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The Second Law of Quantum Complexity
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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 $2^K$ 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.
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Forward citations
Cited by 6 Pith papers
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Quantum complexity measures applied to the Schwinger model reveal nonlocal correlations along the string and show that entanglement and magic give complementary views of string formation and breaking.
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A timelike quantum focusing conjecture implies a complexity-based quantum strong energy condition and a complexity bound analogous to the covariant entropy bound for suitable codimension-0 field theory complexity measures.
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Krylov Complexity
Krylov complexity is a canonical, parameter-independent measure of operator spreading that probes chaotic dynamics to late times and admits a geometric interpretation in holographic duals.
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