Quantum computation has emerged as a powerful computational medium of our time, having demonstrated the remarkable efficiency in solving the integer factoring and searching a database 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 (or equivalently, languages) solved quickly by the appropriately constructed AEQSs.

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绝热量子计算如何适应量子自动机理论？

量子计算已经成为我们这个时代强大的计算媒介，在解决整数因子分解和搜索数据库方面的效率显着高于目前已知的任何经典计算算法。已经研究了量子系统的绝热演化作为物理实现量子计算的潜在手段。迄今为止，关于绝热量子系统的所有研究都涉及多项式时限计算，而很少关注例如仅消耗恒定存储空间的绝热量子系统。这种量子系统可以以类似于量子有限自动机的形式建模。这篇论述敢于提出一个大胆的问题，即如何使绝热量子计算适应快速发展的量子自动机理论框架。作为对这个杰出但意义深远的问题的回答，我们首先在有限的计算资源（大小、能量、光谱间隙等）下构建绝热演化量子系统 (AEQS) 的基础平台，然后确定如何构建这样的系统。通过操作合适的量子有限自动机族来实现 AEQS。我们进一步探索了由适当构造的 AEQS 快速解决的决策问题（或等效的语言）的基本结构特性。