Quantum Chaos is Quantum

Lorenzo Leone; Salvatore F. E. Oliviero; You Zhou; Alioscia Hamma

doi:10.22331/q-2021-05-04-453

Quantum Chaos is Quantum

Lorenzo Leone¹, Salvatore F. E. Oliviero¹, You Zhou^2,3, and Alioscia Hamma¹

¹Physics Department, University of Massachusetts Boston, 02125, USA
²School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore
³Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

Published:	2021-05-04, volume 5, page 453
Eprint:	arXiv:2102.08406v3
Doi:	https://doi.org/10.22331/q-2021-05-04-453
Citation:	Quantum 5, 453 (2021).

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

Featured image: $\mathit{Left}$ : Scheme of the $4$-Doped Clifford circuit. $\mathit{Right}$ : Detail of $K_{C_{4}}$, a unitary single-qubit non Clifford gate $K$ evolved adjointly by a Clifford circuit $C_{4}$. Note that the set formed by these circuits is equivalent to the set of doped Clifford circuits, i.e circuits composed by Clifford unitaries $C_{i}$ interspersed with single-qubit non Clifford gates $K_{i}$.

► BibTeX data

@article{Leone2021quantumchaosis,
  doi = {10.22331/q-2021-05-04-453},
  url = {https://doi.org/10.22331/q-2021-05-04-453},
  title = {Quantum {C}haos is {Q}uantum},
  author = {Leone, Lorenzo and Oliviero, Salvatore F. E. and Zhou, You and Hamma, Alioscia},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {5},
  pages = {453},
  month = may,
  year = {2021}
}

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