有限随机和量子过程的计算
Computation in Finitary Stochastic and Quantum Processes
摘要：
我们引入随机和量子有限状态传感器作为经典随机和量子有限过程的计算理论模型。通过适当的专门化来识别和生成表示过程行为分布的形式化过程语言。我们的特点和比较确定性和非确定性的版本，总结他们的相对计算能力的层次结构的有限过程语言。量子有限态转换器和发生器是对单个重复测量的量子动力学系统进行计算理论分析的第一步。它们通过几个物理系统进行探索，包括迭代分束器，磁场中的原子和离子阱中的原子-其中一个特殊情况实现了Deutsch量子算法。我们表明，这些系统的行为，因此他们的信息处理能力，敏感地依赖于测量协议。
英文摘要：
We introduce stochastic and quantum finite-state transducers as computation-theoretic models of classical stochastic and quantum finitary processes. Formal process languages, representing the distribution over a process's behaviors, are recognized and generated by suitable specializations. We characterize and compare deterministic and nondeterministic versions, summarizing their relative computational power in a hierarchy of finitary process languages. Quantum finite-state transducers and generators are a first step toward a computation-theoretic analysis of individual, repeatedly measured quantum dynamical systems. They are explored via several physical systems, including an iterated beam splitter, an atom in a magnetic field, and atoms in an ion trap--a special case of which implements the Deutsch quantum algorithm. We show that these systems' behaviors, and so their information processing capacity, depends sensitively on the measurement protocol.
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