author | Maxime Tremblay Guillaume Duclos-Cianci Stefanos Kourtis |
| author_facet | Maxime Tremblay Guillaume Duclos-Cianci Stefanos Kourtis |
| author_sort | Maxime Tremblay |
| collection | DOAJ |
| description | We introduce a methodology for generating random multi-qubit stabilizer codes based on solving a constraint satisfaction problem (CSP) on random bipartite graphs. This framework allows us to enforce stabilizer commutation, $X/Z$ balancing, finite rate, sparsity, and maximum-degree constraints simultaneously in a CSP that we can then solve numerically. Using a state-of-the-art CSP solver, we obtain convincing evidence for the existence of a satisfiability threshold. Furthermore, the extent of the satisfiable phase increases with the number of qubits. In that phase, finding sparse codes becomes an easy problem. Moreover, we observe that the sparse codes found in the satisfiable phase practically achieve the channel capacity for erasure noise. Our results show that intermediate-size finite-rate sparse quantum codes are easy to find, while also demonstrating a flexible methodology for generating good codes with custom properties. We therefore establish a complete and customizable pipeline for random quantum code discovery. |
| first_indexed | 2024-04-09T17:07:05Z |
| format | Article |
| id | doaj.art-1aeaf2997139485784c6027c9d7d6af0 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-04-09T17:07:05Z |
| publishDate | 2023-04-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-1aeaf2997139485784c6027c9d7d6af02023-04-20T12:33:31ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2023-04-01798510.22331/q-2023-04-20-98510.22331/q-2023-04-20-985Finite-rate sparse quantum codes aplentyMaxime TremblayGuillaume Duclos-CianciStefanos KourtisWe introduce a methodology for generating random multi-qubit stabilizer codes based on solving a constraint satisfaction problem (CSP) on random bipartite graphs. This framework allows us to enforce stabilizer commutation, $X/Z$ balancing, finite rate, sparsity, and maximum-degree constraints simultaneously in a CSP that we can then solve numerically. Using a state-of-the-art CSP solver, we obtain convincing evidence for the existence of a satisfiability threshold. Furthermore, the extent of the satisfiable phase increases with the number of qubits. In that phase, finding sparse codes becomes an easy problem. Moreover, we observe that the sparse codes found in the satisfiable phase practically achieve the channel capacity for erasure noise. Our results show that intermediate-size finite-rate sparse quantum codes are easy to find, while also demonstrating a flexible methodology for generating good codes with custom properties. We therefore establish a complete and customizable pipeline for random quantum code discovery.https://quantum-journal.org/papers/q-2023-04-20-985/pdf/ |
| spellingShingle | Maxime Tremblay Guillaume Duclos-Cianci Stefanos Kourtis Finite-rate sparse quantum codes aplenty Quantum |
| title | Finite-rate sparse quantum codes aplenty |
| title_full | Finite-rate sparse quantum codes aplenty |
| title_fullStr | Finite-rate sparse quantum codes aplenty |
| title_full_unstemmed | Finite-rate sparse quantum codes aplenty |
| title_short | Finite-rate sparse quantum codes aplenty |
| title_sort | finite rate sparse quantum codes aplenty |
| url | https://quantum-journal.org/papers/q-2023-04-20-985/pdf/ |
| work_keys_str_mv | AT maximetremblay finiteratesparsequantumcodesaplenty AT guillaumeducloscianci finiteratesparsequantumcodesaplenty AT stefanoskourtis finiteratesparsequantumcodesaplenty |