Quantum Chaos is Quantum

Quantum 5, 453 (2021).

https://doi.org/10.22331/q-2021-05-04-453

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.