15,599 research outputs found
Homological Product Codes
Quantum codes with low-weight stabilizers known as LDPC codes have been
actively studied recently due to their simple syndrome readout circuits and
potential applications in fault-tolerant quantum computing. However, all
families of quantum LDPC codes known to this date suffer from a poor distance
scaling limited by the square-root of the code length. This is in a sharp
contrast with the classical case where good families of LDPC codes are known
that combine constant encoding rate and linear distance. Here we propose the
first family of good quantum codes with low-weight stabilizers. The new codes
have a constant encoding rate, linear distance, and stabilizers acting on at
most qubits, where is the code length. For comparison, all
previously known families of good quantum codes have stabilizers of linear
weight. Our proof combines two techniques: randomized constructions of good
quantum codes and the homological product operation from algebraic topology. We
conjecture that similar methods can produce good stabilizer codes with
stabilizer weight for any . Finally, we apply the homological
product to construct new small codes with low-weight stabilizers.Comment: 49 page
A demonstration of centimeter-level monitoring of polar motion with the Global Positioning System
Daily estimates of the Earth's pole position were obtained with the Global Positioning System (GPS) by using measurements obtained during the GPS IERS (International Earth Rotation Service) and Geodynamics (GIG'91) experiment from 22 Jan. to 13 Feb. 1991. Data from a globally distributed network consisting of 21 Rogue GPS receivers were chosen for the analysis. A comparison of the GPS polar motion series with nine 24-hour very long baseline interferometry (VLBI) estimates yielded agreement in the day-to-day pole position of about 1.5 cm for both X and Y polar motion. A similar comparison of GPS and satellite laser ranging (SLR) data showed agreement to about 1.0 cm. These preliminary results indicate that polar motion can be determined by GPS independent of, and at a level comparable to, that which is obtained from either VLBI or SLR. Furthermore, GPS can provide these data with a daily frequency that neither alternative technique can readily achieve. Thus, GPS promises to be a powerful tool for determining high-frequency platform parameter variation, essential for the ultraprecise spacecraft-tracking requirements of the coming years
Schmidt Analysis of Pure-State Entanglement
We examine the application of Schmidt-mode analysis to pure state
entanglement. Several examples permitting exact analytic calculation of Schmidt
eigenvalues and eigenfunctions are included, as well as evaluation of the
associated degree of entanglement.Comment: 5 pages, 3 figures, for C.M. Bowden memoria
Three flavour Quark matter in chiral colour dielectric model
We investigate the properties of quark matter at finite density and
temperature using the nonlinear chiral extension of Colour Dielectric Model
(CCM). Assuming that the square of the meson fields devlop non- zero vacuum
expectation value, the thermodynamic potential for interacting three flavour
matter has been calculated. It is found that remain zero
in the medium whereas changes in the medium. As a result, and
quark masses decrease monotonically as the temperature and density of the quark
matter is increased.In the present model, the deconfinement density and
temperature is found to be lower compared to lattice results. We also study the
behaviour of pressure and energy density above critical temperature.Comment: Latex file. 5 figures available on request. To appear in Phys. Rev.
Half-Life of O
We have measured the half-life of O, a superallowed decay isotope. The O was produced by the
C(He,n)O reaction using a carbon aerogel target. A
low-energy ion beam of O was mass separated and implanted in a thin
beryllium foil. The beta particles were counted with plastic scintillator
detectors. We find s. This result is
higher than an average value from six earlier experiments, but agrees more
closely with the most recent previous measurement.Comment: 10 pages, 5 figure
Quantum Field Theory and Differential Geometry
We introduce the historical development and physical idea behind topological
Yang-Mills theory and explain how a physical framework describing subatomic
physics can be used as a tool to study differential geometry. Further, we
emphasize that this phenomenon demonstrates that the interrelation between
physics and mathematics have come into a new stage.Comment: 29 pages, enlarged version, some typewritten mistakes have been
corrected, the geometric descrition to BRST symmetry, the chain of descent
equations and its application in TYM as well as an introduction to R-symmetry
have been added, as required by mathematicia
The Pfaffian quantum Hall state made simple--multiple vacua and domain walls on a thin torus
We analyze the Moore-Read Pfaffian state on a thin torus. The known six-fold
degeneracy is realized by two inequivalent crystalline states with a four- and
two-fold degeneracy respectively. The fundamental quasihole and quasiparticle
excitations are domain walls between these vacua, and simple counting arguments
give a Hilbert space of dimension for holes and particles
at fixed positions and assign each a charge . This generalizes the
known properties of the hole excitations in the Pfaffian state as deduced using
conformal field theory techniques. Numerical calculations using a model
hamiltonian and a small number of particles supports the presence of a stable
phase with degenerate vacua and quarter charged domain walls also away from the
thin torus limit. A spin chain hamiltonian encodes the degenerate vacua and the
various domain walls.Comment: 4 pages, 1 figure. Published, minor change
27/32
We show that when an N=2 SCFT flows to an N=1 SCFT via giving a mass to the
adjoint chiral superfield in a vector multiplet with marginal coupling, the
central charges a and c of the N=2 theory are related to those of the N=1
theory by a universal linear transformation. In the large N limit, this
relationship implies that the central charges obey a_IR/a_UV=c_IR/c_UV=27/32.
This gives a physical explanation to many examples of this number found in the
literature, and also suggests the existence of a flow between some theories not
previously thought to be connected.Comment: 3 pages. v2: references added, minor typos correcte
- …