用于量子纠错和密度分类的量子元胞自动机
Quantum cellular automata for quantum error correction and density classification
AI总结：
本文针对量子元胞自动机能否纠错的开放问题，基于经典局部多数投票与两线投票规则设计两台准一维量子元胞自动机，并通过逻辑比特翻转前的更新步数模拟验证其量子存储性能。
摘要：
量子元胞自动机是替代量子图灵机和量子线路的量子计算范式。其工作机制本质上是自动化的，因此无需测量，并以平移不变的方式作用于寄存器的所有元胞/量子位，生成一条局部更新元胞状态的全局规则，即仅基于其相邻元胞的状态进行更新。尽管这些特性在许多应用中颇具吸引力，但目前普遍尚不清楚这些完全自动化的离散时间局部更新能在多大程度上于其所作用的（含噪）系统中产生并维持长程有序。特别是，量子元胞自动机能否以及如何执行量子纠错，仍是悬而未决的问题。我们通过提出具备量子纠错能力的量子元胞自动机来弥合这一概念空白。我们基于具有密度分类能力的已知经典元胞自动机规则，即局部多数投票和两线投票，设计并研究了两台（准）一维量子元胞自动机。我们通过模拟其所作用的逻辑信息遭受一次逻辑比特翻转所需的更新步数，考察这些量子元胞自动机作为量子存储组件的性能。所提出的设计为进一步探索具有内建量子纠错能力的新型量子元胞自动机的潜力铺平了道路。
英文摘要：
Quantum cellular automata are alternative quantum-computing paradigms to quantum Turing machines and quantum circuits. Their working mechanisms are inherently automated, therefore measurement free, and they act in a translation invariant manner on all cells/qudits of a register, generating a global rule that updates cell states locally, i.e., based solely on the states of their neighbors. Although desirable features in many applications, it is generally not clear to which extent these fully automated discrete-time local updates can generate and sustain long-range order in the (noisy) systems they act upon. In special, whether and how quantum cellular automata can perform quantum error correction remain open questions. We close this conceptual gap by proposing quantum cellular automata with quantum-error-correction capabilities. We design and investigate two (quasi-)one dimensional quantum cellular automata based on known classical cellular-automata rules with density-classification capabilities, namely the local majority voting and the two-line voting. We investigate the performances of those quantum cellular automata as quantum-memory components by simulating the number of update steps required for the logical information they act upon to be afflicted by a logical bit flip. The proposed designs pave a way to further explore the potential of new types of quantum cellular automata with built-in quantum error correction capabilities.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
