Quantum Chaos is Quantum

TL;DR

This paper establishes that simulating quantum chaotic behavior requires a number of non-Clifford gates proportional to the number of qubits, making classical simulation infeasible.

Contribution

It proves that quantum chaos simulation necessitates a linear number of non-Clifford gates relative to qubits, providing a fundamental limit on classical simulability.

Findings

Simulation of quantum chaos requires O(N) non-Clifford gates.

Classical simulation of quantum chaos is impossible for large systems.

Quantum chaos is characterized by a linear resource threshold.

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 $k=O(N)$. This result implies the impossibility of simulating quantum chaos on a classical computer.