量子迭代深化及其在Halting问题中的应用
Quantum Iterative Deepening with an application to the Halting problem
摘要：
经典的计算模型传统上采用停机方案来查询计算的状态。在这种方案中，计算过程负责通过设置停止位来发出计算结束的信号，这需要由观察者系统地检查。量子计算模型对叠加态进行运算的能力需要另一种方法。从量子的角度来看，任何等效halt量子比特的测量都有可能通过引发状态之间的随机崩溃来固有地干扰计算。这个问题是加剧了不可判定的问题，如\textit{Entscheidungsproblem}，它需要通用的计算模型，\textit{e.g.}的经典图灵机，能够进行无限期。在这项工作中，我们提出了另一种观点的量子计算的基础上生产系统理论结合格罗弗的振幅放大计划，允许（1）检测停止状态，而不干扰计算的最终结果;（2）非终止计算的可能性和（3）固有的加速发生在计算过程中容易并行化。我们讨论如何可以采用这样的策略，以模拟经典图灵机。
英文摘要：
Classical models of computation traditionally resort to halting schemes in order to enquire about the state of a computation. In such schemes, a computational process is responsible for signalling an end of a calculation by setting a halt bit, which needs to be systematically checked by an observer. The capacity of quantum computational models to operate on a superposition of states requires an alternative approach. From a quantum perspective, any measurement of an equivalent halt qubit would have the potential to inherently interfere with the computation by provoking a random collapse amongst the states. This issue is exacerbated by undecidable problems such as the \textit{Entscheidungsproblem} which require universal computational models, \textit{e.g.} the classical Turing machine, to be able to proceed indefinitely. In this work we present an alternative view of quantum computation based on production system theory in conjunction with Grover's amplitude amplification scheme that allows for (1) a detection of halt states without interfering with the final result of a computation; (2) the possibility of non-terminating computation and (3) an inherent speedup to occur during computations susceptible of parallelization. We discuss how such a strategy can be employed in order to simulate classical Turing machines.
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