1,218 research outputs found
Local permutations of products of Bell states and entanglement distillation
We present new algorithms for mixed-state multi-copy entanglement
distillation for pairs of qubits. Our algorithms perform significantly better
than the best known algorithms. Better algorithms can be derived that are tuned
for specific initial states. The new algorithms are based on a characterization
of the group of all locally realizable permutations of the 4^n possible tensor
products of n Bell states.Comment: 6 pages, 1 figur
The computational difficulty of finding MPS ground states
We determine the computational difficulty of finding ground states of
one-dimensional (1D) Hamiltonians which are known to be Matrix Product States
(MPS). To this end, we construct a class of 1D frustration free Hamiltonians
with unique MPS ground states and a polynomial gap above, for which finding the
ground state is at least as hard as factoring. By lifting the requirement of a
unique ground state, we obtain a class for which finding the ground state
solves an NP-complete problem. Therefore, for these Hamiltonians it is not even
possible to certify that the ground state has been found. Our results thus
imply that in order to prove convergence of variational methods over MPS, as
the Density Matrix Renormalization Group, one has to put more requirements than
just MPS ground states and a polynomial spectral gap.Comment: 5 pages. v2: accepted version, Journal-Ref adde
Renormalization algorithm with graph enhancement
We introduce a class of variational states to describe quantum many-body
systems. This class generalizes matrix product states which underly the
density-matrix renormalization group approach by combining them with weighted
graph states. States within this class may (i) possess arbitrarily long-ranged
two-point correlations, (ii) exhibit an arbitrary degree of block entanglement
entropy up to a volume law, (iii) may be taken translationally invariant, while
at the same time (iv) local properties and two-point correlations can be
computed efficiently. This new variational class of states can be thought of as
being prepared from matrix product states, followed by commuting unitaries on
arbitrary constituents, hence truly generalizing both matrix product and
weighted graph states. We use this class of states to formulate a
renormalization algorithm with graph enhancement (RAGE) and present numerical
examples demonstrating that improvements over density-matrix renormalization
group simulations can be achieved in the simulation of ground states and
quantum algorithms. Further generalizations, e.g., to higher spatial
dimensions, are outlined.Comment: 4 pages, 1 figur
Preparing projected entangled pair states on a quantum computer
We present a quantum algorithm to prepare injective PEPS on a quantum
computer, a class of open tensor networks representing quantum states. The
run-time of our algorithm scales polynomially with the inverse of the minimum
condition number of the PEPS projectors and, essentially, with the inverse of
the spectral gap of the PEPS' parent Hamiltonian.Comment: 5 pages, 1 figure. To be published in Physical Review Letters.
Removed heuristics, refined run-time boun
Sequential generation of entangled multi-qubit states
We consider the deterministic generation of entangled multi-qubit states by
the sequential coupling of an ancillary system to initially uncorrelated
qubits. We characterize all achievable states in terms of classes of matrix
product states and give a recipe for the generation on demand of any
multi-qubit state. The proposed methods are suitable for any sequential
generation-scheme, though we focus on streams of single photon time-bin qubits
emitted by an atom coupled to an optical cavity. We show, in particular, how to
generate familiar quantum information states such as W, GHZ, and cluster
states, within such a framework.Comment: 4 pages and 2 figures, submitted for publicatio
Dynamics and Control of a Quasi-1D Spin System
We study experimentally a system comprised of linear chains of spin-1/2
nuclei that provides a test-bed for multi-body dynamics and quantum information
processing. This system is a paradigm for a new class of quantum information
devices that can perform particular tasks even without universal control of the
whole quantum system. We investigate the extent of control achievable on the
system with current experimental apparatus and methods to gain information on
the system state, when full tomography is not possible and in any case highly
inefficient
The computational complexity of PEPS
We determine the computational power of preparing Projected Entangled Pair
States (PEPS), as well as the complexity of classically simulating them, and
generally the complexity of contracting tensor networks. While creating PEPS
allows to solve PP problems, the latter two tasks are both proven to be
#P-complete. We further show how PEPS can be used to approximate ground states
of gapped Hamiltonians, and that creating them is easier than creating
arbitrary PEPS. The main tool for our proofs is a duality between PEPS and
postselection which allows to use existing results from quantum compexity.Comment: 5 pages, 1 figure. Published version, plus a few extra
Relaciones entre el mercado de divisas y el enfoque Elasticidades de la Balanza de Pagos
Fil: Verstraete, Juan M. C. E..
Universidad Nacional de Cuyo. Facultad de Ciencias EconĂłmicasFil: Rada, Daniel A..
Universidad Nacional de Cuyo. Facultad de Ciencias EconĂłmica
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