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

NMR quantum computation with indirectly coupled gates

An NMR realization of a two-qubit quantum gate which processes quantum information indirectly via couplings to a spectator qubit is presented in the context of the Deutsch-Jozsa algorithm. This enables a successful comprehensive NMR implementation of the Deutsch-Jozsa algorithm for functions with three argument bits and demonstrates a technique essential for multi-qubit quantum computation.Comment: 9 pages, 2 figures. 10 additional figures illustrating output spectr

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

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

Quantum computation with linear optics

We present a constructive method to translate small quantum circuits into their optical analogues, using linear components of present-day quantum optics technology only. These optical circuits perform precisely the computation that the quantum circuits are designed for, and can thus be used to test the performance of quantum algorithms. The method relies on the representation of several quantum bits by a single photon, and on the implementation of universal quantum gates using simple optical components (beam splitters, phase shifters, etc.). The optical implementation of Brassard et al.'s teleportation circuit, a non-trivial 3-bit quantum computation, is presented as an illustration.Comment: LaTeX with llncs.cls, 11 pages with 5 postscript figures, Proc. of 1st NASA Workshop on Quantum Computation and Quantum Communication (QCQC 98

Are there static texture?

We consider harmonic maps from Minkowski space into the three sphere. We are especially interested in solutions which are asymptotically constant, i.e. converge to the same value in all directions of spatial infinity. Physical 3-space can then be compactified and can be identified topologically (but not metrically!) with a three sphere. Therefore, at fixed time, the winding of the map is defined. We investigate whether static solutions with non-trivial winding number exist. The answer which we can proof here is only partial: We show that within a certain family of maps no static solutions with non-zero winding number exist. We discuss the existing static solutions in our family of maps. An extension to other maps or a proof that our family of maps is sufficiently general remains an open problem.Comment: 12 page Latex file, 1 postscript figure, submitted to PR

Implementation of the Five Qubit Error Correction Benchmark

The smallest quantum code that can correct all one-qubit errors is based on five qubits. We experimentally implemented the encoding, decoding and error-correction quantum networks using nuclear magnetic resonance on a five spin subsystem of labeled crotonic acid. The ability to correct each error was verified by tomography of the process. The use of error-correction for benchmarking quantum networks is discussed, and we infer that the fidelity achieved in our experiment is sufficient for preserving entanglement.Comment: 6 pages with 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

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

Symmetric coupling of four spin-1/2 systems

We address the non-binary coupling of identical angular momenta based upon the representation theory for the symmetric group. A correspondence is pointed out between the complete set of commuting operators and the reference-frame-free subsystems. We provide a detailed analysis of the coupling of three and four spin-1/2 systems and discuss a symmetric coupling of four spin-1/2 systems.Comment: 20 pages, no figure