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On Kolmogorov Complexity of Unitary Transformations in Quantum Computing

Alexei Kaltchenko*

Wilfrid Laurier University, Waterloo, Ontario, Canada.

Periodicity:July - December'2022
DOI : https://doi.org/10.26634/jmat.11.2.19190

Abstract

We introduce a notion of Kolmogorov complexity of unitary transformation, which can (roughly) be understood as the least possible amount of information required to fully describe and reconstruct a given finite unitary transformation. In the context of quantum computing, it corresponds to the least possible amount of data to define and describe a quantum circuit or quantum computer program. Our Kolmogorov complexity of unitary transformation is built upon Kolmogorov "qubit complexity" of Berthiaume, W. Van Dam and S. Laplante via mapping from unitary transformations to unnormalized density operators, which are subsequently "purified" into unnormalized vectors in Hilbert space. We discuss the optimality of our notion of Kolmogorov complexity in a broad sense.

Keywords

Quantum Information Theory, Information Theory, Quantum, Kolmogorov Complexity, Quantum Computing, Quantum Information, Unitary, Quantum State.

How to Cite this Article?

Kaltchenko, A. (2022). On Kolmogorov Complexity of Unitary Transformations in Quantum Computing. i-manager’s Journal on Mathematics, 11(2), 1-7. https://doi.org/10.26634/jmat.11.2.19190

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