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Quantum complexity and the virial theorem

By Ning Bao and Junyu Liu


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

Topics: AdS-CFT Correspondence, Black Holes, Random Systems, Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798
Publisher: SpringerOpen
Year: 2018
DOI identifier: 10.1007/JHEP08(2018)144
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