Simulating lattice gauge theories on a quantum computer

We examine the problem of simulating lattice gauge theories on a universal quantum computer. The basic strategy of our approach is to transcribe lattice gauge theories in the Hamiltonian formulation into a Hamiltonian involving only Pauli spin operators such that the simulation can be performed on a quantum computer using only one and two qubit manipulations. We examine three models, the U(1), SU(2), and SU(3) lattice gauge theories which are transcribed into a spin Hamiltonian up to a cutoff in the Hilbert space of the gauge fields on the lattice. The number of qubits required for storing a particular state is found to have a linear dependence with the total number of lattice sites. The number of qubit operations required for performing the time evolution corresponding to the Hamiltonian is found to be between a linear to quadratic function of the number of lattice sites, depending on the arrangement of qubits in the quantum computer. We remark that our results may also be easily generalized to higher SU(N) gauge theories.Comment: 15 pages, 4 figures, 3 table

N=4 Supersymmetric Yang-Mills on S^3 in Plane Wave Matrix Model at Finite Temperature

We investigate the large N reduced model of gauge theory on a curved spacetime through the plane wave matrix model. We formally derive the action of the N=4 supersymmetric Yang-Mills theory on R \times S^3 from the plane wave matrix model in the large N limit. Furthermore, we evaluate the effective action of the plane wave matrix model up to the two-loop level at finite temperature. We find that the effective action is consistent with the free energy of the N=4 supersymmetric Yang-Mills theory on S^3 at high temperature limit where the planar contributions dominate. We conclude that the plane wave matrix model can be used as a large N reduced model to investigate nonperturbative aspects of the N=4 supersymmetric Yang-Mills theory on R \times S^3.Comment: 31pages: added comments and reference

Highly nonclassical photon statistics in parametric down conversion

We use photon counters to obtain the joint photon counting statistics from twin-beam non-degenerate parametric down conversion, and we demonstrate directly, and with no auxiliary assumptions, that these twin beams are nonclassical

Quantum computers based on electron spins controlled by ultra-fast, off-resonant, single optical pulses

We describe a fast quantum computer based on optically controlled electron spins in charged quantum dots that are coupled to microcavities. This scheme uses broad-band optical pulses to rotate electron spins and provide the clock signal to the system. Non-local two-qubit gates are performed by phase shifts induced by electron spins on laser pulses propagating along a shared waveguide. Numerical simulations of this scheme demonstrate high-fidelity single-qubit and two-qubit gates with operation times comparable to the inverse Zeeman frequency.Comment: 4 pages, 4 figures, introduction is clarified, the section on two-qubit gates was expanded and much more detail about gate fidelities is given, figures were modified, one figure replaced with a figure showing gate fidelities for relevant parameter

Infra-red effects of Non-linear sigma model in de Sitter space

We extend our investigation on a possible de Sitter symmetry breaking mechanism in non-linear sigma models. The scale invariance of the quantum fluctuations could make the cosmological constant time dependent signaling the de Sitter symmetry breaking. To understand such a symmetry breaking mechanism, we investigate the energy-momentum tensor. We show that the leading infra-red logarithms cancel to all orders in perturbation theory in a generic non-linear sigma model. When the target space is an N sphere, the de Sitter symmetry is preserved in the large N limit. For a less symmetric target space, the infra-red logarithms appear at the three loop level. However there is a counter term to precisely cancel it. The leading infra-red logarithms do not cancel for higher derivative interactions. We investigate such a model in which the infra-red logarithms first appear at the three loop level. A nonperturbative investigation in the large N limit shows that they eventually grow as large as the one loop effect.Comment: 39page

Interplay between elastic fields due to gravity and a partial dislocation for a hard-sphere crystal coherently grown under gravity: driving force for defect disappearance

