Quantum Fibrations: Quantum Computation on an Arbitrary Topological Space
Date
2024-07-10
Authors
Ikeda, Kazuki
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Springer
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Abstract
Using operator algebras, we extend the theory of quantum computation on a graph to a theory of computation on an arbitrary topological space. Quantum computation is usually implemented on finite discrete sets, and the purpose of this study is to extend this to theories on arbitrary sets. The conventional theory of quantum computers can be viewed as a simplified algebraic geometry theory in which the action of SU(2) is defined on each point of a discrete set. In this study, we extend this in general as a theory of quantum fibrations in which the action of the von Neumann algebra is defined on an arbitrary topological space. The quantum channel is then naturally extended as a net of von Neumann algebras. This allows for a more mathematically rigorous discussion of general theories, including physics and chemistry, which are defined on sets that are not necessarily discrete, from the perspective of quantum computer science.
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This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s10114-024-3338-0.
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Keywords
Quantum computation, operator algebra, von Neumann algebra, fibration, quantum computational chemistry, complexity theory
Citation
Ikeda, K. Quantum Fibrations: Quantum Computation on an Arbitrary Topological Space. Acta. Math. Sin.-English Ser. (2024). https://doi.org/10.1007/s10114-024-3338-0
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Citation
Ikeda, K. Quantum Fibrations: Quantum Computation on an Arbitrary Topological Space. Acta. Math. Sin.-English Ser. (2024). https://doi.org/10.1007/s10114-024-3338-0
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DOI
10.1007/s10114-024-3338-0