1,636 research outputs found
Minimal and Robust Composite Two-Qubit Gates with Ising-Type Interaction
We construct a minimal robust controlled-NOT gate with an Ising-type
interaction by which elementary two-qubit gates are implemented. It is robust
against inaccuracy of the coupling strength and the obtained quantum circuits
are constructed with the minimal number (N=3) of elementary two-qubit gates and
several one-qubit gates. It is noteworthy that all the robust circuits can be
mapped to one-qubit circuits robust against a pulse length error. We also prove
that a minimal robust SWAP gate cannot be constructed with N=3, but requires
N=6 elementary two-qubit gates.Comment: 7 pages, 2 figure
Existence and topological stability of Fermi points in multilayered graphene
We study the existence and topological stability of Fermi points in a
graphene layer and stacks with many layers. We show that the discrete
symmetries (spacetime inversion) stabilize the Fermi points in monolayer,
bilayer and multilayer graphene with orthorhombic stacking. The bands near
and in multilayers with the Bernal stacking depend on the
parity of the number of layers, and Fermi points are unstable when the number
of layers is odd. The low energy changes in the electronic structure induced by
commensurate perturbations which mix the two Dirac points are also
investigated.Comment: 6 pages, 6 figures. Expanded version as will appear in PR
A gauge theoretical view of the charge concept in Einstein gravity
We will discuss some analogies between internal gauge theories and gravity in
order to better understand the charge concept in gravity. A dimensional
analysis of gauge theories in general and a strict definition of elementary,
monopole, and topological charges are applied to electromagnetism and to
teleparallelism, a gauge theoretical formulation of Einstein gravity.
As a result we inevitably find that the gravitational coupling constant has
dimension , the mass parameter of a particle dimension ,
and the Schwarzschild mass parameter dimension l (where l means length). These
dimensions confirm the meaning of mass as elementary and as monopole charge of
the translation group, respectively. In detail, we find that the Schwarzschild
mass parameter is a quasi-electric monopole charge of the time translation
whereas the NUT parameter is a quasi-magnetic monopole charge of the time
translation as well as a topological charge. The Kerr parameter and the
electric and magnetic charges are interpreted similarly. We conclude that each
elementary charge of a Casimir operator of the gauge group is the source of a
(quasi-electric) monopole charge of the respective Killing vector.Comment: LaTeX2e, 16 pages, 1 figure; enhanced discussio
Realization of Arbitrary Gates in Holonomic Quantum Computation
Among the many proposals for the realization of a quantum computer, holonomic
quantum computation (HQC) is distinguished from the rest in that it is
geometrical in nature and thus expected to be robust against decoherence. Here
we analyze the realization of various quantum gates by solving the inverse
problem: Given a unitary matrix, we develop a formalism by which we find loops
in the parameter space generating this matrix as a holonomy. We demonstrate for
the first time that such a one-qubit gate as the Hadamard gate and such
two-qubit gates as the CNOT gate, the SWAP gate and the discrete Fourier
transformation can be obtained with a single loop.Comment: 8 pages, 6 figure
Gauge Invariant Factorisation and Canonical Quantisation of Topologically Massive Gauge Theories in Any Dimension
Abelian topologically massive gauge theories (TMGT) provide a topological
mechanism to generate mass for a bosonic p-tensor field in any spacetime
dimension. These theories include the 2+1 dimensional Maxwell-Chern-Simons and
3+1 dimensional Cremmer-Scherk actions as particular cases. Within the
Hamiltonian formulation, the embedded topological field theory (TFT) sector
related to the topological mass term is not manifest in the original phase
space. However through an appropriate canonical transformation, a gauge
invariant factorisation of phase space into two orthogonal sectors is feasible.
