Steven H. Simon

Non-Abelian Anyons and Topological Quantum Computation

Topological quantum computation has emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as non-Abelian anyons, meaning that they obey non-Abelian braiding statistics. Quantum information is stored in states with multiple quasiparticles, which have a topological degeneracy. The unitary gate operations that are necessary for quantum computation are carried out by braiding quasiparticles and then measuring the multiquasiparticle states. The fault tolerance of a topological quantum computer arises from the nonlocal encoding of the quasiparticle states, which makes them immune to errors caused by local perturbations. To date, the only such topological states thought to have been found in nature are fractional quantum Hall states, most prominently the

Optimizing MIMO antenna systems with channel covariance feedback

\ensuremath{\nu}=5∕2

Communication through a diffusive medium : Coherence and capacity

state, although several other prospective candidates have been proposed in systems as disparate as ultracold atoms in optical lattices and thin-film superconductors. In this review article, current research in this field is described, focusing on the general theoretical concepts of non-Abelian statistics as it relates to topological quantum computation, on understanding non-Abelian quantum Hall states, on proposed experiments to detect non-Abelian anyons, and on proposed architectures for a topological quantum computer. Both the mathematical underpinnings of topological quantum computation and the physics of the subject are addressed, using the

Capacity of a Gaussian MIMO channel with nonzero mean

\ensuremath{\nu}=5∕2

Capacity and Character Expansions: Moment-Generating Function and Other Exact Results for MIMO Correlated Channels

fractional quantum Hall state as the archetype of a non-Abelian topological state enabling fault-tolerant quantum computation.

SCALING OF THE QUASIPARTICLE SPECTRUM FOR D-WAVE SUPERCONDUCTORS

We consider a narrowband point-to-point communication system with n/sub T/ transmitters and n/sub R/ receivers. We assume the receiver has perfect knowledge of the channel, while the transmitter has no channel knowledge. We consider the case where the receiving antenna array has uncorrelated elements, while the elements of the transmitting array are arbitrarily correlated. Focusing on the case where n/sub T/=2, we derive simple analytic expressions for the ergodic average and the cumulative distribution function of the mutual information for arbitrary input (transmission) signal covariance. We then determine the ergodic and outage capacities and the associated optimal input signal covariances. We thus show how a transmitter with covariance knowledge should correlate its transmissions to maximize throughput. These results allow us to derive an exact condition (both necessary and sufficient) that determines when beamforming is optimal for systems with arbitrary number of transmitters and receivers.

Braid topologies for quantum computation.

Coherent wave propagation in disordered media gives rise to many fascinating phenomena as diverse as universal conductance fluctuations in mesoscopic metals and speckle patterns in light scattering. Here, the theory of electromagnetic wave propagation in diffusive media is combined with information theory to show how interference affects the information transmission rate between antenna arrays. Nontrivial dependencies of the information capacity on the nature of the antenna arrays are found, such as the dimensionality of the arrays and their direction with respect to the local scattering medium. This approach provides a physical picture for understanding the importance of scattering in the transfer of information through wireless communications.

Charge Separation of Dense Two-Dimensional Electron-Hole Gases: Mechanism for Exciton Ring Pattern Formation

We characterize the input covariance that maximizes the ergodic capacity of a flat-fading, multiple-input-multiple-output (MIMO) channel with additive white Gaussian noise, when the entries of the channel matrix are independent, circularly symmetric, complex Gaussian random variables of nonzero (and possibly different) means and identical variances. We show that the optimal transmit covariance must have the same eigenvectors as the squared mean channel, thereby reducing the computation of the optimal covariance to a simple convex optimization. This generalizes existing results for multiple-input-single-output (MISO) channels and MIMO channels restricted to have a mean of unit rank.

On the Outage Capacity of Correlated Multiple-Path MIMO Channels

A promising new method from the field of representations of Lie groups is applied to calculate integrals over unitary groups, which are important for multiantenna communications. To demonstrate the power and simplicity of this technique, a number of recent results are rederived, using only a few simple steps. In particular, we derive the joint probability distribution of eigenvalues of the matrix GGdagger , with G a nonzero mean or a semicorrelated Gaussian random matrix. These joint probability distribution functions can then be used to calculate the moment generating function of the mutual information for Gaussian multiple-input multiple-output (MIMO) channels with these probability distribution of their channel matrices G. We then turn to the previously unsolved problem of calculating the moment generating function of the mutual information of MIMO channels, which are correlated at both the receiver and the transmitter. From this moment generating function we obtain the ergodic average of the mutual information and study the outage probability. These methods can be applied to a number of other problems. As a particular example, we examine unitary encoded space-time transmission of MIMO systems and we derive the received signal distribution when the channel matrix is correlated at the transmitter end

Communication in a disordered world

In finite magnetic field H, the excitation spectrum of the low energy quasiparticles in a two-dimensional d-wave superconductor exhibits a scaling with respect to H{sup 1/2}. This property can be used to calculate scaling relations for various physical quantities at low temperature T, such as the finite magnetic field specific heat, quasiparticle magnetic susceptibility, optical conductivity tensor, and thermal conductivity tensor. These predictions are compatible with existing experimental data. Most notably, the measured thermal Hall coefficient {kappa}{sub xy} in YBCO is found to scale as {kappa}{sub xy}{approximately}T{sup 2}F({alpha}T/ H{sup 1/2}) for T{approx_lt}30K in agreement with our predictions. {copyright} {ital 1997} {ital The American Physical Society}