Unified model for vortex-string network evolution

We describe and numerically test the velocity-dependent one-scale (VOS) string evolution model, a simple analytic approach describing a string network with the averaged correlation length and velocity. We show that it accurately reproduces the large-scale behaviour (in particular the scaling laws) of numerical simulations of both Goto-Nambu and field theory string networks. We explicitly demonstrate the relation between the high-energy physics approach and the damped and non-relativistic limits which are relevant for condensed matter physics. We also reproduce experimental results in this context and show that the vortex-string density is significantly reduced by loop production, an effect not included in the usual `coarse-grained' approach.Comment: 5 pages; v2: cosmetic changes, version to appear in PR

Quantum Computation and Spin Physics

A brief review is given of the physical implementation of quantum computation within spin systems or other two-state quantum systems. The importance of the controlled-NOT or quantum XOR gate as the fundamental primitive operation of quantum logic is emphasized. Recent developments in the use of quantum entanglement to built error-robust quantum states, and the simplest protocol for quantum error correction, are discussed.Comment: 21 pages, Latex, 3 eps figures, prepared for the Proceedings of the Annual MMM Meeting, November, 1996, to be published in J. Appl. Phy

Angular distribution of photoluminescence as a probe of Bose Condensation of trapped excitons

Recent experiments on two-dimensional exciton systems have shown the excitons collect in shallow in-plane traps. We find that Bose condensation in a trap results in a dramatic change of the exciton photoluminescence (PL) angular distribution. The long-range coherence of the condensed state gives rise to a sharply focussed peak of radiation in the direction normal to the plane. By comparing the PL profile with and without Bose Condensation we provide a simple diagnostic for the existence of a Bose condensate. The PL peak has strong temperature dependence due to the thermal order parameter phase fluctuations across the system. The angular PL distribution can also be used for imaging vortices in the trapped condensate. Vortex phase spatial variation leads to destructive interference of PL radiation in certain directions, creating nodes in the PL distribution that imprint the vortex configuration.Comment: 4 pages, 3 figure

Separability of very noisy mixed states and implications for NMR quantum computing

We give a constructive proof that all mixed states of N qubits in a sufficiently small neighborhood of the maximally mixed state are separable. The construction provides an explicit representation of any such state as a mixture of product states. We give upper and lower bounds on the size of the neighborhood, which show that its extent decreases exponentially with the number of qubits. We also discuss the implications of the bounds for NMR quantum computing.Comment: 4 pages, extensively revised, references adde

ROM-based quantum computation: Experimental explorations using Nuclear Magnetic Resonance, and future prospects

ROM-based quantum computation (QC) is an alternative to oracle-based QC. It has the advantages of being less ``magical'', and being more suited to implementing space-efficient computation (i.e. computation using the minimum number of writable qubits). Here we consider a number of small (one and two-qubit) quantum algorithms illustrating different aspects of ROM-based QC. They are: (a) a one-qubit algorithm to solve the Deutsch problem; (b) a one-qubit binary multiplication algorithm; (c) a two-qubit controlled binary multiplication algorithm; and (d) a two-qubit ROM-based version of the Deutsch-Jozsa algorithm. For each algorithm we present experimental verification using NMR ensemble QC. The average fidelities for the implementation were in the ranges 0.9 - 0.97 for the one-qubit algorithms, and 0.84 - 0.94 for the two-qubit algorithms. We conclude with a discussion of future prospects for ROM-based quantum computation. We propose a four-qubit algorithm, using Grover's iterate, for solving a miniature ``real-world'' problem relating to the lengths of paths in a network.Comment: 11 pages, 5 figure

Experimental Realization of A Two Bit Phase Damping Quantum Code

Using nuclear magnetic resonance techniques, we experimentally investigated the effects of applying a two bit phase error detection code to preserve quantum information in nuclear spin systems. Input states were stored with and without coding, and the resulting output states were compared with the originals and with each other. The theoretically expected result, net reduction of distortion and conditional error probabilities to second order, was indeed observed, despite imperfect coding operations which increased the error probabilities by approximately 5%. Systematic study of the deviations from the ideal behavior provided quantitative measures of different sources of error, and good agreement was found with a numerical model. Theoretical questions in quantum error correction in bulk nuclear spin systems including fidelity measures, signal strength and syndrome measurements are discussed.Comment: 21 pages, 17 figures, mypsfig2, revtex. Minor changes made to appear in PR

A Driving Performance Forecasting System Based on Brain Dynamic State Analysis Using 4-D Convolutional Neural Networks.

Vehicle accidents are the primary cause of fatalities worldwide. Most often, experiencing fatigue on the road leads to operator errors and behavioral lapses. Thus, there is a need to predict the cognitive state of drivers, particularly their fatigue level. Electroencephalography (EEG) has been demonstrated to be effective for monitoring changes in the human brain state and behavior. Thirty-seven subjects participated in this driving experiment and performed a perform lane-keeping task in a visual-reality environment. Three domains, namely, frequency, temporal, and 2-D spatial information, of the EEG channel location were comprehensively considered. A 4-D convolutional neural-network (4-D CNN) algorithm was then proposed to associate all information from the EEG signals and the changes in the human state and behavioral performance. A 4-D CNN achieves superior forecasting performance over 2-D CNN, 3-D CNN, and shallow networks. The results showed a 3.82% improvement in the root mean-square error, a 3.45% improvement in the error rate, and a 11.98% improvement in the correlation coefficient with 4-D CNN compared with 3-D CNN. The 4-D CNN algorithm extracts the significant θ and alpha activations in the frontal and posterior cingulate cortices under distinct fatigue levels. This work contributes to enhancing our understanding of deep learning methods in the analysis of EEG signals. We even envision that deep learning might serve as a bridge between translation neuroscience and further real-world applications

Efficient implementation of selective recoupling in heteronuclear spin systems using Hadamard matrices

We present an efficient scheme which couples any designated pair of spins in heteronuclear spin systems. The scheme is based on the existence of Hadamard matrices. For a system of $n$ spins with pairwise coupling, the scheme concatenates $cn$ intervals of system evolution and uses at most $c n^2$ pulses where $c \approx 1$. Our results demonstrate that, in many systems, selective recoupling is possible with linear overhead, contrary to common speculation that exponential effort is always required.Comment: 7 pages, 4 figures, mypsfig2, revtex, submitted April 27, 199

An Alternative Topological Field Theory of Generalized Complex Geometry

We propose a new topological field theory on generalized complex geometry in two dimension using AKSZ formulation. Zucchini's model is $A$ model in the case that the generalized complex structuredepends on only a symplectic structure. Our new model is $B$ model in the case that the generalized complex structure depends on only a complex structure.Comment: 29 pages, typos and references correcte