Quantum Chaos is Quantum

Lorenzo Leone1, Salvatore F. E. Oliviero1, You Zhou2,3, 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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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.

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[4] Sarah True and Alioscia Hamma, "Transitions in Entanglement Complexity in Random Circuits", Quantum 6, 818 (2022).

[5] Troy J. Sewell and Christopher David White, "Mana and thermalization: Probing the feasibility of near-Clifford Hamiltonian simulation", Physical Review B 106 12, 125130 (2022).

[6] Joonho Kim, Yaron Oz, and Dario Rosa, "Quantum chaos and circuit parameter optimization", Journal of Statistical Mechanics: Theory and Experiment 2023 2, 023104 (2023).

[7] Tobias Haug and Lorenzo Piroli, "Quantifying nonstabilizerness of matrix product states", Physical Review B 107 3, 035148 (2023).

[8] Lorenzo Leone, Salvatore F. E. Oliviero, and Alioscia Hamma, "Nonstabilizerness determining the hardness of direct fidelity estimation", Physical Review A 107 2, 022429 (2023).

[9] Lorenzo Leone, Salvatore F. E. Oliviero, and Alioscia Hamma, "Stabilizer Rényi Entropy", Physical Review Letters 128 5, 050402 (2022).

[10] Stefano Piemontese, Tommaso Roscilde, and Alioscia Hamma, "Entanglement complexity of the Rokhsar-Kivelson-sign wavefunctions", Physical Review B 107 13, 134202 (2023).

[11] Tom Farshi, Jonas Richter, Daniele Toniolo, Arijeet Pal, and Lluis Masanes, "Absence of Localization in Two-Dimensional Clifford Circuits", PRX Quantum 4 3, 030302 (2023).

[12] Salvatore F. E. Oliviero, Lorenzo Leone, and Alioscia Hamma, "Magic-state resource theory for the ground state of the transverse-field Ising model", Physical Review A 106 4, 042426 (2022).

[13] Salvatore F. E. Oliviero, Lorenzo Leone, Alioscia Hamma, and Seth Lloyd, "Measuring magic on a quantum processor", npj Quantum Information 8 1, 148 (2022).

[14] Kanato Goto, Tomoki Nosaka, and Masahiro Nozaki, "Probing chaos by magic monotones", Physical Review D 106 12, 126009 (2022).

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[19] You Zhou and Qing Liu, "Performance analysis of multi-shot shadow estimation", Quantum 7, 1044 (2023).

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[22] Davide Rattacaso, Lorenzo Leone, Salvatore F. E. Oliviero, and Alioscia Hamma, "Stabilizer entropy dynamics after a quantum quench", Physical Review A 108 4, 042407 (2023).

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[24] Xhek Turkeshi, Marco Schirò, and Piotr Sierant, "Measuring nonstabilizerness via multifractal flatness", Physical Review A 108 4, 042408 (2023).

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[26] Cahit Kargi, Juan Pablo Dehollain, Lukas M. Sieberer, Fabio Henriques, Tobias Olsacher, Philipp Hauke, Markus Heyl, Peter Zoller, and Nathan K. Langford, "Quantum Chaos and Universal Trotterisation Behaviours in Digital Quantum Simulations", arXiv:2110.11113, (2021).

[27] Salvatore F. E. Oliviero, Lorenzo Leone, and Alioscia Hamma, "Transitions in entanglement complexity in random quantum circuits by measurements", Physics Letters A 418, 127721 (2021).

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The above citations are from Crossref's cited-by service (last updated successfully 2023-12-07 09:43:28) and SAO/NASA ADS (last updated successfully 2023-12-07 09:43:29). The list may be incomplete as not all publishers provide suitable and complete citation data.