2017/01/04 by Adam R. Brown, Leonard Susskind · 1 voice · 13 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #gr-qc #hep-th #quant-ph
paper · pdf · doi:10.1103/physrevd.97.086015
arxiv published 2017/01/04 · openalex publication_date 2018/04/25 · arxiv updated 2018/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
We give arguments for the existence of a thermodynamics of quantum complexity that includes a ``second law of complexity.'' To guide us, we derive a correspondence between the computational (circuit) complexity of a quantum system of K qubits, and the positional entropy of a related classical system with 2K degrees of freedom. We also argue that the kinetic entropy of the classical system is equivalent to the Kolmogorov complexity of the quantum Hamiltonian. We observe that the expected pattern of growth of the complexity of the quantum system parallels the growth of entropy of the classical system. We argue that the property of having less-than-maximal complexity (uncomplexity) is a resource that can be expended to perform directed quantum computation. Although this paper is not primarily about black holes, we find a surprising interpretation of the uncomplexity resource as the accessible volume of spacetime behind a black hole horizon.