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Quantum complexity and the virial theorem

Bao, Ning and Liu, Junyu (2018) Quantum complexity and the virial theorem. Journal of High Energy Physics, 2018 (8). Art. No. 144. ISSN 1126-6708. http://resolver.caltech.edu/CaltechAUTHORS:20180823-140218375

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/JHEP08(2018)144DOIArticle
https://arxiv.org/abs/1804.03242arXivDiscussion Paper
ORCID:
AuthorORCID
Bao, Ning0000-0002-3296-1039
Liu, Junyu0000-0003-1669-8039
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.
Group:IQIM, Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
NSF82248-13067-44-PHPXH
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSFPHY-1125565
Gordon and Betty Moore FoundationGBMF-2644
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
SCOAP3UNSPECIFIED
Subject Keywords:AdS-CFT Correspondence, Black Holes, Random Systems
Record Number:CaltechAUTHORS:20180823-140218375
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180823-140218375
Official Citation:Bao, N. & Liu, J. J. High Energ. Phys. (2018) 2018: 144. https://doi.org/10.1007/JHEP08(2018)144
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:89094
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:23 Aug 2018 21:10
Last Modified:23 Aug 2018 21:10

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