绝热量子计算如何融入量子自动机理论？
How Does Adiabatic Quantum Computation Fit into Quantum Automata Theory?
AI总结：
本研究针对绝热量子计算与量子自动机理论的融合问题，搭建受限资源的绝热演化量子系统基础平台，提出用量子有限自动族群构建该系统的方法，并探究其求解问题的结构性质。
摘要：
量子计算已成为当代强大的计算媒介，在正整数分解和数据库搜索方面展现出远超目前已知经典计算算法的显著效率。量子系统的绝热演化已被研究作为物理实现量子计算的一种潜在途径。截至目前，所有绝热量子系统的研究都围绕多项式时间有界计算展开，对仅消耗常数内存空间的绝热量子系统等方向关注甚少。这类量子系统可以用类似量子有限自动机的形式建模。本阐述大胆提出一个问题：如何让绝热量子计算融入快速发展的量子自动机理论框架？作为对这一重要且深刻问题的解答，我们首先搭建了一个基础平台，用于实现计算资源（规模、能量、谱隙等）受限的绝热演化量子系统（AEQSs），随后论证了如何通过运行合适的量子有限自动族群来构建此类AEQSs。我们进一步探究了由恰当构建的AEQSs快速求解的判定问题（以及promise问题）的基本结构性质。
英文摘要：
Quantum computation has emerged as a powerful computational medium of our time, having demonstrated the remarkable efficiency in factoring a positive integer and searching databases faster than any currently known classical computing algorithm. Adiabatic evolution of quantum systems have been studied as a potential means that physically realizes quantum computation. Up to now, all the research on adiabatic quantum systems has dealt with polynomial time-bounded computation and little attention has been paid to, for instance, adiabatic quantum systems consuming only constant memory space. Such quantum systems can be modeled in a form similar to quantum finite automata. This exposition dares to ask a bold question of how to make adiabatic quantum computation fit into the rapidly progressing framework of quantum automata theory. As our answer to this eminent but profound question, we first lay out a fundamental platform to carry out adiabatic evolutionary quantum systems (AEQSs) with limited computational resources (in size, energy, spectral gap, etc.) and then establish how to construct such AEQSs by operating suitable families of quantum finite automata. We further explore fundamental structural properties of decision problems (as well as promise problems) solved quickly by the appropriately constructed AEQSs.
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