Continuous theory of operator expansions of finite dimensional Hilbert spaces, continuous structures of quantum circuits and decidability

2018/05/06 by А. А. Иванов, Ivanov, A.
Computer Science · Mathematics · #03B50 #03B70 #03C52 #03C57 #20E26 #Advanced Algebra and Logic #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1805.03070

openalex publication_date 2018/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider continuous structures which are obtained from finite dimensional Hilbert spaces over 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).

Related

• Continuous structures of quantum circuits
• Quantum Logic and Quantum Computation
• Approximation by Quantum Circuits
• Strongly continuous representations in the Hilbert space: a far-reaching\n concept
• Dirac - von Neumann axioms in the setting of Continuous Model Theory