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)

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

Transforming quantum operations: quantum supermaps

We introduce the concept of quantum supermap, describing the most general transformation that maps an input quantum operation into an output quantum operation. Since quantum operations include as special cases quantum states, effects, and measurements, quantum supermaps describe all possible transformations between elementary quantum objects (quantum systems as well as quantum devices). After giving the axiomatic definition of supermap, we prove a realization theorem, which shows that any supermap can be physically implemented as a simple quantum circuit. Applications to quantum programming, cloning, discrimination, estimation, information-disturbance trade-off, and tomography of channels are outlined.Comment: 6 pages, 1 figure, published versio

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

Quantum Clock Synchronization Based on Shared Prior Entanglement

We demonstrate that two spatially separated parties (Alice and Bob) can utilize shared prior quantum entanglement, and classical communications, to establish a synchronized pair of atomic clocks. In contrast to classical synchronization schemes, the accuracy of our protocol is independent of Alice or Bob's knowledge of their relative locations or of the properties of the intervening medium.Comment: 4 page

Wall-crossing, open BPS counting and matrix models

We consider wall-crossing phenomena associated to the counting of D2-branes attached to D4-branes wrapping lagrangian cycles in Calabi-Yau manifolds, both from M-theory and matrix model perspective. Firstly, from M-theory viewpoint, we review that open BPS generating functions in various chambers are given by a restriction of the modulus square of the open topological string partition functions. Secondly, we show that these BPS generating functions can be identified with integrands of matrix models, which naturally arise in the free fermion formulation of corresponding crystal models. A parameter specifying a choice of an open BPS chamber has a natural, geometric interpretation in the crystal model. These results extend previously known relations between open topological string amplitudes and matrix models to include chamber dependence.Comment: 25 pages, 8 figures, published versio

Magnetism and Charge Dynamics in Iron Pnictides

In a wide variety of materials, such as copper oxides, heavy fermions, organic salts, and the recently discovered iron pnictides, superconductivity is found in close proximity to a magnetically ordered state. The character of the proximate magnetic phase is thus believed to be crucial for understanding the differences between the various families of unconventional superconductors and the mechanism of superconductivity. Unlike the AFM order in cuprates, the nature of the magnetism and of the underlying electronic state in the iron pnictide superconductors is not well understood. Neither density functional theory nor models based on atomic physics and superexchange, account for the small size of the magnetic moment. Many low energy probes such as transport, STM and ARPES measured strong anisotropy of the electronic states akin to the nematic order in a liquid crystal, but there is no consensus on its physical origin, and a three dimensional picture of electronic states and its relations to the optical conductivity in the magnetic state is lacking. Using a first principles approach, we obtained the experimentally observed magnetic moment, optical conductivity, and the anisotropy of the electronic states. The theory connects ARPES, which measures one particle electronic states, optical spectroscopy, probing the particle hole excitations of the solid and neutron scattering which measures the magnetic moment. We predict a manifestation of the anisotropy in the optical conductivity, and we show that the magnetic phase arises from the paramagnetic phase by a large gain of the Hund's rule coupling energy and a smaller loss of kinetic energy, indicating that iron pnictides represent a new class of compounds where the nature of magnetism is intermediate between the spin density wave of almost independent particles, and the antiferromagnetic state of local moments.Comment: 4+ pages with additional one-page supplementary materia

Anisotropic Energy Gaps of Iron-based Superconductivity from Intra-band Quasiparticle Interference in LiFeAs

If strong electron-electron interactions between neighboring Fe atoms mediate the Cooper pairing in iron-pnictide superconductors, then specific and distinct anisotropic superconducting energy gaps \Delta_i(k) should appear on the different electronic bands i. Here we introduce intra-band Bogoliubov quasiparticle scattering interference (QPI) techniques for determination of \Delta_i(k) in such materials, focusing on LiFeAs. We identify the three hole-like bands assigned previously as \gamma, \alpha_2 and \alpha_1, and we determine the anisotropy, magnitude and relative orientations of their \Delta_i(k). These measurements will advance quantitative theoretical analysis of the mechanism of Cooper pairing in iron-based superconductivity

Can quantum chaos enhance stability of quantum computation?

We consider stability of a general quantum algorithm with respect to a fixed but unknown residual interaction between qubits, and show a surprising fact, namely that the average fidelity of quantum computation increases by decreasing average time correlation function of the perturbing operator in sequences of consecutive quantum gates. Our thinking is applied to the quantum Fourier transformation where an alternative 'less regular' quantum algorithm is devised which is qualitatively more robust against static random residual n-qubit interaction.Comment: 4 pages, 5 eps figures (3 color

Cosmic String Formation from Correlated Fields

We simulate the formation of cosmic strings at the zeros of a complex Gaussian field with a power spectrum $P(k) \propto k^n$, specifically addressing the issue of the fraction of length in infinite strings. We make two improvements over previous simulations: we include a non-zero random background field in our box to simulate the effect of long-wavelength modes, and we examine the effects of smoothing the field on small scales. The inclusion of the background field significantly reduces the fraction of length in infinite strings for $n < -2$. Our results are consistent with the possibility that infinite strings disappear at some $n = n_c$ in the range $-3 \le n_c < -2.2$, although we cannot rule out $n_c = -3$, in which case infinite strings would disappear only at the point where the mean string density goes to zero. We present an analytic argument which suggests the latter case. Smoothing on small scales eliminates closed loops on the order of the lattice cell size and leads to a ``lattice-free" estimate of the infinite string fraction. As expected, this fraction depends on the type of window function used for smoothing.Comment: 24 pages, latex, 10 figures, submitted to Phys Rev