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arXiv:quant-ph/0305153

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

Howard M. Wiseman

Published May 25, 2003• 0 citations
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Abstract

In quant-ph/0303042, Poulin, Laflamme, Milburn and Paz consider the problem of distinguishing quantum chaos from quantum integrability for dynamics in an $N$-dimensional Hilbert space. They claim that this can be done by deterministic quantum computing with a single bit using $O(\sqrt{N})$ physical resources, compared to O(N) physical resources classically. I point out what seems to be a fatal flaw with their proposal.

DOI
10.48550/arxiv.quant-ph/0305153

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Modeling quantum scattering of fundamental particles by classical, deterministic processes

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We point out that results obtained by M. Ribaric and L. Sustersic, hep-th/0403084, and by M. Blasone, P. Jizba and H. Kleinert, quant-ph/0409021, suggest that the path-integral formalism is the key to a derivation of quantum physics from classical, deterministic physics in the four-dimensional space-time. These results and the 't Hooft conjecture, hep-th/0104219, suggest to consider a relativistic, non-material medium, an ether, as a base for non-local hidden-variable models of the physical universe.

arXiv:0809.2457•Sep 15, 2008•1 citation
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.
We show that deterministic quantum computing with a single bit can determine whether the classical limit of a quantum system is chaotic or integrable using O(N)O(N)O(N) physical resources, where N is the dimension of the Hilbert space of the system under study. This is a square-root improvement over all known classical procedures. Our study relies strictly on the random matrix conjecture. We also present numerical results for the nonlinear kicked top.
We suggest an efficient scheme for quantum computation with linear optical elements, where the qubits are encoded in single photon states. The scheme reduces the resources required per logical gate by several orders of magnitude, compared to an earlier proposal of Knill, Laflamme, and Milburn, while the resource overhead per gate is independent of the length of the computation. A central feature of the scheme, enabling these improvements, is the prior construction of a "linked" photon state designed according to the particular quantum circuit one wishes to process. Once this state has been successfully prepared, the computation is pursued deterministically by a sequence of teleportation steps.
We point out that results obtained by M. Ribaric and L. Sustersic, hep-th/0403084, and by M. Blasone, P. Jizba and H. Kleinert, quant-ph/0409021, suggest that the path-integral formalism is the key to a derivation of quantum physics from classical, deterministic physics in the four-dimensional space-time. These results and the 't Hooft conjecture, hep-th/0104219, suggest to consider a relativistic, non-material medium, an ether, as a base for non-local hidden-variable models of the physical universe.