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• W2984865113 abstract "For any quantum algorithm given by a path in the space of unitary operators we define the computational complexity as the typical computational time associated with the path. This time is defined using a quantum time estimator associated with the path. This quantum time estimator is fully characterized by the Lyapunov generator of the path and the corresponding quantum Fisher information. The computational metric associated with this definition of computational complexity leads to a natural characterization of cost factors on the Lie algebra generators. Operator complexity growth in time is analyzed from this perspective leading to a simple characterization of the Lyapunov exponent in the case of chaotic Hamiltonians. The connection between complexity and entropy is expressed using the relation between quantum Fisher information about quantum time estimation and von Neumann entropy. This relation suggests a natural bound on computational complexity that generalizes the standard time energy quantum uncertainty. The connection between Lyapunov and modular Hamiltonian is briefly discussed. In the case of theories with holographic duals and for those reduced density matrix defined by tracing over a bounded region of the bulk, quantum estimation theory is crucial to estimate quantum mechanically the geometry of the tracing region. It is suggested that the corresponding quantum Fisher information associated with this estimation problem is at the root of the holographic bulk geometry." @default.
• W2984865113 created "2019-11-22" @default.
• W2984865113 creator A5014969672 @default.
• W2984865113 date "2020-03-25" @default.
• W2984865113 modified "2023-09-23" @default.
• W2984865113 title "Complexity and time" @default.
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• W2984865113 doi "https://doi.org/10.1103/physrevd.101.065016" @default.
• W2984865113 hasPublicationYear "2020" @default.
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