Quantum walks on circles in phase space via superconducting circuit quantum electrodynamics

We show how a quantum walk can be implemented for the first time in a quantum quincunx created via superconducting circuit quantum electrodynamics (QED), and how interpolation from quantum to random walk is implemented by controllable decoherence using a two resonator system. Direct control over the coin qubit is difficult to achieve in either cavity or circuit QED, but we show that a Hadamard coin flip can be effected via direct driving of the cavity, with the result that the walker jumps between circles in phase space but still exhibits quantum walk behavior over 15 steps.Comment: 8 pages, 4 figures, 2 table

Bi-fractional Wigner functions

YesTwo fractional Fourier transforms are used to define bi-fractional displacement operators, which interpolate between displacement operators and parity operators. They are used to define bi-fractional coherent states. They are also used to define the bi-fractional Wigner function, which is a two-parameter family of functions that interpolates between the Wigner function and the Weyl function. Links to the extended phase space formalism are also discussed

Uniform approximation for the overlap caustic of a quantum state with its translations

The semiclassical Wigner function for a Bohr-quantized energy eigenstate is known to have a caustic along the corresponding classical closed phase space curve in the case of a single degree of freedom. Its Fourier transform, the semiclassical chord function, also has a caustic along the conjugate curve defined as the locus of diameters, i.e. the maximal chords of the original curve. If the latter is convex, so is its conjugate, resulting in a simple fold caustic. The uniform approximation through this caustic, that is here derived, describes the transition undergone by the overlap of the state with its translation, from an oscillatory regime for small chords, to evanescent overlaps, rising to a maximum near the caustic. The diameter-caustic for the Wigner function is also treated.Comment: 14 pages, 9 figure

Two dimensional smoothing via an optimised Whittaker smoother

Background In many applications where moderate to large datasets are used, plotting relationships between pairs of variables can be problematic. A large number of observations will produce a scatter-plot which is difficult to investigate due to a high concentration of points on a simple graph. In this article we review the Whittaker smoother for enhancing scatter-plots and smoothing data in two dimensions. To optimise the behaviour of the smoother an algorithm is introduced, which is easy to programme and computationally efficient. Results The methods are illustrated using a simple dataset and simulations in two dimensions. Additionally, a noisy mammography is analysed. When smoothing scatterplots the Whittaker smoother is a valuable tool that produces enhanced images that are not distorted by the large number of points. The methods is also useful for sharpening patterns or removing noise in distorted images. Conclusion The Whittaker smoother can be a valuable tool in producing better visualisations of big data or filter distorted images. The suggested optimisation method is easy to programme and can be applied with low computational cost

Steering of a Bosonic Mode with a Double Quantum Dot

We investigate the transport and coherence properties of a double quantum dot coupled to a single damped boson mode. Our numerically results reveal how the properties of the boson distribution can be steered by altering parameters of the electronic system such as the energy difference between the dots. Quadrature amplitude variances and the Wigner function are employed to illustrate how the state of the boson mode can be controlled by a stationary electron current through the dots.Comment: 10 pages, 6 figures, to appear in Phys. Rev.

Optical Holonomic Quantum Computer

In this paper the idea of holonomic quantum computation is realized within quantum optics. In a non-linear Kerr medium the degenerate states of laser beams are interpreted as qubits. Displacing devices, squeezing devices and interferometers provide the classical control parameter space where the adiabatic loops are performed. This results into logical gates acting on the states of the combined degenerate subspaces of the lasers, producing any one qubit rotations and interactions between any two qubits. Issues such as universality, complexity and scalability are addressed and several steps are taken towards the physical implementation of this model.Comment: 16 pages, 3 figures, REVTE

Image reconstruction from an efficient number of moment-based projections

This paper presents a new technique for computed tomography that is based on moment reconstruction. The proposed technique employs the Fourier and Haar coefficients for spectral and spatial moment-based image analyses, respectively. It provides a new approach to the problem of tomographic image reconstruction, where an X-ray image is obtained from a set of line projections. The experimental evaluation includes reconstructions of standard tomographic images in the presence of blur, caused by uniform linear motions. The results lead to the conclusion that the proposed method is more selective, efficient and robust. Another issue considered is the noise associated with normal transmission. © 2013 Copyright Taylor and Francis Group, LLC