强泛量子图灵机与Kolmogorov复杂性不变性
Strongly Universal Quantum Turing Machines and Invariance of Kolmogorov Complexity
摘要：
我们证明了存在一个通用的量子图灵机（UQTM），它可以模拟每一个其他的QTM，直到其他QTM已经停止，然后以概率1停止自己。这扩展了Bernstein和Vazirani的工作，他们已经证明存在一个UQTM，可以模拟任意但预先分配的时间步长的每一个其他QTM。作为这个结果的推论，我们给出了严格的证明，量子Kolmogorov复杂性定义的Berthiaume等人。是不变的，即取决于选择的UQTM只有一个附加常数。我们的证明是基于一个新的数学框架QTM，包括彻底分析其停机行为。我们引入相互正交的停顿空间的概念，并表明，在输入量子比特串编码的信息总是可以有效地分解成一个经典的和量子的一部分。
英文摘要：
We show that there exists a universal quantum Turing machine (UQTM) that can simulate every other QTM until the other QTM has halted and then halt itself with probability one. This extends work by Bernstein and Vazirani who have shown that there is a UQTM that can simulate every other QTM for an arbitrary, but preassigned number of time steps. As a corollary to this result, we give a rigorous proof that quantum Kolmogorov complexity as defined by Berthiaume et al. is invariant, i.e. depends on the choice of the UQTM only up to an additive constant. Our proof is based on a new mathematical framework for QTMs, including a thorough analysis of their halting behaviour. We introduce the notion of mutually orthogonal halting spaces and show that the information encoded in an input qubit string can always be effectively decomposed into a classical and a quantum part.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
