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arXiv:quant-ph/0110026 · Physical Review Letters

Comment on “Stable Quantum Computation of Unstable Classical Chaos”

Lajos Diósi

Published May 9, 2002• 2 citations
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Abstract

I think the title and content of the recent Letter by Georgeot and Shepelyanski [PRL 86, 5393 (2001), also quant-ph/0101004)] are not correct. As long as the classical Arnold map is considered, the classical computational algorithm can be made exactly equivalent with the quantum one. The claimed advantage of the Letter's quantum algorithm disappears if we correctly restrict the statistical analysis for the classical Arnold system.

DOI
10.1103/physrevlett.88.219801

Related papers

Comment on "Stable Quantum Computation of Unstable Classical Chaos"

Christof Zalka

This is a 1-page comment on a wrong paper that recently appeared in PRL (Phys. Rev. Lett. 86 (23), 5393 (2001), also quant-ph/0101004). The authors claim to have shown that using a quantum computer gives an "exponential advantage" for simulating and studying classical chaotic systems.

arXiv:quant-ph/0110019•Oct 2, 2001•1 citation

Stable Quantum Computation of Unstable Classical Chaos

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We show on the example of the Arnold cat map that classical chaotic systems can be simulated with exponential efficiency on a quantum computer. Although classical computer errors grow exponentially with time, the quantum algorithm with moderate imperfections is able to simulate accurately the unstable chaotic classical nonlinear dynamics for long times. The algorithm can be easily implemented on systems of a few qubits.

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Georgeot and Shepelyansky Reply:

Bertrand Georgeot, Dima L. Shepelyansky

We show explicitly that high harmonics of the classical Liouville density distribution in the chaotic regime can be obtained efficiently on a quantum computer [1,2]. As was stated in [1], this provides information unaccessible for classical computer simulations, and replies to the questions raised in [3,4].

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Comment on ``Testing integrability with a single bit of quantum information''

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How long does the quantum chaos last?

G. Casati, Boris V. Chirikov, O. V. Zhirov

The main purpose of this Comment is to point out that besides the short time scale of quantum chaos, confirmed once more in recent paper by Alicki et al, there is generally another time scale t_R, which is much longer and on which a partial quantum-classical correspondence persists. Namely, the quantum diffusion closely follows the classical one even though the former is dynamically stable. The absence of the long scale t_R in model studied by Alicki et al. is a result of a special choice for one model's parameters value.

arXiv:chao-dyn/9702012•Feb 18, 1997•1 citation
I think the title and content of the recent Letter by Georgeot and Shepelyanski [PRL 86, 5393 (2001), also quant-ph/0101004)] are not correct. As long as the classical Arnold map is considered, the classical computational algorithm can be made exactly equivalent with the quantum one. The claimed advantage of the Letter's quantum algorithm disappears if we correctly restrict the statistical analysis for the classical Arnold system.
In quant-ph/0303042, Poulin, Laflamme, Milburn and Paz consider the problem of distinguishing quantum chaos from quantum integrability for dynamics in an NNN-dimensional Hilbert space. They claim that this can be done by deterministic quantum computing with a single bit using O(N)O(\sqrt{N})O(N​) physical resources, compared to O(N) physical resources classically. I point out what seems to be a fatal flaw with their proposal.
The main purpose of this Comment is to point out that besides the short time scale of quantum chaos, confirmed once more in recent paper by Alicki et al, there is generally another time scale t_R, which is much longer and on which a partial quantum-classical correspondence persists. Namely, the quantum diffusion closely follows the classical one even though the former is dynamically stable. The absence of the long scale t_R in model studied by Alicki et al. is a result of a special choice for one model's parameters value.