In this paper, we introduce classically time-controlled quantum automata or CTQA, which is a reasonable modification of Moore-Crutchfield quantum finite automata that uses time-dependent evolution and a "scheduler" defining how long each Hamiltonian will run. Surprisingly enough, time-dependent evolution provides a significant change in the computational power of quantum automata with respect to a discrete quantum model. Indeed, we show that if a scheduler is not computationally restricted, then a CTQA can decide the Halting problem. In order to unearth the computational capabilities of CTQAs we study the case of a computationally restricted scheduler. In particular, we showed that depending on the type of restriction imposed on the scheduler, a CTQA can (i) recognize non-regular languages with cut-point, even in the presence of Karp-Lipton advice, and (ii) recognize non-regular promise languages with bounded-error. Furthermore, we study the cutpoint-union of cutpoint languages by introducing a new model of Moore-Crutchfield quantum finite automata with a rotating tape head. CTQA presents itself as a new model of computation that provides a different approach to a formal study of "classical control, quantum data" schemes in quantum computing.
翻译:在本文中,我们引入了传统时间控制的量子自动数据或 CTQA, 这是一种对摩尔- 克鲁奇菲尔德量子有限量子自动数据的合理修改, 它使用时间的进化, 并使用一个“ 缓冲” 来定义每个汉密尔顿人要运行多久。 令人惊讶的是, 时间的进化为量子离散模型的量子自动数据计算能力提供了巨大的变化。 事实上, 我们显示, 如果一个定时器没有计算上的限制, 那么CTQA就可以决定停止的问题。 为了挖掘计算限制排程的摩尔- 克鲁奇菲尔德的计算能力, 我们研究了计算限制排程的计算器案例。 特别是, 我们显示, CTQA 取决于对排程的限制类型, CTQA 可以( 一) 承认带有切分点的不固定语言的计算能力。 即便存在Karp- Lipton 的建议, 并且 (二) 承认非定期的承诺语言与约束的高度。 此外, 我们研究切割点语言的切合点组合语言, 我们通过引入一个新的摩质- Cruggrchfielfal- celchalalalalal acal comcal acal decal commaxal maxal decal decal maxal maxal maxal maxal acal maxal maxal acal maxal maxal acal maxal maxalgal 。