369 research outputs found
Quantum measurements and the Abelian Stabilizer Problem
We present a polynomial quantum algorithm for the Abelian stabilizer problem
which includes both factoring and the discrete logarithm. Thus we extend famous
Shor's results. Our method is based on a procedure for measuring an eigenvalue
of a unitary operator. Another application of this procedure is a polynomial
quantum Fourier transform algorithm for an arbitrary finite Abelian group. The
paper also contains a rather detailed introduction to the theory of quantum
computation.Comment: 22 pages, LATE
Exact results for spin dynamics and fractionization in the Kitaev Model
We present certain exact analytical results for dynamical spin correlation
functions in the Kitaev Model. It is the first result of its kind in
non-trivial quantum spin models. The result is also novel: in spite of presence
of gapless propagating Majorana fermion excitations, dynamical two spin
correlation functions are identically zero beyond nearest neighbor separation,
showing existence of a gapless but short range spin liquid. An unusual,
\emph{all energy scale fractionization}of a spin -flip quanta, into two
infinitely massive -fluxes and a dynamical Majorana fermion, is shown to
occur. As the Kitaev Model exemplifies topological quantum computation, our
result presents new insights into qubit dynamics and generation of topological
excitations.Comment: 4 pages, 2 figures. Typose corrected, figure made better, clarifying
statements and references adde
Connection Formulae for Asymptotics of Solutions of the Degenerate Third Painlev\'{e} Equation. I
The degenerate third Painlev\'{e} equation, , where ,
and , and the associated tau-function are studied via the
Isomonodromy Deformation Method. Connection formulae for asymptotics of the
general as and solution and general regular as and solution are obtained.Comment: 40 pages, LaTeX2
Zeta functions and Dynamical Systems
In this brief note we present a very simple strategy to investigate dynamical
determinants for uniformly hyperbolic systems. The construction builds on the
recent introduction of suitable functional spaces which allow to transform
simple heuristic arguments in rigorous ones. Although the results so obtained
are not exactly optimal the straightforwardness of the argument makes it
noticeable.Comment: 7 pages, no figuer
Decoherence Free Subspace and entanglement by interaction with a common squeezed bath
In this work we find explicitly the decoherence free subspace (DFS) for a two
two-level system in a common squeezed vacuum bath. We also find an orthogonal
basis for the DFS composed of a symmetrical and an antisymmetrical (under
particle permutation) entangled state. For any initial symmetrical state, the
master equation has one stationary state which is the symmetrical entangled
decoherence free state. In this way, one can generate entanglement via common
squeezed bath of the two systems. If the initial state does not have a definite
parity, the stationary state depends strongly on the initial conditions of the
system and it has a statistical mixture of states which belong to the DFS. We
also study the effect of the coupling between the two-level systems on the DFS.Comment: 4 pages, 1 figur
Lattice model of three-dimensional topological singlet superconductor with time-reversal symmetry
We study topological phases of time-reversal invariant singlet
superconductors in three spatial dimensions. In these particle-hole symmetric
systems the topological phases are characterized by an even-numbered winding
number . At a two-dimensional (2D) surface the topological properties of
this quantum state manifest themselves through the presence of flavors of
gapless Dirac fermion surface states, which are robust against localization
from random impurities. We construct a tight-binding model on the diamond
lattice that realizes a topologically nontrivial phase, in which the winding
number takes the value . Disorder corresponds to a (non-localizing)
random SU(2) gauge potential for the surface Dirac fermions, leading to a
power-law density of states . The bulk
effective field theory is proposed to be the (3+1) dimensional SU(2) Yang-Mills
theory with a theta-term at .Comment: 5 pages, 3 figure
Exploring Contractor Renormalization: Tests on the 2-D Heisenberg Antiferromagnet and Some New Perspectives
Contractor Renormalization (CORE) is a numerical renormalization method for
Hamiltonian systems that has found applications in particle and condensed
matter physics. There have been few studies, however, on further understanding
of what exactly it does and its convergence properties. The current work has
two main objectives. First, we wish to investigate the convergence of the
cluster expansion for a two-dimensional Heisenberg Antiferromagnet(HAF). This
is important because the linked cluster expansion used to evaluate this formula
non-perturbatively is not controlled by a small parameter. Here we present a
study of three different blocking schemes which reveals some surprises and in
particular, leads us to suggest a scheme for defining successive terms in the
cluster expansion. Our second goal is to present some new perspectives on CORE
in light of recent developments to make it accessible to more researchers,
including those in Quantum Information Science. We make some comparison to
entanglement-based approaches and discuss how it may be possible to improve or
generalize the method.Comment: Completely revised version accepted by Phy Rev B; 13 pages with added
material on entropy in COR
- …