The first of these sectors includes canonically conjugate gauge invariant
variables with free massive excitations. The second sector, which decouples
from the total Hamiltonian, is equivalent to the phase space description of the
associated non dynamical pure TFT. Within canonical quantisation, a likewise
factorisation of quantum states thus arises for the full spectrum of TMGT in
any dimension. This new factorisation scheme also enables a definition of the
usual projection from TMGT onto topological quantum field theories in a most
natural and transparent way. None of these results rely on any gauge fixing
procedure whatsoever.Comment: 1+25 pages, no figure
Generalised Wick Transform in Dimensionally Reduced Gravity
In the context of canonical quantum gravity, we study an alternative real
quantisation scheme, which is arising by relating simpler Riemannian quantum
theory to the more complicated physical Lorentzian theory - the generalised
Wick transform. On the symmetry reduced models, homogenous Bianchi cosmology
and 2+1 gravity, we investigate its generalised construction principle,
demonstrate that the emerging quantum theory is equivalent to the one obtained
from standard quantisation and how to obtain physical states in Lorentzian
gravity from Wick transforming solutions of Riemannian quantum theory.Comment: 25 pages, 3 figures, revtex4; v.2: referencing improve
Infinite temperature limit of meson spectral functions calculated on the lattice
We analyze the cut-off dependence of mesonic spectral functions calculated at
finite temperature on Euclidean lattices with finite temporal extent. In the
infinite temperature limit we present analytic results for lattice spectral
functions calculated with standard Wilson fermions as well as a truncated
perfect action. We explicitly determine the influence of `Wilson doublers' on
the high momentum structure of the mesonic spectral functions and show that
this cut-off effect is strongly suppressed when using an improved fermion
action.Comment: 25 pages, 8 figure
Intrinsic frustration effects in anisotropic superconductors
Lattice distortions in which the axes are locally rotated provide an
intrinsic source of frustration in anisotropic superconductors. A general
framework to study this effect is presented. The influence of lattice defects
and phonons in and layered superconductors is studied.Comment: enlarged versio
A cosmological model in Weyl-Cartan spacetime: I. Field equations and solutions
In this first article of a series on alternative cosmological models we
present an extended version of a cosmological model in Weyl-Cartan spacetime.
The new model can be viewed as a generalization of a model developed earlier
jointly with Tresguerres. Within this model the non-Riemannian quantities, i.e.
torsion and nonmetricity , are proportional to
the Weyl 1-form. The hypermomentum depends on our
ansatz for the nonmetricity and vice versa. We derive the explicit form of the
field equations for different cases and provide solutions for a broad class of
parameters. We demonstrate that it is possible to construct models in which the
non-Riemannian quantities die out with time. We show how our model fits into
the more general framework of metric-affine gravity (MAG).Comment: 22 pages, 2 figures, uses IOP preprint styl
Exactly solvable scale-free network model
We study a deterministic scale-free network recently proposed by
Barab\'{a}si, Ravasz and Vicsek. We find that there are two types of nodes: the
hub and rim nodes, which form a bipartite structure of the network. We first
derive the exact numbers of nodes with degree for the hub and rim
nodes in each generation of the network, respectively. Using this, we obtain
the exact exponents of the distribution function of nodes with
degree in the asymptotic limit of . We show that the degree
distribution for the hub nodes exhibits the scale-free nature, with , while the degree
distribution for the rim nodes is given by with
. Second, we numerically as well as analytically
calculate the spectra of the adjacency matrix for representing topology of
the network. We also analytically obtain the exact number of degeneracy at each
eigenvalue in the network. The density of states (i.e., the distribution
function of eigenvalues) exhibits the fractal nature with respect to the
degeneracy. Third, we study the mathematical structure of the determinant of
the eigenequation for the adjacency matrix. Fourth, we study hidden symmetry,
zero modes and its index theorem in the deterministic scale-free network.
Finally, we study the nature of the maximum eigenvalue in the spectrum of the
deterministic scale-free network. We will prove several theorems for it, using
some mathematical theorems. Thus, we show that most of all important quantities
in the network theory can be analytically obtained in the deterministic
scale-free network model of Barab\'{a}si, Ravasz and Vicsek. Therefore, we may
call this network model the exactly solvable scale-free network.Comment: 18 pages, 5 figure
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