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 has 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 demonstrate 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.

量子计算已经成为我们这个时代强大的计算媒介，它证明了在分解正整数和搜索数据库方面的卓越效率，比任何目前已知的经典计算算法都要快。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。到目前为止，关于绝热量子系统的所有研究都涉及多项式时界计算，而很少关注例如仅消耗恒定存储空间的绝热量子系统。这种量子系统可以用类似于量子有限自动机的形式建模。本次展览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。作为我们对这个显着但深刻问题的回答，我们首先设计了一个基本平台，以在有限的计算资源（大小、能量、光谱间隙等）下执行绝热进化量子系统（AEQS），然后演示如何构建这样的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建的 AEQS 快速解决的决策问题（以及承诺问题）的基本结构特性。