Search

Quantum computers hold the promise to solve certain problems exponentially faster than their classical counterparts. Trapped atomic ions are among the physical systems in which building such a computing device seems viable. In this work we present a small-scale quantum information processor based on a string of 40Ca+ ions confined in a macroscopic linear Paul trap. We review our set of operations which includes non-coherent operations allowing us to realize arbitrary Markovian processes. In order to build a larger quantum information processor it is mandatory to reduce the error rate of the available operations which is only possible if the physics of the noise processes is well understood. We identify the dominant noise sources in our system and discuss their effects on different algorithms. Finally we demonstrate how our entire set of operations can be used to facilitate the implementation of algorithms by examples of the quantum Fourier transform and the quantum order finding algorithm. [ABSTRACT FROM AUTHOR]

A number of elegant approaches have been developed for the identification of quantum circuits which can be efficiently simulated on a classical computer. Recently, these methods have been employed to demonstrate the classical simulability of the quantum Fourier transform (QFT). Here we show that one can demonstrate a number of simulability results for QFT circuits in a straightforward manner using Griffiths and Niu's semi-classical QFT construction (Griffiths and Niu 1996 Phys. Rev. Lett. 76 3228). We use this to analyse the simulability properties of the QFT with a variety of classes of entangled input states. We then discuss the consequences of these results in the context of Shor's factorization algorithm. [ABSTRACT FROM AUTHOR]

Radio interferometers consisting of identical antennas arranged on a regular lattice permit fast Fourier transform beamforming, which reduces the correlation cost from in the number of antennas to . We develop a formalism for describing this process and apply this formalism to derive a number of algorithms with a range of observational applications. These include algorithms for forming arbitrarily pointed tied-array beams from the regularly spaced Fourier transform–formed beams, sculpting the beams to suppress sidelobes while only losing percent-level sensitivity, and optimally estimating the position of a detected source from its observed brightness in the set of beams. We also discuss the effect that correlations in the visibility-space noise, due to cross talk and sky contributions, have on the optimality of Fourier transform beamforming, showing that it does not strictly preserve the sky information of the n2 correlation, even for an idealized array. Our results have applications to a number of upcoming interferometers, in particular the Canadian Hydrogen Intensity Mapping Experiment–Fast Radio Burst (CHIME/FRB) project. [ABSTRACT FROM AUTHOR]