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)[1]. 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.
Quantum chaos is quantum / Leone, Lorenzo; Oliviero, Salvatore F. E.; Zhou, You; Hamma, Alioscia. - In: QUANTUM. - ISSN 2521-327X. - 5:(2021), pp. 1-20. [10.22331/q-2021-05-04-453]
Quantum chaos is quantum
Alioscia Hamma
2021
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)[1]. 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.File in questo prodotto:
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