On Quantum Complexity

• URL: http://arxiv.org/abs/2209.14689v3
• Date: Sun, 13 Aug 2023 09:17:47 GMT
• Title: On Quantum Complexity
• Authors: Mohsen Alishahiha
• Abstract summary: We consider a certain quantity as a possible candidate for quantum complexity. For explicit examples we have considered in this paper, there are infinitely many quantities exhibiting similar behavior.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The ETH ansatz for matrix elements of a given operator in the energy eigenstate basis results in a notion of thermalization for a chaotic system. In this context for a certain quantity - to be found for a given model - one may impose a particular condition on its matrix elements in the energy eigenstate basis so that the corresponding quantity exhibit linear growth at late times. The condition is to do with a possible pole structure the corresponding matrix elements may have. Based on the general expectation of complexity one may want to think of this quantity as a possible candidate for the quantum complexity. We note, however, that for the explicit examples we have considered in this paper, there are infinitely many quantities exhibiting similar behavior.

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