标题： 基于同步词的量子重置协议 显示英文标题

标题： Quantum Resetting Protocols Based on Synchronizing Words

摘要： 重置一个系统的状态在物理学、工程学、计算机科学以及许多其他领域中起着基础性作用。 在这里我们关注一种最初在自动机理论中提出的重置方法。 自动机的状态根据一组规则演化。 这些规则形成一个字母表，可以依次应用这些规则。 这样的一系列规则被称为单词。 某些特定的单词，称为同步化单词，能够使系统无论初始配置如何都演化到预定状态。 这一过程本质上是不可逆的，乍一看似乎与量子力学的幺正性相冲突。 幺正演化保留信息，因此禁止这种经典的重置到预定状态的操作。 在这项工作中，我们引入了一种基于量子同步化单词的新重置协议，通过引入辅助量子比特来实现，这些辅助量子比特的状态编码了自动机字母表中的规则。 我们进一步提出了一个量子电路来实现该协议，并且可以在量子计算机上实现。 此外，我们还建立了这种方法与Kraus通道之间的联系，表明量子同步化单词可以通过不显式参考辅助量子比特的状态来实现。 我们的结果连接了经典和量子同步化单词的概念，揭示了量子信息处理与非幺正动力学之间的相互作用。 显示英文摘要

摘要： Resetting a system's state plays a fundamental role in physics, engineering, computer science, and many other fields. Here we focus on a method originally proposed in automata theory. The state of an automaton evolves according to a set of rules. These rules form an alphabet, and one can apply these rules one after another. Such a sequence of rules is known as a word. Some particular words, known as synchronizing words, enable a system to evolve into a predetermined state regardless of its initial configuration. This process, which is inherently irreversible, appears at first glance to be incompatible with the unitarity of quantum mechanics. Unitary evolution preserves information, hence forbids such classical resetting to a predetermined state. In this work, we introduce a novel resetting protocol based on quantum-synchronizing words by incorporating auxiliary qubits whose states encode rules of the automaton's alphabet. We further propose a quantum circuit that realizes this protocol and can be implemented on a quantum computer. Additionally, we establish a connection between this approach and Kraus channels, showing that quantum synchronizing words can be achieved without explicit reference to the states of ancillary qubits. Our results bridge classical and quantum notions of synchronizing words, shedding light on the interplay between quantum information processing and non-unitary dynamics.