{"title":"从神奇状态蒸馏到动力系统","authors":"Yunzhe Zheng, Dong E. Liu","doi":"10.22331/q-2025-09-15-1858","DOIUrl":null,"url":null,"abstract":"Magic State Distillation (MSD) has been a research focus for fault-tolerant quantum computing due to the need for non-Clifford resource in gaining quantum advantage. Although many of the MSD protocols so far are based on stabilizer codes with transversal $T$ gates, there exists quite several protocols that don't fall into this class. Here we propose a method to map MSD protocols to iterative dynamical systems under the framework of stabilizer reduction. With the proposed mapping, we are able to analyze the performance of MSD protocols using techniques from dynamical systems theory, easily simulate the distillation process of input states under arbitrary noise and visualize it using flow diagram. We apply our mapping to common MSD protocols for $|T\\rangle$ state and find some interesting properties: The $[[15, 1, 3]]$ code may distill states corresponding to $\\sqrt{T}$ gate and the $[[5, 1, 3]]$ code can distill the magic state corresponding to the $T$ gate. Besides, we examine the exotic MSD protocols that may distill into other magic states proposed in [Eur. Phys. J. D 70, 55 (2016)] and identify the condition for distillable magic states. We also study new MSD protocols generated by concatenating different codes and numerically demonstrate that concatenation can generate MSD protocols with various magic states. By concatenating efficient codes with exotic codes, we can reduce the overhead of the exotic MSD protocols. We believe our proposed method will be a useful tool for simulating and visualization MSD protocols for canonical MSD protocols on $|T\\rangle$ as well as other unexplored MSD protocols for other states.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"1 1","pages":""},"PeriodicalIF":5.1000,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"From Magic State Distillation to Dynamical Systems\",\"authors\":\"Yunzhe Zheng, Dong E. Liu\",\"doi\":\"10.22331/q-2025-09-15-1858\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Magic State Distillation (MSD) has been a research focus for fault-tolerant quantum computing due to the need for non-Clifford resource in gaining quantum advantage. Although many of the MSD protocols so far are based on stabilizer codes with transversal $T$ gates, there exists quite several protocols that don't fall into this class. Here we propose a method to map MSD protocols to iterative dynamical systems under the framework of stabilizer reduction. With the proposed mapping, we are able to analyze the performance of MSD protocols using techniques from dynamical systems theory, easily simulate the distillation process of input states under arbitrary noise and visualize it using flow diagram. We apply our mapping to common MSD protocols for $|T\\\\rangle$ state and find some interesting properties: The $[[15, 1, 3]]$ code may distill states corresponding to $\\\\sqrt{T}$ gate and the $[[5, 1, 3]]$ code can distill the magic state corresponding to the $T$ gate. Besides, we examine the exotic MSD protocols that may distill into other magic states proposed in [Eur. Phys. J. D 70, 55 (2016)] and identify the condition for distillable magic states. We also study new MSD protocols generated by concatenating different codes and numerically demonstrate that concatenation can generate MSD protocols with various magic states. By concatenating efficient codes with exotic codes, we can reduce the overhead of the exotic MSD protocols. We believe our proposed method will be a useful tool for simulating and visualization MSD protocols for canonical MSD protocols on $|T\\\\rangle$ as well as other unexplored MSD protocols for other states.\",\"PeriodicalId\":20807,\"journal\":{\"name\":\"Quantum\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":5.1000,\"publicationDate\":\"2025-09-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Quantum\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.22331/q-2025-09-15-1858\",\"RegionNum\":2,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quantum","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.22331/q-2025-09-15-1858","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
摘要
由于在获得量子优势的过程中需要使用非clifford资源,Magic State Distillation (MSD)一直是容错量子计算的研究热点。尽管到目前为止,许多MSD协议都是基于具有横向$T$门的稳定器代码,但仍有相当多的协议不属于这一类。本文提出了一种在稳定器约简框架下将MSD协议映射到迭代动力系统的方法。利用所提出的映射,我们能够利用动力系统理论的技术分析MSD协议的性能,轻松地模拟任意噪声下输入状态的蒸馏过程,并使用流程图将其可视化。我们将我们的映射应用于常见的MSD协议$ b| T\rangle$ state,并发现了一些有趣的属性:$[[15,1,3]]$代码可以提取对应于$\sqrt{T}$ gate的状态,$[[5,1,3]]$代码可以提取对应于$T$ gate的魔法状态。此外,我们还研究了可能提炼成[欧洲]中提出的其他神奇状态的外来MSD协议。理论物理。[j] D 70, 55(2016)]并确定可蒸馏魔法状态的条件。我们还研究了通过连接不同的代码生成新的MSD协议,并通过数值证明了连接可以生成具有不同魔力状态的MSD协议。通过将高效代码与外部代码连接起来,我们可以减少外部MSD协议的开销。我们相信我们提出的方法将成为模拟和可视化MSD协议的有用工具,用于$ b| T\rangle$上的规范MSD协议以及其他未开发的其他状态的MSD协议。
From Magic State Distillation to Dynamical Systems
Magic State Distillation (MSD) has been a research focus for fault-tolerant quantum computing due to the need for non-Clifford resource in gaining quantum advantage. Although many of the MSD protocols so far are based on stabilizer codes with transversal $T$ gates, there exists quite several protocols that don't fall into this class. Here we propose a method to map MSD protocols to iterative dynamical systems under the framework of stabilizer reduction. With the proposed mapping, we are able to analyze the performance of MSD protocols using techniques from dynamical systems theory, easily simulate the distillation process of input states under arbitrary noise and visualize it using flow diagram. We apply our mapping to common MSD protocols for $|T\rangle$ state and find some interesting properties: The $[[15, 1, 3]]$ code may distill states corresponding to $\sqrt{T}$ gate and the $[[5, 1, 3]]$ code can distill the magic state corresponding to the $T$ gate. Besides, we examine the exotic MSD protocols that may distill into other magic states proposed in [Eur. Phys. J. D 70, 55 (2016)] and identify the condition for distillable magic states. We also study new MSD protocols generated by concatenating different codes and numerically demonstrate that concatenation can generate MSD protocols with various magic states. By concatenating efficient codes with exotic codes, we can reduce the overhead of the exotic MSD protocols. We believe our proposed method will be a useful tool for simulating and visualization MSD protocols for canonical MSD protocols on $|T\rangle$ as well as other unexplored MSD protocols for other states.
QuantumPhysics and Astronomy-Physics and Astronomy (miscellaneous)
CiteScore
9.20
自引率
10.90%
发文量
241
审稿时长
16 weeks
期刊介绍:
Quantum is an open-access peer-reviewed journal for quantum science and related fields. Quantum is non-profit and community-run: an effort by researchers and for researchers to make science more open and publishing more transparent and efficient.