822 research outputs found
Using level-2 fuzzy sets to combine uncertainty and imprecision in fuzzy regions
In many applications, spatial data need to be considered but are prone to uncertainty or imprecision. A fuzzy region - a fuzzy set over a two dimensional domain - allows the representation of such imperfect spatial data. In the original model, points of the fuzzy region where treated independently, making it impossible to model regions where groups of points should be considered as one basic element or subregion. A first extension overcame this, but required points within a group to have the same membership grade. In this contribution, we will extend this further, allowing a fuzzy region to contain subregions in which not all points have the same membership grades. The concept can be used as an underlying model in spatial applications, e.g. websites showing maps and requiring representation of imprecise features or websites with routing functions needing to handle concepts as walking distance or closeby
Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
This article reviews recent developments in the theoretical understanding and
the numerical implementation of variational renormalization group methods using
matrix product states and projected entangled pair states.Comment: Review from 200
Efficient Evaluation of Partition Functions of Inhomogeneous Many-Body Spin Systems
We present a numerical method to evaluate partition functions and associated correlation functions of inhomogeneous 2D classical spin systems and 1D quantum spin systems. The method is scalable and has a controlled error. We illustrate the algorithm by calculating the finite-temperature properties of bosonic particles in 1D optical lattices, as realized in current experiments
Variational study of hard-core bosons in a 2-D optical lattice using Projected Entangled Pair States (PEPS)
We have studied the system of hard-core bosons on a 2-D optical lattice using
a variational algorithm based on projected entangled-pair states (PEPS). We
have investigated the ground state properties of the system as well as the
responses of the system to sudden changes in the parameters. We have compared
our results to mean field results based on a Gutzwiller ansatz.Comment: 9 pages, 9 figure
Tree tensor network state with variable tensor order: an efficient multireference method for strongly correlated systems
We study the tree-tensor-network-state (TTNS) method with variable tensor orders for quantum chemistry. TTNS is a variational method to efficiently approximate complete active space (CAS) configuration interaction (CI) wave functions in a tensor product form. TTNS can be considered as a higher order generalization of the matrix product state (MPS) method. The MPS wave function is formulated as products of matrices in a multiparticle basis spanning a truncated Hilbert space of the original CAS-CI problem. These matrices belong to active orbitals organized in a one-dimensional array, while tensors in TTNS are defined upon a tree-like arrangement of the same orbitals. The tree-structure is advantageous since the distance between two arbitrary orbitals in the tree scales only logarithmically with the number of orbitals N, whereas the scaling is linear in the MPS array. It is found to be beneficial from the computational costs point of view to keep strongly correlated orbitals in close vicinity in both arrangements; therefore, the TTNS ansatz is better suited for multireference problems with numerous highly correlated orbitals. To exploit the advantages of TTNS a novel algorithm is designed to optimize the tree tensor network topology based on quantum information theory and entanglement. The superior performance of the TTNS method is illustrated on the ionic-neutral avoided crossing of LiF. It is also shown that the avoided crossing of LiF can be localized using only ground state properties, namely one-orbital entanglement
Superpressure balloon flights from Christchurch, New Zealand, July 1968 - December 1969
Strain gages on superpressure balloon flights from Christchurch, New Zealand - Jul. 1968 to Dec. 196
Multipartite entanglement in 2 x 2 x n quantum systems
We classify multipartite entangled states in the 2 x 2 x n (n >= 4) quantum
system, for example the 4-qubit system distributed over 3 parties, under local
filtering operations. We show that there exist nine essentially different
classes of states, and they give rise to a five-graded partially ordered
structure, including the celebrated Greenberger-Horne-Zeilinger (GHZ) and W
classes of 3 qubits. In particular, all 2 x 2 x n-states can be
deterministically prepared from one maximally entangled state, and some
applications like entanglement swapping are discussed.Comment: 9 pages, 3 eps figure
The Algebraic Bethe Ansatz and Tensor Networks
We describe the Algebraic Bethe Ansatz for the spin-1/2 XXX and XXZ
Heisenberg chains with open and periodic boundary conditions in terms of tensor
networks. These Bethe eigenstates have the structure of Matrix Product States
with a conserved number of down-spins. The tensor network formulation suggestes
possible extensions of the Algebraic Bethe Ansatz to two dimensions
Faster Methods for Contracting Infinite 2D Tensor Networks
We revisit the corner transfer matrix renormalization group (CTMRG) method of
Nishino and Okunishi for contracting two-dimensional (2D) tensor networks and
demonstrate that its performance can be substantially improved by determining
the tensors using an eigenvalue solver as opposed to the power method used in
CTMRG. We also generalize the variational uniform matrix product state (VUMPS)
ansatz for diagonalizing 1D quantum Hamiltonians to the case of 2D transfer
matrices and discuss similarities with the corner methods. These two new
algorithms will be crucial to improving the performance of variational infinite
projected entangled pair state (PEPS) methods.Comment: 20 pages, 5 figures, V. Zauner-Stauber previously also published
under the name V. Zaune
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