有限维希尔伯特空间算子展开的连续理论、量子电路的连续结构和可判定性
Continuous theory of operator expansions of finite dimensional Hilbert spaces, continuous structures of quantum circuits and decidability
摘要：
考虑了$\mathbb{C}$上有限维希尔伯特空间通过加入一些酉算子而得到的连续结构.量子自动机和电路在这样的结构中自然是可解释的。我们认为适当的算法问题，这些结构的自然类的连续理论。我们将它们与度量组近似的主题联系起来。本文对A. Ivanov，“Continuous structures of quantum circuits”，arXiv：1406.4635。替换版本包含一个新章节（第4.4节）。
英文摘要：
We consider continuous structures which are obtained from finite dimensional Hilbert spaces over $\mathbb{C}$ by adding some unitary operators. Quantum automata and circuits are naturally interpretable in such structures. We consider appropriate algorithmic problems concerning continuous theories of natural classes of these structures. We connect them with the topic of approximations by metric groups. This paper extends and corrects the paper A. Ivanov, "Continuous structures of quantum circuits", arXiv: 1406.4635. Replacing version contains a new section (Section 4.4).
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