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Published August 2018 | Submitted + Published
Journal Article Open

Quantum complexity and the virial theorem

Abstract

It is conjectured that in the geometric formulation of quantum computing, one can study quantum complexity through classical entropy of statistical ensembles established non-relativistically in the group manifold of unitary operators. The kinetic and positional decompositions of statistical entropy are conjectured to correspond to the Kolmogorov complexity and computational complexity, respectively, of corresponding quantum circuits. In this paper, we claim that by applying the virial theorem to the group manifold, one can derive a generic relation between Kolmogorov complexity and computational complexity in the thermal equilibrium.

Additional Information

© The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: May 16, 2018; Revised: July 30, 2018; Accepted: August 20, 2018; Published: August 23, 2018. We thank Elizabeth Crosson, Beni Yoshida, Nicole Yunger Halpern and Shangnan Zhou for helpful discussions. We thank the anonymous JHEP referee for valuable communications. NB is supported by the National Science Foundation, under grant number 82248-13067-44-PHPXH. JL is supported in part by the Institute for Quantum Information and Matter (IQIM), an NSF Physics Frontiers Center (NSF Grant PHY-1125565) with support from the Gordon and Betty Moore Foundation (GBMF-2644), and by the Walter Burke Institute for Theoretical Physics.

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Published - Bao-Liu2018_Article_QuantumComplexityAndTheVirialT.pdf

Submitted - 1804.03242.pdf

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August 19, 2023
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