5,730 research outputs found
The ALPS project release 1.3: open source software for strongly correlated systems
We present release 1.3 of the ALPS (Algorithms and Libraries for Physics
Simulations) project, an international open source software project to develop
libraries and application programs for the simulation of strongly correlated
quantum lattice models such as quantum magnets, lattice bosons, and strongly
correlated fermion systems. Development is centered on common XML and binary
data formats, on libraries to simplify and speed up code development, and on
full-featured simulation programs. The programs enable non-experts to start
carrying out numerical simulations by providing basic implementations of the
important algorithms for quantum lattice models: classical and quantum Monte
Carlo (QMC) using non-local updates, extended ensemble simulations, exact and
full diagonalization (ED), as well as the density matrix renormalization group
(DMRG). Changes in the new release include a DMRG program for interacting
models, support for translation symmetries in the diagonalization programs, the
ability to define custom measurement operators, and support for inhomogeneous
systems, such as lattice models with traps. The software is available from our
web server at http://alps.comp-phys.org/
Quantum Graphical Models and Belief Propagation
Belief Propagation algorithms acting on Graphical Models of classical
probability distributions, such as Markov Networks, Factor Graphs and Bayesian
Networks, are amongst the most powerful known methods for deriving
probabilistic inferences amongst large numbers of random variables. This paper
presents a generalization of these concepts and methods to the quantum case,
based on the idea that quantum theory can be thought of as a noncommutative,
operator-valued, generalization of classical probability theory. Some novel
characterizations of quantum conditional independence are derived, and
definitions of Quantum n-Bifactor Networks, Markov Networks, Factor Graphs and
Bayesian Networks are proposed. The structure of Quantum Markov Networks is
investigated and some partial characterization results are obtained, along the
lines of the Hammersely-Clifford theorem. A Quantum Belief Propagation
algorithm is presented and is shown to converge on 1-Bifactor Networks and
Markov Networks when the underlying graph is a tree. The use of Quantum Belief
Propagation as a heuristic algorithm in cases where it is not known to converge
is discussed. Applications to decoding quantum error correcting codes and to
the simulation of many-body quantum systems are described.Comment: 58 pages, 9 figure
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