A claimed identification of Virasoro circuit complexity with the Berry connection fails a basic consistency check for pure rotations.
Holographic Complexity and Charged Scalar Fields
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abstract
We construct a time-dependent expression of the computational complexity of a quantum system which consists of two conformal complex scalar field theories in d dimensions coupled to constant electric potentials and defined on the boundaries of a charged AdS black hole in (d+1) dimensions. Using a suitable choice of the reference state, Hamiltonian gates and the metric on the manifold of unitaries, we find that the complexity grows linearly for a relatively large interval of time. We also remark that for scalar fields with very small charges the rate of variation of the complexity cannot exceed a maximum value known as the Lloyd bound.
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hep-th 1years
2019 1verdicts
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Reflections on Virasoro circuit complexity and Berry phase
A claimed identification of Virasoro circuit complexity with the Berry connection fails a basic consistency check for pure rotations.