Quantum Chaos is Quantum

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