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Fractal Fidelity as a signature of Quantum Chaos

Franco Pellegrini·Simone Montangero
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Abstract

We analyze the fidelity of a quantum simulation and we show that it displays fractal fluctuations iff the simulated dynamics is chaotic. This analysis allows us to investigate a given simulated dynamics without any prior knowledge. In the case of integrable dynamics, the appearance of fidelity fractal fluctuations is a signal of a highly corrupted simulation. We conjecture that fidelity fractal fluctuations are a signature of the appearance of quantum chaos. Our analysis can be realized already by a few qubit quantum processor.

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Franco Pellegrini, Simone Montangero. 2007-01-09. Fractal Fidelity as a signature of Quantum Chaos. https://doi.org/10.1103/physreva.76.052327

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