M. Davydova, Nathanan Tantivasadakarn, S. Balasubramanian
{"title":"没有父子系统代码的Floquet代码","authors":"M. Davydova, Nathanan Tantivasadakarn, S. Balasubramanian","doi":"10.1103/PRXQuantum.4.020341","DOIUrl":null,"url":null,"abstract":"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 Floquet 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 Floquet 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 towards the development of practical fault-tolerant random codes.","PeriodicalId":74587,"journal":{"name":"PRX quantum : a Physical Review journal","volume":null,"pages":null},"PeriodicalIF":9.3000,"publicationDate":"2022-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"20","resultStr":"{\"title\":\"Floquet Codes without Parent Subsystem Codes\",\"authors\":\"M. Davydova, Nathanan Tantivasadakarn, S. Balasubramanian\",\"doi\":\"10.1103/PRXQuantum.4.020341\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"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 Floquet 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 Floquet 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 towards the development of practical fault-tolerant random codes.\",\"PeriodicalId\":74587,\"journal\":{\"name\":\"PRX quantum : a Physical Review journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":9.3000,\"publicationDate\":\"2022-10-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"20\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"PRX quantum : a Physical Review journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1103/PRXQuantum.4.020341\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"PHYSICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"PRX quantum : a Physical Review journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1103/PRXQuantum.4.020341","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, APPLIED","Score":null,"Total":0}
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 Floquet 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 Floquet 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 towards the development of practical fault-tolerant random codes.