2,635 research outputs found
Simulating quantum mechanics on a quantum computer
Algorithms are described for efficiently simulating quantum mechanical
systems on quantum computers. A class of algorithms for simulating the
Schrodinger equation for interacting many-body systems are presented in some
detail. These algorithms would make it possible to simulate nonrelativistic
quantum systems on a quantum computer with an exponential speedup compared to
simulations on classical computers. Issues involved in simulating relativistic
systems of Dirac and gauge particles are discussed.Comment: 22 pages LaTeX; Expanded version of a talk given by WT at the
PhysComp '96 conference, BU, Boston MA, November 1996. Minor corrections
made, references adde
Matrix product states represent ground states faithfully
We quantify how well matrix product states approximate exact ground states of
1-D quantum spin systems as a function of the number of spins and the entropy
of blocks of spins. We also investigate the convex set of local reduced density
operators of translational invariant systems. The results give a theoretical
justification for the high accuracy of renormalization group algorithms, and
justifies their use even in the case of critical systems
FPT-algorithms for some problems related to integer programming
In this paper, we present FPT-algorithms for special cases of the shortest
lattice vector, integer linear programming, and simplex width computation
problems, when matrices included in the problems' formulations are near square.
The parameter is the maximum absolute value of rank minors of the corresponding
matrices. Additionally, we present FPT-algorithms with respect to the same
parameter for the problems, when the matrices have no singular rank
sub-matrices.Comment: arXiv admin note: text overlap with arXiv:1710.00321 From author:
some minor corrections has been don
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
The Color-Flavor Transformation and Lattice QCD
We present the color-flavor transformation for gauge group SU(N_c) and
discuss its application to lattice QCD.Comment: 6 pages, Lattice2002(theoretical), typo in Ref.[1] correcte
Diagonalizing transfer matrices and matrix product operators: a medley of exact and computational methods
Transfer matrices and matrix product operators play an ubiquitous role in the
field of many body physics. This paper gives an ideosyncratic overview of
applications, exact results and computational aspects of diagonalizing transfer
matrices and matrix product operators. The results in this paper are a mixture
of classic results, presented from the point of view of tensor networks, and of
new results. Topics discussed are exact solutions of transfer matrices in
equilibrium and non-equilibrium statistical physics, tensor network states,
matrix product operator algebras, and numerical matrix product state methods
for finding extremal eigenvectors of matrix product operators.Comment: Lecture notes from a course at Vienna Universit
Lattice QCD at the end of 2003
I review recent developments in lattice QCD. I first give an overview of its
formalism, and then discuss lattice discretizations of fermions. We then turn
to a description of the quenched approximation and why it is disappearing as a
vehicle for QCD phenomenology. I describe recent claims for progress in
simulations which include dynamical fermions and the interesting theoretical
problems they raise. I conclude with brief descriptions of the calculations of
matrix elements in heavy flavor systems and for kaons.Comment: Review for Int J Mod Phys A. 58 pages, latex, WSPC macros,, 22
postscript figure
QCD dynamics in a constant chromomagnetic field
We investigate the phase transition in full QCD with two flavors of staggered
fermions in presence of a constant abelian chromomagnetic field. We find that
the critical temperature depends on the strength of the chromomagnetic field
and that the deconfined phase extends to very low temperatures for strong
enough fields. As in the case of zero external field, a single transition is
detected, within statistical uncertainties, where both deconfinement and chiral
symmetry restoration take place. We also find that the chiral condensate
increases with the strength of the chromomagnetic field.Comment: 18 pages, 8 figures, 1 tabl
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