Fast Algorithm for Finding the Eigenvalue Distribution of Very Large Matrices

A theoretical analysis is given of the equation of motion method, due to Alben et al., to compute the eigenvalue distribution (density of states) of very large matrices. The salient feature of this method is that for matrices of the kind encountered in quantum physics the memory and CPU requirements of this method scale linearly with the dimension of the matrix. We derive a rigorous estimate of the statistical error, supporting earlier observations that the computational efficiency of this approach increases with matrix size. We use this method and an imaginary-time version of it to compute the energy and the specific heat of three different, exactly solvable, spin-1/2 models and compare with the exact results to study the dependence of the statistical errors on sample and matrix size.Comment: 24 pages, 24 figure

Computer simulation of Wheeler's delayed choice experiment with photons

We present a computer simulation model of Wheeler's delayed choice experiment that is a one-to-one copy of an experiment reported recently (V. Jacques {\sl et al.}, Science 315, 966 (2007)). The model is solely based on experimental facts, satisfies Einstein's criterion of local causality and does not rely on any concept of quantum theory. Nevertheless, the simulation model reproduces the averages as obtained from the quantum theoretical description of Wheeler's delayed choice experiment. Our results prove that it is possible to give a particle-only description of Wheeler's delayed choice experiment which reproduces the averages calculated from quantum theory and which does not defy common sense.Comment: Europhysics Letters (in press

Gate-error analysis in simulations of quantum computers with transmon qubits

In the model of gate-based quantum computation, the qubits are controlled by a sequence of quantum gates. In superconducting qubit systems, these gates can be implemented by voltage pulses. The success of implementing a particular gate can be expressed by various metrics such as the average gate fidelity, the diamond distance, and the unitarity. We analyze these metrics of gate pulses for a system of two superconducting transmon qubits coupled by a resonator, a system inspired by the architecture of the IBM Quantum Experience. The metrics are obtained by numerical solution of the time-dependent Schr\"odinger equation of the transmon system. We find that the metrics reflect systematic errors that are most pronounced for echoed cross-resonance gates, but that none of the studied metrics can reliably predict the performance of a gate when used repeatedly in a quantum algorithm

Real-time broadening of non-equilibrium density profiles and the role of the specific initial-state realization

The real-time broadening of density profiles starting from non-equilibrium states is at the center of transport in condensed-matter systems and dynamics in ultracold atomic gases. Initial profiles close to equilibrium are expected to evolve according to linear response, e.g., as given by the current correlator evaluated exactly at equilibrium. Significantly off equilibrium, linear response is expected to break down and even a description in terms of canonical ensembles is questionable. We unveil that single pure states with density profiles of maximum amplitude yield a broadening in perfect agreement with linear response, if the structure of these states involves randomness in terms of decoherent off-diagonal density-matrix elements. While these states allow for spin diffusion in the XXZ spin-1/2 chain at large exchange anisotropies, coherences yield entirely different behavior.Comment: 7 pages, 7 figures, accepted for publication in Phys. Rev.

Corpuscular model of two-beam interference and double-slit experiments with single photons

We introduce an event-based corpuscular simulation model that reproduces the wave mechanical results of single-photon double slit and two-beam interference experiments and (of a one-to-one copy of an experimental realization) of a single-photon interference experiment with a Fresnel biprism. The simulation comprises models that capture the essential features of the apparatuses used in the experiment, including the single-photon detectors recording individual detector clicks. We demonstrate that incorporating in the detector model, simple and minimalistic processes mimicking the memory and threshold behavior of single-photon detectors is sufficient to produce multipath interference patterns. These multipath interference patterns are built up by individual particles taking one single path to the detector where they arrive one-by-one. The particles in our model are not corpuscular in the standard, classical physics sense in that they are information carriers that exchange information with the apparatuses of the experimental set-up. The interference pattern is the final, collective outcome of the information exchanges of many particles with these apparatuses. The interference patterns are produced without making reference to the solution of a wave equation and without introducing signalling or non-local interactions between the particles or between different detection points on the detector screen.Comment: Accepted for publication in J. Phys. Soc. Jpn

Corpuscular Event-by-Event Simulation of Quantum Optics Experiments: Application to a Quantum-Controlled Delayed-Choice Experiment

A corpuscular simulation model of optical phenomena that does not require the knowledge of the solution of a wave equation of the whole system and reproduces the results of Maxwell's theory by generating detection events one-by-one is discussed. The event-based corpuscular model gives a unified description of multiple-beam fringes of a plane parallel plate and single-photon Mach-Zehnder interferometer, Wheeler's delayed choice, photon tunneling, quantum eraser, two-beam interference, Einstein-Podolsky-Rosen-Bohm and Hanbury Brown-Twiss experiments. The approach is illustrated by application to a recent proposal for a quantum-controlled delayed choice experiment, demonstrating that also this thought experiment can be understood in terms of particle processes only.Comment: Invited paper presented at FQMT11. Accepted for publication in Physica Scripta 27 June 201

Decoherence by a chaotic many-spin bath

We numerically investigate decoherence of a two-spin system (central system) by a bath of many spins 1/2. By carefully adjusting parameters, the dynamical regime of the bath has been varied from quantum chaos to regular, while all other dynamical characteristics have been kept practically intact. We explicitly demonstrate that for a many-body quantum bath, the onset of quantum chaos leads to significantly faster and stronger decoherence compared to an equivalent non-chaotic bath. Moreover, the non-diagonal elements of the system's density matrix decay differently for chaotic and non-chaotic baths. Therefore, knowledge of the basic parameters of the bath (strength of the system-bath interaction, bath's spectral density of states) is not always sufficient, and much finer details of the bath's dynamics can strongly affect the decoherence process.Comment: 4 pages, RevTeX, 5 eps figure

Hidden assumptions in the derivation of the Theorem of Bell

John Bell's inequalities have already been considered by Boole in 1862. Boole established a one-to-one correspondence between experimental outcomes and mathematical abstractions of his probability theory. His abstractions are two-valued functions that permit the logical operations AND, OR and NOT and are the elements of an algebra. Violation of the inequalities indicated to Boole an inconsistency of definition of the abstractions and/or the necessity to revise the algebra. It is demonstrated in this paper, that a violation of Bell's inequality by Einstein-Podolsky-Rosen type of experiments can be explained by Boole's ideas. Violations of Bell's inequality also call for a revision of the mathematical abstractions and corresponding algebra. It will be shown that this particular view of Bell's inequalities points toward an incompleteness of quantum mechanics, rather than to any superluminal propagation or influences at a distance

Long-Time Correlations in Single-Neutron Interferometry Data

We present a detailed analysis of the time series of time-stamped neutron counts obtained by single-neutron interferometry. The neutron counting statistics display the usual Poissonian behavior, but the variance of the neutron counts does not. Instead, the variance is found to exhibit a dependence on the phase-shifter setting which can be explained by a probabilistic model that accounts for fluctuations of the phase shift. The time series of the detection events exhibit long-time correlations with amplitudes that also depend on the phase-shifter setting. These correlations appear as damped oscillations with a period of about 2.8 s. By simulation, we show that the correlations of the time differences observed in the experiment can be reproduced by assuming that, for a fixed setting of the phase shifter, the phase shift experienced by the neutrons varies periodically in time with a period of 2.8 s. The same simulations also reproduce the behavior of the variance. Our analysis of the experimental data suggests that time-stamped data of singleparticle interference experiments may exhibit transient features that require a description in terms of non-stationary processes, going beyond the standard quantum model of independent random events