How does adiabatic quantum computation fit into quantum automata theory?

Quantum computation has emerged as a powerful computational medium of our time, having demonstrated the remarkable efficiency in factoring positive integer and searching databases faster than any currently known classical computing algorithm. Adiabatic evolution quantum systems been studied potential means that physically realizes computation. Up to now, all research on adiabatic dealt with polynomial time-bounded little attention paid to, for instance, consuming only constant memory space. Such can be modeled form similar finite automata. This exposition dares ask bold question how make fit into rapidly progressing framework automata theory. As answer this eminent but profound question, we first lay out fundamental platform carry evolutionary (AEQSs) limited resources (in size, energy, spectral gap, etc.) then demonstrate construct such AEQSs by operating suitable families We further explore structural properties decision problems (as well promise problems) solved quickly appropriately constructed AEQSs.