15 research outputs found
Pattern recognition on a quantum computer
By means of a simple example it is demonstrated that the task of finding and
identifying certain patterns in an otherwise (macroscopically) unstructured
picture (data set) can be accomplished efficiently by a quantum computer.
Employing the powerful tool of the quantum Fourier transform the proposed
quantum algorithm exhibits an exponential speed-up in comparison with its
classical counterpart. The digital representation also results in a
significantly higher accuracy than the method of optical filtering. PACS:
03.67.Lx, 03.67.-a, 42.30.Sy, 89.70.+c.Comment: 6 pages RevTeX, 1 figure, several correction
Gauge theories of Josephson junction arrays
We show that the zero-temperature physics of planar Josephson junction arrays in the self-dual approximation is governed by an Abelian gauge theory with periodic mixed Chern-Simons term describing the charge-vortex coupling. The periodicity requires the existence of (Euclidean) topological excitations which determine the quantum phase structure of the model. The electric-magnetic duality leads to a quantum phase transition between a superconductor and a superinsulator at the self-dual point. We also discuss in this framework the recently proposed quantum Hall phases for charges and vortices in presence of external offset charges and magnetic fluxes: we show how the periodicity of the charge-vortex coupling can lead to transitions to anyon superconductivity phases. We finally generalize our results to three dimensions, where the relevant gauge theory is the so-called BF system, with an antisymmetric Kalb-Ramond gauge field.We show that the zero-temperature physics of planar Josephson junction arrays in the self-dual approximation is governed by an Abelian gauge theory with periodic mixed Chern-Simons term describing the charge-vortex coupling. The periodicity requires the existence of (Euclidean) topological excitations which determine the quantum phase structure of the model. The electric-magnetic duality leads to a quantum phase transition between a superconductor and a superinsulator at the self-dual point. We also discuss in this framework the recently proposed quantum Hall phases for charges and vortices in presence of external offset charges and magnetic fluxes: we show how the periodicity of the charge-vortex coupling can lead to transitions to anyon superconductivity phases. We finally generalize our results to three dimensions, where the relevant gauge theory is the so-called BF system, with an antisymmetric Kalb-Ramond gauge field.We show that the zero-temperature physics of planar Josephson junction arrays in the self-dual approximation is governed by an Abelian gauge theory with a periodic mixed Chern-Simons term describing the charge-vortex coupling. The periodicity requires the existence of (Euclidean) topological excitations which determine the quantum phase structure of the model. The electric-magnetic duality leads to a quantum phase transition between a superconductor and a superinsulator at the self-dual point. We also discuss in this framework the recently proposed quantum Hall phases for charges and vortices in presence of external offset charges and magnetic fluxes: we show how the periodicity of the charge-vortex coupling can lead to transitions to anyon superconductivity phases. We finally generalize our results to three dimensions, where the relevant gauge theory is the so-called BF system with an antisymmetric Kalb-Ramond gauge field
Universality Class of Confining Strings
A recently proposed model of confining strings has a non-local world-sheet
action induced by a space-time Kalb-Ramond tensor field. Here we show that, in
the large-D approximation, an infinite set of ghost- and tachyon-free
truncations of the derivative expansion of this action all lead to c=1 models.
Their infrared limit describes smooth strings with world-sheets of Hausdorff
dimension D_H=2 and long-range orientational order, as expected for QCD
strings.Comment: 11 pages, harvma
Quantum computing for pattern classification
It is well known that for certain tasks, quantum computing outperforms
classical computing. A growing number of contributions try to use this
advantage in order to improve or extend classical machine learning algorithms
by methods of quantum information theory. This paper gives a brief introduction
into quantum machine learning using the example of pattern classification. We
introduce a quantum pattern classification algorithm that draws on
Trugenberger's proposal for measuring the Hamming distance on a quantum
computer (CA Trugenberger, Phys Rev Let 87, 2001) and discuss its advantages
using handwritten digit recognition as from the MNIST database.Comment: 14 pages, 3 figures, presented at the 13th Pacific Rim International
Conference on Artificial Intelligenc
Probabilistic implementation of universal quantum processors
We present a probabilistic quantum processor for qudits. The processor itself
is represented by a fixed array of gates. The input of the processor consists
of two registers. In the program register the set of instructions (program) is
encoded. This program is applied to the data register. The processor can
perform any operation on a single qudit of the dimension N with a certain
probability. If the operation is unitary, the probability is in general 1/N^2,
but for more restricted sets of operators the probability can be higher. In
fact, this probability can be independent of the dimension of the qudit Hilbert
space of the qudit under some conditions.Comment: 7 revtex pages, 1 eps figur
Self Duality and Oblique Confinement in Planar Gauge Theories
We investigate the non-perturbative structure of two planar
lattice gauge models and discuss their relevance to two-dimensional condensed
matter systems and Josephson junction arrays. Both models involve two compact
U(1) gauge fields with Chern-Simons interactions, which break the symmetry down
to . By identifying the relevant topological excitations
(instantons) and their interactions we determine the phase structure of the
models. Our results match observed quantum phase transitions in Josephson
junction arrays and suggest also the possibility of {\it oblique confining
ground states} corresponding to quantum Hall regimes for either charges or
vortices.Comment: 32 pages, harvma
Semiclassical Quantization for the Spherically Symmetric Systems under an Aharonov-Bohm magnetic flux
The semiclassical quantization rule is derived for a system with a
spherically symmetric potential and an
Aharonov-Bohm magnetic flux. Numerical results are presented and compared with
known results for models with . It is shown that the
results provided by our method are in good agreement with previous results. One
expects that the semiclassical quantization rule shown in this paper will
provide a good approximation for all principle quantum number even the rule is
derived in the large principal quantum number limit . We also discuss
the power parameter dependence of the energy spectra pattern in this
paper.Comment: 13 pages, 4 figures, some typos correcte
Quantum Hall Fluids
We review the effective field theory treatment of topological quantum fluids,
focussing on the Hall fluids.Comment: 82 pages, TeX, Preprint ITP (This version comes with ALL the MACROS
appended at the end of the file)