81 research outputs found
Magnetic exponents of two-dimensional Ising spin glasses
The magnetic critical properties of two-dimensional Ising spin glasses are
controversial. Using exact ground state determination, we extract the
properties of clusters flipped when increasing continuously a uniform field. We
show that these clusters have many holes but otherwise have statistical
properties similar to those of zero-field droplets. A detailed analysis gives
for the magnetization exponent delta = 1.30 +/- 0.02 using lattice sizes up to
80x80; this is compatible with the droplet model prediction delta = 1.282. The
reason for previous disagreements stems from the need to analyze both singular
and analytic contributions in the low-field regime.Comment: 4 pages, 4 figures, title now includes "Ising
Optimized Noise Suppression for Quantum Circuits
Quantum computation promises to advance a wide range of computational tasks.
However, current quantum hardware suffers from noise and is too small for error
correction. Thus, accurately utilizing noisy quantum computers strongly relies
on noise characterization, mitigation, and suppression. Crucially, these
methods must also be efficient in terms of their classical and quantum
overhead. Here, we efficiently characterize and mitigate crosstalk noise, which
is a severe error source in, e.g., cross-resonance based superconducting
quantum processors. For crosstalk characterization, we develop a simplified
measurement experiment. Furthermore, we analyze the problem of optimal
experiment scheduling and solve it for common hardware architectures. After
characterization, we mitigate noise in quantum circuits by a noise-aware qubit
routing algorithm. Our integer programming algorithm extends previous work on
optimized qubit routing by swap insertion. We incorporate the measured
crosstalk errors in addition to other, more easily accessible noise data in the
objective function. Furthermore, we strengthen the underlying integer linear
model by proving a convex hull result about an associated class of polytopes,
which has applications beyond this work. We evaluate the proposed method by
characterizing crosstalk noise for a complete 27 qubit chip and leverage the
resulting data to improve the approximation ratio of the Quantum Approximate
Optimization Algorithm by up to 10 % compared to other established noise-aware
routing methods. Our work clearly demonstrates the gains of including noise
data when mapping abstract quantum circuits to hardware native ones
Exact Ground States of Large Two-Dimensional Planar Ising Spin Glasses
Studying spin-glass physics through analyzing their ground-state properties
has a long history. Although there exist polynomial-time algorithms for the
two-dimensional planar case, where the problem of finding ground states is
transformed to a minimum-weight perfect matching problem, the reachable system
sizes have been limited both by the needed CPU time and by memory requirements.
In this work, we present an algorithm for the calculation of exact ground
states for two-dimensional Ising spin glasses with free boundary conditions in
at least one direction. The algorithmic foundations of the method date back to
the work of Kasteleyn from the 1960s for computing the complete partition
function of the Ising model. Using Kasteleyn cities, we calculate exact ground
states for huge two-dimensional planar Ising spin-glass lattices (up to
3000x3000 spins) within reasonable time. According to our knowledge, these are
the largest sizes currently available. Kasteleyn cities were recently also used
by Thomas and Middleton in the context of extended ground states on the torus.
Moreover, they show that the method can also be used for computing ground
states of planar graphs. Furthermore, we point out that the correctness of
heuristically computed ground states can easily be verified. Finally, we
evaluate the solution quality of heuristic variants of the Bieche et al.
approach.Comment: 11 pages, 5 figures; shortened introduction, extended results; to
appear in Physical Review E 7
Universality-class dependence of energy distributions in spin glasses
We study the probability distribution function of the ground-state energies
of the disordered one-dimensional Ising spin chain with power-law interactions
using a combination of parallel tempering Monte Carlo and branch, cut, and
price algorithms. By tuning the exponent of the power-law interactions we are
able to scan several universality classes. Our results suggest that mean-field
models have a non-Gaussian limiting distribution of the ground-state energies,
whereas non-mean-field models have a Gaussian limiting distribution. We compare
the results of the disordered one-dimensional Ising chain to results for a
disordered two-leg ladder, for which large system sizes can be studied, and
find a qualitative agreement between the disordered one-dimensional Ising chain
in the short-range universality class and the disordered two-leg ladder. We
show that the mean and the standard deviation of the ground-state energy
distributions scale with a power of the system size. In the mean-field
universality class the skewness does not follow a power-law behavior and
converges to a nonzero constant value. The data for the Sherrington-Kirkpatrick
model seem to be acceptably well fitted by a modified Gumbel distribution.
