Quantum Chaos is Quantum

Lorenzo Leone1, Salvatore F. E. Oliviero1, You Zhou2,3, and Alioscia Hamma1

1Physics Department, University of Massachusetts Boston, 02125, USA
2School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore
3Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

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Abstract

It is well known that a quantum circuit on $N$ qubits composed of Clifford gates with the addition of $k$ non Clifford gates can be simulated on a classical computer by an algorithm scaling as $\text{poly}(N)\exp(k)$[1]. We show that, for a quantum circuit to simulate quantum chaotic behavior, it is both necessary and sufficient that $k=\Theta(N)$. This result implies the impossibility of simulating quantum chaos on a classical computer.

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[18] Lorenzo Leone, Salvatore F. E. Oliviero, and Alioscia Hamma, "Isospectral Twirling and Quantum Chaos", Entropy 23 8, 1073 (2021).

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