Quantum Chaos Is Quantum

Republished By Plato

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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

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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}<br /> }

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Cited by

[1] Salvatore F. E. Oliviero, Lorenzo Leone, and Alioscia Hamma, “Transitions in entanglement complexity in random quantum circuits by measurements”, arXiv:2103.07481.

The above citations are from SAO/NASA ADS (last updated successfully 2021-05-08 00:12:08). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref’s cited-by service no data on citing works was found (last attempt 2021-05-08 00:12:07).

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.

Source: https://quantum-journal.org/papers/q-2021-05-04-453/

Time Stamp: May 4, 2021

Time Stamp: Nov 8, 2023

Quantum Chaos is Quantum

Republished By Plato

Abstract

► BibTeX data

► References

Cited by

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