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Quantum Chaos is Quantum
Lorenzo Leone (University of Massachusetts Boston), Salvatore F. E. Oliviero (University of Massachusetts Boston), You Zhou (Harvard University, Nanyang Technological University), Alioscia Hamma (University of Massachusetts Boston)
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 poly ( N ) exp ( k ) \cite{bravyi2016improved}. We show that, for a quantum circuit to simulate quantum chaotic behavior, it is both necessary and sufficient that k = Θ ( N ) . This result implies the impossibility of simulating quantum chaos on a classical computer.