Where are the Hedgehogs in Nematics?

In experiments which take a liquid crystal rapidly from the isotropic to the nematic phase, a dense tangle of defects is formed. In nematics, there are in principle both line and point defects (``hedgehogs''), but no point defects are observed until the defect network has coarsened appreciably. In this letter the expected density of point defects is shown to be extremely low, approximately $10^{-8}$ per initially correlated domain, as result of the topology (specifically, the homology) of the order parameter space.Comment: 6 pages, latex, 1 figure (self-unpacking PostScript)

Cryogenic-coolant He4-superconductor dynamic and static interactions

A composite superconducting material (NbTi-Cu) was evaluated with emphasis on post quench solid cooling interaction regimes. The quasi-steady runs confirm the existence of a thermodynamic limiting thickness for insulating coatings. Two distinctly different post quench regimes of coated composites are shown to relate to the limiting thickness. Only one regime,, from quench onset to the peak value, revealed favorable coolant states, in particular in He2. Transient recovery shows favorable recovery times from this post quench regime (not drastically different from bare conductors) for both single coated specimens and a coated conductor bundle

Local invariants of stabilizer codes

In [Phys. Rev. A 58, 1833 (1998)] a family of polynomial invariants which separate the orbits of multi-qubit density operators $\rho$ under the action of the local unitary group was presented. We consider this family of invariants for the class of those $\rho$ which are the projection operators describing stabilizer codes and give a complete translation of these invariants into the binary framework in which stabilizer codes are usually described. Such an investigation of local invariants of quantum codes is of natural importance in quantum coding theory, since locally equivalent codes have the same error-correcting capabilities and local invariants are powerful tools to explore their structure. Moreover, the present result is relevant in the context of multipartite entanglement and the development of the measurement-based model of quantum computation known as the one-way quantum computer.Comment: 10 pages, 1 figure. Minor changes. Accepted in Phys. Rev.

Incomplete quantum process tomography and principle of maximal entropy

The main goal of this paper is to extend and apply the principle of maximum entropy (MaxEnt) to incomplete quantum process estimation tasks. We will define a so-called process entropy function being the von Neumann entropy of the state associated with the quantum process via Choi-Jamiolkowski isomorphism. It will be shown that an arbitrary process estimation experiment can be reformulated in a unified framework and MaxEnt principle can be consistently exploited. We will argue that the suggested choice for the process entropy satisfies natural list of properties and it reduces to the state MaxEnt principle, if applied to preparator devices.Comment: 8 pages, comments welcome, references adde

Geometric quantum computation using fictitious spin- 1/2 subspaces of strongly dipolar coupled nuclear spins

Geometric phases have been used in NMR, to implement controlled phase shift gates for quantum information processing, only in weakly coupled systems in which the individual spins can be identified as qubits. In this work, we implement controlled phase shift gates in strongly coupled systems, by using non-adiabatic geometric phases, obtained by evolving the magnetization of fictitious spin-1/2 subspaces, over a closed loop on the Bloch sphere. The dynamical phase accumulated during the evolution of the subspaces, is refocused by a spin echo pulse sequence and by setting the delay of transition selective pulses such that the evolution under the homonuclear coupling makes a complete $2\pi$ rotation. A detailed theoretical explanation of non-adiabatic geometric phases in NMR is given, by using single transition operators. Controlled phase shift gates, two qubit Deutsch-Jozsa algorithm and parity algorithm in a qubit-qutrit system have been implemented in various strongly dipolar coupled systems obtained by orienting the molecules in liquid crystal media.Comment: 37 pages, 17 figure

Dynamics of a Quantum Phase Transition

We present two approaches to the dynamics of a quench-induced phase transition in quantum Ising model. The first one retraces steps of the standard approach to thermodynamic second order phase transitions in the quantum setting. The second one is purely quantum, based on the Landau-Zener formula for transition probabilities in avoided level crossings. We show that the two approaches yield compatible results for the scaling of the defect density with the quench rate. We exhibit similarities between them, and comment on the insights they give into dynamics of quantum phase transitions.Comment: 4 pages, 3 figures. Replaced by revised versio

Quantum Bit Regeneration

Decoherence and loss will limit the practicality of quantum cryptography and computing unless successful error correction techniques are developed. To this end, we have discovered a new scheme for perfectly detecting and rejecting the error caused by loss (amplitude damping to a reservoir at T=0), based on using a dual-rail representation of a quantum bit. This is possible because (1) balanced loss does not perform a ``which-path'' measurement in an interferometer, and (2) balanced quantum nondemolition measurement of the ``total'' photon number can be used to detect loss-induced quantum jumps without disturbing the quantum coherence essential to the quantum bit. Our results are immediately applicable to optical quantum computers using single photonics devices.Comment: 4 pages, postscript only, figures available at http://feynman.stanford.edu/qcom

Factoring in a Dissipative Quantum Computer

We describe an array of quantum gates implementing Shor's algorithm for prime factorization in a quantum computer. The array includes a circuit for modular exponentiation with several subcomponents (such as controlled multipliers, adders, etc) which are described in terms of elementary Toffoli gates. We present a simple analysis of the impact of losses and decoherence on the performance of this quantum factoring circuit. For that purpose, we simulate a quantum computer which is running the program to factor N = 15 while interacting with a dissipative environment. As a consequence of this interaction randomly selected qubits may spontaneously decay. Using the results of our numerical simulations we analyze the efficiency of some simple error correction techniques.Comment: plain tex, 18 pages, 8 postscript figure

Implementing universal multi-qubit quantum logic gates in three and four-spin systems at room temperature

In this paper, we present the experimental realization of multi-qubit gates $$ in macroscopic ensemble of three-qubit and four-qubit molecules. Instead of depending heavily on the two-bit universal gate, which served as the basic quantum operation in quantum computing, we use pulses of well-defined frequency and length that simultaneously apply to all qubits in a quantum register. It appears that this method is experimentally convenient when this procedure is extended to more qubits on some quantum computation, and it can also be used in other physical systems.Comment: 5 Pages, 2 Figure

Classical model for bulk-ensemble NMR quantum computation

We present a classical model for bulk-ensemble NMR quantum computation: the quantum state of the NMR sample is described by a probability distribution over the orientations of classical tops, and quantum gates are described by classical transition probabilities. All NMR quantum computing experiments performed so far with three quantum bits can be accounted for in this classical model. After a few entangling gates, the classical model suffers an exponential decrease of the measured signal, whereas there is no corresponding decrease in the quantum description. We suggest that for small numbers of quantum bits, the quantum nature of NMR quantum computation lies in the ability to avoid an exponential signal decrease.Comment: 14 pages, no figures, revte