一种用于同步有限状态转换系统的量子模型

中文摘要 AI 辅助

我们提出了一个量子模型来寻找重置输入序列（RS），该序列能将有限状态转换系统（FA）带至特定状态，而与当前状态无关。寻找此类序列对各种类型的FA而言复杂度可能为NP难甚至PSPACE完全。为此，我们在量子空间中表示FA的状态、输入和转移函数。接着提出一个模型来表示从初始FA状态开始执行特定长度\(l\)的输入序列。该模型通过考虑将长度为\(l\)的所有输入序列叠加到FA的初始状态进行扩展，还通过考虑将所有输入序列应用于FA的所有初始状态进行进一步扩展，记录每个输入序列应用于FA所有状态后到达的状态集合（有序列表）。然后使用振幅放大算法，它在保留到达这些集合的所有输入序列的同时合并相似的到达状态集合。通过对元素对应相同FA状态的到达集合进行格罗弗搜索为FA提供RS。我们的方法相较于传统暴力方法的指数复杂度有二次增益，传统暴力方法是唯一可应用于一般FA类的方法。作为概念验证，我们在量子模拟器上提供了几个模拟FA的结果。

英文摘要

We propose a quantum model for finding a resetting input sequence (RS) which can take a finite state transition system (FA), to particular state independent of its current state. The complexity of finding such sequences for various types of FA can be NP-Hard or even PSPACE-Complete. To this end, we represent the FA states, inputs, and transition function in quantum space. Accordingly, we propose a model to represent the execution of an input sequence of a particular length $l$ starting form an initial FA state. The model is extended considering the application in superposition of all input sequences of length $l$ to an initial state of the FA. The model is further extended considering the application of all input sequences to all initial states of the FA capturing for every input sequence the collection (ordered list) of states reached by applying the sequence to all states of the FA. The amplitude amplification algorithm is then used as it combines similar collections of reached states while preserving all input sequences that reach these collections. A Grover search for a reached collection where its elements correspond to the same FA state provides a RS for the FA. Our approach offers a quadratic gain over the exponential complexity of traditional brute-force method, which is the only method that can be applied to a general FA class.

发表机构

• Hiroshima City University（广岛市立大学）
• Aemerican University of Sharjah（沙迦美国大学）
• University of Lancaster（兰开斯特大学）

机构由 AI 辅助整理，请以论文原文为准。

补充信息

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13 pages, 7 Figures