We previously observed that an intrinsic staking fault shrunk through a glide of a Shockley partial dislocation terminating its lower end in a hard-sphere crystal under gravity coherently grown in by Monte Carlo simulations [Mori et al., Molec. Phys. 105, 1377 (2007)]; it was an answer to a one-decade long standing question why the stacking disorder in colloidal crystals reduced under gravity [Zhu et al., Nature 387, 883 (1997)]. Here, we present an elastic energy calculation; in addition to the self-energy of the partial dislocation [Mori et al., Prog. Theor. Phys. Suppl. 178, 33 (2009)] we calculate the cross-coupling term between elastic field due to gravity and that due to a Shockley partial dislocation. The cross term is a increasing function of the linear dimension R over which the elastic field expands, showing that a driving force arises for the partial dislocation moving toward the upper boundary of a grain.Comment: 8pages, 4figures, to be published in Molecular Physic

A New Opinion Polarization Index Developed by Integrating Expert Judgments

Opinion polarization is increasingly becoming an issue in today’s society, producing both unrest at the societal level, and conflict within small scale communications between people of opposite opinion. Often, opinion polarization is conceptualized as the direct opposite of agreement and consequently operationalized as an index of dispersion. However, in doing so, researchers fail to account for the bimodality that is characteristic of a polarized opinion distribution. A valid measurement of opinion polarization would enable us to predict when, and on what issues conflict may arise. The current study is aimed at developing and validating a new index of opinion polarization. The weights of this index were derived from utilizing the knowledge of 58 international experts on polarization through an expert survey. The resulting Opinion Polarization Index predicted expert polarization scores in opinion distributions better than common measures of polarization, such as the standard deviation, Van der Eijk’s polarization measure and Esteban and Ray’s polarization index. We reflect on the use of expert ratings for the development of measurements in this case, and more in general

Quantum Degenerate Exciton-Polaritons in Thermal Equilibrium

We study the momentum distribution and relaxation dynamics of semiconductor microcavity polaritons by angle-resolved and time-resolved spectroscopy. Above a critical pump level, the thermalization time of polaritons at positive detunings becomes shorter than their lifetime, and the polaritons form a quantum degenerate Bose-Einstein distribution in thermal equilibrium with the lattice.Comment: Updated with the published versio

On the origin of non-monotonic doping dependence of the in-plane resistivity anisotropy in Ba(Fe1−xTx_{1-x}T_x)2_2As2_2, TT = Co, Ni and Cu

The in-plane resistivity anisotropy has been measured for detwinned single crystals of Ba(Fe$_{1-x}$Ni$_x$)$_2$As$_2$ and Ba(Fe$_{1-x}$Cu$_x$)$_2$As$_2$. The data reveal a non-monotonic doping dependence, similar to previous observations for Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$. Magnetotransport measurements of the parent compound reveal a non-linear Hall coefficient and a strong linear term in the transverse magnetoresistance. Both effects are rapidly suppressed with chemical substitution over a similar compositional range as the onset of the large in-plane resistivity anisotropy. It is suggested that the relatively small in-plane anisotropy of the parent compound in the spin density wave state is due to the presence of an isotropic, high mobility pocket of reconstructed Fermi surface. Progressive suppression of the contribution to the conductivity arising from this isotropic pocket with chemical substitution eventually reveals the underlying in-plane anisotropy associated with the remaining FS pockets.Comment: 12 pages, 9 figure

Graviton Propagators on Fuzzy G/H

We describe closed string modes by open Wilson lines in noncommutative (NC) gauge theories on compact fuzzy G/H in IIB matrix model. In this construction the world sheet cut-off is related to the spacetime cut-off since the string bit of the symmetric traced Wilson line carries the minimum momentum on G/H. We show that the two point correlation functions of graviton type Wilson lines in 4 dimensional NC gauge theories behave as 1/(momentum)^2. This result suggests that graviton is localized on D3-brane, so we can naturally interpret D3-branes as our universe. Our result is not limited to D3-brane system, and we generalize our analysis to other dimensions and even to any topology of D-brane worldvolume within fuzzy G/H.Comment: 22 pages, 1 figure. minor correction