Continuous structures of quantum circuits
Aleksander Ivanov
TL;DR
This paper explores the continuous mathematical structures derived from finite-dimensional quantum systems, focusing on their logical properties and algorithmic problems related to quantum automata and circuits.
Contribution
It introduces a framework for analyzing continuous structures in quantum computing, connecting finite-dimensional Hilbert spaces with logical and algorithmic questions.
Findings
Characterization of continuous structures from quantum systems
Analysis of algorithmic problems in quantum automata
Framework for logical analysis of quantum circuits
Abstract
We consider continuous structures which are obtained from finite dimensional Hilbert spaces over by adding some unitary operators. Quantum automata and quantum circuits are naturally interpretable in such structures. We consider appropriate algorithmic problems concerning continuous theories of natural classes of these structures.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Computability, Logic, AI Algorithms · Complexity and Algorithms in Graphs