Comment on "Stable Quantum Computation of Unstable Classical Chaos"

A Comment on "Semiquantum Chaos"

The identification of the particle creation and distruction operators is discussed.

Comment on "Can Two-Photon Correlation of Chaotic Light be Considered as Correlation of Intensity Fluctuations ?"

A Comment on the Letter by G. Scarcelli, V. Berardi and Y. Shih, Phys. Rev. Lett. 96, 063602 (2006).

Comments on `Stable Quantum Computation of Unstable Classical Chaos,' `Efficient Quantum Computing Insensitive to Phase Errors,' and `Quantum Computer Inverting Time Arrow for Macroscopic Systems'

Recently, the paper B. Georgeot and D.L. Shepelyansky, Phys. Rev. Lett._86_, 5393 (2001) has been criticized [C. Zalka, quant-ph/0110019; L. Di'osi, quant-ph/0110026]. The Letter claims an exponential speedup and reduction in error sensitivity, when phase-space density evolution under the Arnold cat map is performed on a quantum computer. On the one hand, some points have not yet been made by previous respondents. On the other, the authors' reaction [quant-ph/0110142] raises new issues. The present note addresses both.

Nonlinear dynamics of a semiquantum Hamiltonian in the vicinity of quantum unstable regimes

We examine the emergence of chaos in a non-linear model derived from a semiquantum Hamiltonian describing the coupling between a classical field and a quantum system. The latter corresponds to a bosonic version of a BCS-like Hamiltonian, and possesses stable and unstable regimes. The dynamics of the whole system is shown to be strongly influenced by the quantum subsystem. In particular, chaos is seen to arise in the vicinity of a quantum critical case, which separates the stable and unstable regimes of the bosonic system.

Comment on "Entanglement and the Thermodynamic Arrow of Time" and Correct Reply on "Comment on "Quantum Solution to the Arrow-of-Time Dilemma"" of David Jennings and Terry Rudolph

Recently David Jennings and Terry Rudolph published two papers as reaction on Maccone's paper "Quantum Solution to the Arrow-of-Time Dilemma". In these papers, the authors suppose that second law of thermodynamics is not relevant for quantum systems. Unfortunately, these papers did not get relevant reply from Maccone. The reason of this is following. Both Maccone and the above-mentioned authors use thermodynamic law and thermodynamic-like terminology for non-thermodynamic systems, for example, microscopic system of three qubits. However, big size of a system (quantum or classic) is also not an…

Estimating the spectral density of unstable scars

In quantum chaos, the spectral statistics generally follows the predictions of Random Matrix Theory (RMT). A notable exception is given by scar states, that enhance probability density around unstable periodic orbits of the classical system, therefore causing significant deviations of the spectral density from RMT expectations. In this work, the problem is considered of both RMT-ruled and scarred chaotic systems coupled to an opening. In particular, predictions are derived for the spectral density of a chaotic Hamiltonian scattering into a single- or multiple channels. The results are tested o…

Reply to Comment on "Quantification of Macroscopic Quantum Superpositions within Phase Space"

Gong points out [quant-ph arXiv:1106.0062] a "direct connection" between our measure [PRL 106, 220401 (2011)] recently proposed to quantify macroscopic quantum superpositions and a previously studied quantity introduced to study classical and quantum chaos. We point out that the two measures are obviously different for some mixed states, and the previous one does not work as a sensible measure to quantify quantum superpositions.

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

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.

Impact of chaos on precursors of quantum criticality

Excited-state quantum phase transitions (ESQPTs) are critical phenomena that generate singularities in the spectrum of quantum systems. {For systems with a classical counterpart,} these phenomena have their origin in the classical limit when the separatrix of an unstable periodic orbit divides phase space into different regions. Using a semiclassical theory of wave propagation based on the manifolds of unstable periodic orbits, we describe the quantum states associated with an ESQPT {for the quantum standard map: a paradigmatic example of a kicked quantum system}. {Moreover, we show that finit…

来自不稳定周期轨道的量子多体疤痕

Quantum many-body scars from unstable periodic orbits

本文首次发现源自混沌相空间不稳定周期轨道的量子多体疤痕，并证明其满足本征态热化假说，揭示了热化前由近似等间距态塔导致的反常振荡动力学，同时为研究热与非热量子多体疤痕之间的过渡提供了模型。

Quantum Computing of Classical Chaos: Smile of the Arnold-Schrodinger Cat

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 dynamics for long times. The algorithm can be easily implemented on systems of a few qubits.