174 research outputs found
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
Quantum communication cost of preparing multipartite entanglement
We study the preparation and distribution of high-fidelity multi-party
entangled states via noisy channels and operations. In the particular case of
GHZ and cluster states, we study different strategies using bipartite or
multipartite purification protocols. The most efficient strategy depends on the
target fidelity one wishes to achieve and on the quality of transmission
channel and local operations. We show the existence of a crossing point beyond
which the strategy making use of the purification of the state as a whole is
more efficient than a strategy in which pairs are purified before they are
connected to the final state. We also study the efficiency of intermediate
strategies, including sequences of purification and connection. We show that a
multipartite strategy is to be used if one wishes to achieve high fidelity,
whereas a bipartite strategy gives a better yield for low target fidelity.Comment: 21 pages, 17 figures; accepted for publication in Phys. Rev. A; v2:
corrections in figure
Carotid artery stiffness in metabolic syndrome: Sex differences
Introduction: The effect of metabolic syndrome (MS) on carotid stiffness (CS) in the context of gender is under research. Objective: We examined the relationship between the MS and CS in men (M) and women (W) and investigated if the impact of cardiovascular risk factors on CS is modulated by gender. Patients and Methods: The study included 419 subjects (mean age 54.3 years): 215 (51%) with MS (109 W and 106 M) and 204 (49%) without MS (98 W and 106 M). Carotid intima-media thickness (IMT) and CS parameters (beta stiffness index (beta), Peterson’s elastic modulus (Ep), arterial compliance (AC) and one-point pulse wave velocity (PWV-beta)) were measured with the echo-tracking (eT) system. Results: ANCOVA demonstrated that MS was associated with elevated CS indices (p = 0.003 for beta and 0.025 for PWV-beta), although further sex-specific analysis revealed that this relationship was significant only in W (p = 0.021 for beta). Age was associated with CS in both M and W, pulse pressure (PP) and body mass index turned out to be determinants of CS solely in W, while the effect of mean arterial pressure (MAP) and heart rate was more pronounced in M. MANOVA performed in subjects with MS revealed that age and diabetes mellitus type 2 were determinants of CS in both sexes, diastolic blood pressure and MAP – solely in M and systolic blood pressure, PP and waist circumference – solely in W (the relationship between the waist circumference and AC was paradoxical). Conclusion: The relationship between MS and CS is stronger in W than in M. In subjects with MS, various components of arterial pressure exert different sex-specific effects on CS – with the impact of the pulsative component of arterial pressure (PP) observed in W and the impact of the steady component (MAP) observed in M
Optimal purification of thermal graph states
In this paper, a purification protocol is presented and its performance is
proven to be optimal when applied to a particular subset of graph states that
are subject to local Z-noise. Such mixed states can be produced by bringing a
system into thermal equilibrium, when it is described by a Hamiltonian which
has a particular graph state as its unique ground state. From this protocol, we
derive the exact value of the critical temperature above which purification is
impossible, as well as the related optimal purification rates. A possible
simulation of graph Hamiltonians is proposed, which requires only bipartite
interactions and local magnetic fields, enabling the tuning of the system
temperature.Comment: 5 pages, 4 figures v2: published versio
Entanglement entropy of two disjoint intervals in c=1 theories
We study the scaling of the Renyi entanglement entropy of two disjoint blocks
of critical lattice models described by conformal field theories with central
charge c=1. We provide the analytic conformal field theory result for the
second order Renyi entropy for a free boson compactified on an orbifold
describing the scaling limit of the Ashkin-Teller (AT) model on the self-dual
line. We have checked this prediction in cluster Monte Carlo simulations of the
classical two dimensional AT model. We have also performed extensive numerical
simulations of the anisotropic Heisenberg quantum spin-chain with tree-tensor
network techniques that allowed to obtain the reduced density matrices of
disjoint blocks of the spin-chain and to check the correctness of the
predictions for Renyi and entanglement entropies from conformal field theory.
In order to match these predictions, we have extrapolated the numerical results
by properly taking into account the corrections induced by the finite length of
the blocks to the leading scaling behavior.Comment: 37 pages, 23 figure
Urinary C-Peptide of Insulin as a Non-Invasive Marker of Nutritional Status: Some Practicalities
Nutritional status is a critical element of many aspects of animal ecology, but has proven difficult to measure non-invasively in studies of free-ranging animals. Urinary C-peptide of insulin (UCP), a small polypeptide cleaved in an equimolar ratio from proinsulin when the body converts it to insulin, offers great promise in this regard, and recent studies of several non-human primate species have utilized it with encouraging results. Despite this, there are a number of unresolved issues related to the collection, processing, storage and transport of samples. These include: contamination of samples on collection (most commonly by dirt or faeces), short-term storage before returning to a field station, differences in processing and long-term storage methods (blotting onto filter paper, freezing, lyophilizing), and for frozen samples, transportation while keeping samples frozen. Such issues have been investigated for urine samples in particular with respect to their effects on steroid hormone metabolites, but there has been little investigation of their effects on UCP measurement. We collected samples from captive macaques, and undertook a series of experiments where we systematically manipulated samples and tested the effects on subsequent UCP measurements. We show that contamination of urine samples by faeces led to a decrease in UCP levels by >90%, but that contamination with dirt did not have substantial effects. Short-term storage (up to 12 hours) of samples on ice did not affect UCP levels significantly, but medium-term storage (up to 78 hours) did. Freezing and lyophilization for long-term storage did not affect UCP levels, but blotting onto filter paper did. A transportation simulation showed that transporting frozen samples packed in ice and insulated should be acceptable, but only if it can be completed within a period of a few days and if freeze-thaw can be avoided. We use our data to make practical recommendations for fieldworkers
Concatenated tensor network states
We introduce the concept of concatenated tensor networks to efficiently
describe quantum states. We show that the corresponding concatenated tensor
network states can efficiently describe time evolution and possess arbitrary
block-wise entanglement and long-ranged correlations. We illustrate the
approach for the enhancement of matrix product states, i.e. 1D tensor networks,
where we replace each of the matrices of the original matrix product state with
another 1D tensor network. This procedure yields a 2D tensor network, which
includes -- already for tensor dimension two -- all states that can be prepared
by circuits of polynomially many (possibly non-unitary) two-qubit quantum
operations, as well as states resulting from time evolution with respect to
Hamiltonians with short-ranged interactions. We investigate the possibility to
efficiently extract information from these states, which serves as the basic
step in a variational optimization procedure. To this aim we utilize known
exact and approximate methods for 2D tensor networks and demonstrate some
improvements thereof, which are also applicable e.g. in the context of 2D
projected entangled pair states. We generalize the approach to higher
dimensional- and tree tensor networks.Comment: 16 pages, 4 figure
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