Floquet Codes without Parent Subsystem Codes
We propose a new class of error-correcting dynamic codes in two and three dimensions that has no explicit connection to any parent subsystem code. The two-dimensional code, which we call the CSS (Calderbank-Shor-Steane) honeycomb code, is geometrically similar to that of the honeycomb code by Hastin...
| Main Authors: | , , |
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| Format: | Article |
| Language: | en_US |
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American Physical Society (APS)
2024
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| Online Access: | https://hdl.handle.net/1721.1/153485 |
| _version_ | 1811094896157655040 |
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| author | Davydova, Margarita Tantivasadakarn, Nathanan Balasubramanian, Shankar |
| author_facet | Davydova, Margarita Tantivasadakarn, Nathanan Balasubramanian, Shankar |
| author_sort | Davydova, Margarita |
| collection | MIT |
| description | We propose a new class of error-correcting dynamic codes in two and three dimensions that has no explicit connection to any parent subsystem code. The two-dimensional code, which we call the CSS (Calderbank-Shor-Steane) honeycomb code, is geometrically similar to that of the honeycomb code by Hastings and Haah and also dynamically embeds an instantaneous toric code. However, unlike the honeycomb code, it possesses an explicit CSS structure and its gauge checks do not form a subsystem code. Nevertheless, we show that our dynamic protocol conserves logical information and possesses a threshold for error correction. We generalize this construction to three dimensions and obtain a code that fault tolerantly alternates between realizing two type-I fracton models, the checkerboard and the X-cube model. Finally, we show the compatibility of our CSS honeycomb-code protocol and the honeycomb code by showing the possibility of randomly switching between the two protocols without information loss while still measuring error syndromes. We call this more general aperiodic structure “dynamic tree codes,” which we also generalize to three dimensions. We construct a probabilistic finite automaton prescription that generates dynamic tree codes correcting any single-qubit Pauli errors and can be viewed as a step toward the development of practical fault-tolerant random codes. |
| first_indexed | 2024-09-23T16:07:12Z |
| format | Article |
| id | mit-1721.1/153485 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:07:12Z |
| publishDate | 2024 |
| publisher | American Physical Society (APS) |
| record_format | dspace |
| spelling | mit-1721.1/1534852024-02-10T03:04:37Z Floquet Codes without Parent Subsystem Codes Davydova, Margarita Tantivasadakarn, Nathanan Balasubramanian, Shankar General Physics and Astronomy Mathematical Physics Applied Mathematics Electronic, Optical and Magnetic Materials Electrical and Electronic Engineering General Computer Science We propose a new class of error-correcting dynamic codes in two and three dimensions that has no explicit connection to any parent subsystem code. The two-dimensional code, which we call the CSS (Calderbank-Shor-Steane) honeycomb code, is geometrically similar to that of the honeycomb code by Hastings and Haah and also dynamically embeds an instantaneous toric code. However, unlike the honeycomb code, it possesses an explicit CSS structure and its gauge checks do not form a subsystem code. Nevertheless, we show that our dynamic protocol conserves logical information and possesses a threshold for error correction. We generalize this construction to three dimensions and obtain a code that fault tolerantly alternates between realizing two type-I fracton models, the checkerboard and the X-cube model. Finally, we show the compatibility of our CSS honeycomb-code protocol and the honeycomb code by showing the possibility of randomly switching between the two protocols without information loss while still measuring error syndromes. We call this more general aperiodic structure “dynamic tree codes,” which we also generalize to three dimensions. We construct a probabilistic finite automaton prescription that generates dynamic tree codes correcting any single-qubit Pauli errors and can be viewed as a step toward the development of practical fault-tolerant random codes. 2024-02-09T18:01:39Z 2024-02-09T18:01:39Z 2023-06-13 Article http://purl.org/eprint/type/JournalArticle 2691-3399 https://hdl.handle.net/1721.1/153485 Davydova, Margarita, Tantivasadakarn, Nathanan and Balasubramanian, Shankar. 2023. "Floquet Codes without Parent Subsystem Codes." 4 (2). en_US 10.1103/prxquantum.4.020341 Creative Commons Attribution https://creativecommons.org/licenses/by/4.0/ application/pdf American Physical Society (APS) American Physical Society |
| spellingShingle | General Physics and Astronomy Mathematical Physics Applied Mathematics Electronic, Optical and Magnetic Materials Electrical and Electronic Engineering General Computer Science Davydova, Margarita Tantivasadakarn, Nathanan Balasubramanian, Shankar Floquet Codes without Parent Subsystem Codes |
| title | Floquet Codes without Parent Subsystem Codes |
| title_full | Floquet Codes without Parent Subsystem Codes |
| title_fullStr | Floquet Codes without Parent Subsystem Codes |
| title_full_unstemmed | Floquet Codes without Parent Subsystem Codes |
| title_short | Floquet Codes without Parent Subsystem Codes |
| title_sort | floquet codes without parent subsystem codes |
| topic | General Physics and Astronomy Mathematical Physics Applied Mathematics Electronic, Optical and Magnetic Materials Electrical and Electronic Engineering General Computer Science |
| url | https://hdl.handle.net/1721.1/153485 |
| work_keys_str_mv | AT davydovamargarita floquetcodeswithoutparentsubsystemcodes AT tantivasadakarnnathanan floquetcodeswithoutparentsubsystemcodes AT balasubramanianshankar floquetcodeswithoutparentsubsystemcodes |