Finally, we discuss the distribution of the internal energy of the
Sherrington-Kirkpatrick model at finite temperatures and show that it behaves
similar to the ground-state energy of the system if the temperature is smaller
than the critical temperature.Comment: 15 pages, 20 figures, 1 tabl
Low Energy Excitations in Spin Glasses from Exact Ground States
We investigate the nature of the low-energy, large-scale excitations in the
three-dimensional Edwards-Anderson Ising spin glass with Gaussian couplings and
free boundary conditions, by studying the response of the ground state to a
coupling-dependent perturbation introduced previously. The ground states are
determined exactly for system sizes up to 12^3 spins using a branch and cut
algorithm. The data are consistent with a picture where the surface of the
excitations is not space-filling, such as the droplet or the ``TNT'' picture,
with only minimal corrections to scaling. When allowing for very large
corrections to scaling, the data are also consistent with a picture with
space-filling surfaces, such as replica symmetry breaking. The energy of the
excitations scales with their size with a small exponent \theta', which is
compatible with zero if we allow moderate corrections to scaling. We compare
the results with data for periodic boundary conditions obtained with a genetic
algorithm, and discuss the effects of different boundary conditions on
corrections to scaling. Finally, we analyze the performance of our branch and
cut algorithm, finding that it is correlated with the existence of
large-scale,low-energy excitations.Comment: 18 Revtex pages, 16 eps figures. Text significantly expanded with
more discussion of the numerical data. Fig.11 adde
Spin glasses and algorithm benchmarks: A one-dimensional view
Spin glasses are paradigmatic models that deliver concepts relevant for a
variety of systems. However, rigorous analytical results are difficult to
obtain for spin-glass models, in particular for realistic short-range models.
Therefore large-scale numerical simulations are the tool of choice. Concepts
and algorithms derived from the study of spin glasses have been applied to
diverse fields in computer science and physics. In this work a one-dimensional
long-range spin-glass model with power-law interactions is discussed. The model
has the advantage over conventional systems in that by tuning the power-law
exponent of the interactions the effective space dimension can be changed thus
effectively allowing the study of large high-dimensional spin-glass systems to
address questions as diverse as the existence of an Almeida-Thouless line,
ultrametricity and chaos in short range spin glasses. Furthermore, because the
range of interactions can be changed, the model is a formidable test-bed for
optimization algorithms.Comment: 10 pages, 8 figures (two in crappy quality due to archive
restrictions). Proceedings of the International Workshop on
Statistical-Mechanical Informatics 2007, Kyoto (Japan) September 16-19, 200
Oxidoreductases on their way to industrial biotransformations
Fungi produce heme-containing peroxidases and peroxygenases, flavin-containing oxidases and dehydrogenases, and different copper-containing oxidoreductases involved in the biodegradation of lignin and other recalcitrant compounds. Heme peroxidases comprise the classical ligninolytic peroxidases and the new dye-decolorizing peroxidases, while heme peroxygenases belong to a still largely unexplored superfamily of heme-thiolate proteins. Nevertheless, basidiomycete unspecific peroxygenases have the highest biotechnological interest due to their ability to catalyze a variety of regio- and stereo-selective monooxygenation reactions with H2O2 as the source of oxygen and final electron acceptor. Flavo-oxidases are involved in both lignin and cellulose decay generating H2O2 that activates peroxidases and generates hydroxyl radical. The group of copper oxidoreductases also includes other H2O2 generating enzymes - copper-radical oxidases - together with classical laccases that are the oxidoreductases with the largest number of reported applications to date. However, the recently described lytic polysaccharide monooxygenases have attracted the highest attention among copper oxidoreductases, since they are capable of oxidatively breaking down crystalline cellulose, the disintegration of which is still a major bottleneck in lignocellulose biorefineries, along with lignin degradation. Interestingly, some flavin-containing dehydrogenases also play a key role in cellulose breakdown by directly/indirectly "fueling" electrons for polysaccharide monooxygenase activation. Many of the above oxidoreductases have been engineered, combining rational and computational design with directed evolution, to attain the selectivity, catalytic efficiency and stability properties required for their industrial utilization. Indeed, using ad hoc software and current computational capabilities, it is now possible to predict substrate access to the active site in biophysical simulations, and electron transfer efficiency in biochemical simulations, reducing in orders of magnitude the time of experimental work in oxidoreductase screening and engineering. What has been set out above is illustrated by a series of remarkable oxyfunctionalization and oxidation reactions developed in the frame of an intersectorial and multidisciplinary European RTD project. The optimized reactions include enzymatic synthesis of 1-naphthol, 25-hydroxyvitamin D3, drug metabolites, furandicarboxylic acid, indigo and other dyes, and conductive polyaniline, terminal oxygenation of alkanes, biomass delignification and lignin oxidation, among others. These successful case stories demonstrate the unexploited potential of oxidoreductases in medium and large-scale biotransformations
A Fixed-Parameter Algorithm for the Max-Cut Problem on Embedded 1-Planar Graphs
We propose a fixed-parameter tractable algorithm for the \textsc{Max-Cut}
problem on embedded 1-planar graphs parameterized by the crossing number of
the given embedding. A graph is called 1-planar if it can be drawn in the plane
with at most one crossing per edge. Our algorithm recursively reduces a
1-planar graph to at most planar graphs, using edge removal and node
contraction. The \textsc{Max-Cut} problem is then solved on the planar graphs
using established polynomial-time algorithms. We show that a maximum cut in the
given 1-planar graph can be derived from the solutions for the planar graphs.
Our algorithm computes a maximum cut in an embedded 1-planar graph with
nodes and edge crossings in time .Comment: conference version from IWOCA 201
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