119 research outputs found
Quantum algorithms for classical lattice models
We give efficient quantum algorithms to estimate the partition function of
(i) the six vertex model on a two-dimensional (2D) square lattice, (ii) the
Ising model with magnetic fields on a planar graph, (iii) the Potts model on a
quasi 2D square lattice, and (iv) the Z_2 lattice gauge theory on a
three-dimensional square lattice. Moreover, we prove that these problems are
BQP-complete, that is, that estimating these partition functions is as hard as
simulating arbitrary quantum computation. The results are proven for a complex
parameter regime of the models. The proofs are based on a mapping relating
partition functions to quantum circuits introduced in [Van den Nest et al.,
Phys. Rev. A 80, 052334 (2009)] and extended here.Comment: 21 pages, 12 figure
Mapping all classical spin models to a lattice gauge theory
In our recent work [Phys. Rev. Lett. 102, 230502 (2009)] we showed that the
partition function of all classical spin models, including all discrete
standard statistical models and all Abelian discrete lattice gauge theories
(LGTs), can be expressed as a special instance of the partition function of a
4-dimensional pure LGT with gauge group Z_2 (4D Z_2 LGT). This provides a
unification of models with apparently very different features into a single
complete model. The result uses an equality between the Hamilton function of
any classical spin model and the Hamilton function of a model with all possible
k-body Ising-type interactions, for all k, which we also prove. Here, we
elaborate on the proof of the result, and we illustrate it by computing
quantities of a specific model as a function of the partition function of the
4D Z_2 LGT. The result also allows one to establish a new method to compute the
mean-field theory of Z_2 LGTs with d > 3, and to show that computing the
partition function of the 4D Z_2 LGT is computationally hard (#P hard). The
proof uses techniques from quantum information.Comment: 21 pages, 21 figures; published versio
Testing equivalence of pure quantum states and graph states under SLOCC
A set of necessary and sufficient conditions are derived for the equivalence
of an arbitrary pure state and a graph state on n qubits under stochastic local
operations and classical communication (SLOCC), using the stabilizer formalism.
Because all stabilizer states are equivalent to a graph state by local unitary
transformations, these conditions constitute a classical algorithm for the
determination of SLOCC-equivalence of pure states and stabilizer states. This
algorithm provides a distinct advantage over the direct solution of the
SLOCC-equivalence condition for an unknown invertible local operator S, as it
usually allows for easy detection of states that are not SLOCC-equivalent to
graph states.Comment: 9 pages, to appear in International Journal of Quantum Information;
Minor typos corrected, updated references
Fundamental limitations in the purifications of tensor networks
We show a fundamental limitation in the description of quantum many-body
mixed states with tensor networks in purification form. Namely, we show that
there exist mixed states which can be represented as a translationally
invariant (TI) matrix product density operator (MPDO) valid for all system
sizes, but for which there does not exist a TI purification valid for all
system sizes. The proof is based on an undecidable problem and on the
uniqueness of canonical forms of matrix product states. The result also holds
for classical states.Comment: v1: 11 pages, 1 figure. v2: very minor changes. About to appear in
Journal of Mathematical Physic
Unifying all classical spin models in a Lattice Gauge Theory
We show that the partition function of all classical spin models, including
all discrete Standard Statistical Models and all abelian discrete Lattice Gauge
Theories (LGTs), can be expressed as a special instance of the partition
function of the 4D Z_2 LGT. In this way, all classical spin models with
apparently very different features are unified in a single complete model, and
a physical relation between all models is established. As applications of this
result, we present a new method to do mean field theory for abelian discrete
LGTs with d>3, and we show that the computation of the partition function of
the 4D Z_2 LGT is a computationally hard (#P-hard) problem. We also extend our
results to abelian continuous models, where we show the approximate
completeness of the 4D Z_2 LGT. All results are proven using quantum
information techniques.Comment: Published version. One new figure and some minor change
Single-channel transmission in gold one-atom contacts and chains
We induce superconductivity by proximity effect in thin layers of gold and
study the number of conduction channels which contribute to the current in
one-atom contacts and atomic wires. The atomic contacts and wires are
fabricated with a Scanning Tunneling Microscope. The set of transmission
probabilities of the conduction channels is obtained from the analysis of the
characteristic curve which is highly non-linear due to multiple Andreev
reflections. In agreement with theoretical calculations we find that there is
only one channel which is almost completely open.Comment: 4 pages, 2 figures. To be published in Phys. Rev. B, Rapid
Communications (2003
Completeness of classical spin models and universal quantum computation
We study mappings between distinct classical spin systems that leave the
partition function invariant. As recently shown in [Phys. Rev. Lett. 100,
110501 (2008)], the partition function of the 2D square lattice Ising model in
the presence of an inhomogeneous magnetic field, can specialize to the
partition function of any Ising system on an arbitrary graph. In this sense the
2D Ising model is said to be "complete". However, in order to obtain the above
result, the coupling strengths on the 2D lattice must assume complex values,
and thus do not allow for a physical interpretation. Here we show how a
complete model with real -and, hence, "physical"- couplings can be obtained if
the 3D Ising model is considered. We furthermore show how to map general
q-state systems with possibly many-body interactions to the 2D Ising model with
complex parameters, and give completeness results for these models with real
parameters. We also demonstrate that the computational overhead in these
constructions is in all relevant cases polynomial. These results are proved by
invoking a recently found cross-connection between statistical mechanics and
quantum information theory, where partition functions are expressed as quantum
mechanical amplitudes. Within this framework, there exists a natural
correspondence between many-body quantum states that allow universal quantum
computation via local measurements only, and complete classical spin systems.Comment: 43 pages, 28 figure
Mixed Th2 and non-Th2 inflammatory pattern in the asthma-COPD overlap : a network approach
Altres ajuts: The authors are grateful to all the patients who participated in the study. A number of investigators contributed to the study logistics and they are listed in the Supplementary materials. The project was endorsed by the COPD and Asthma Research Board (PII de EPOC y asma) of the Spanish Society of Pneumology and Thoracic Surgery (SEPAR).The asthma-chronic obstructive pulmonary disease (COPD) overlap (ACO) is a clinical condition that combines features of those two diseases, and that is difficult to define due to the lack of understanding of the underlying mechanisms. Determining systemic mediators may help clarify the nature of inflammation in patients with ACO. We aimed at investigating the role and interaction of common markers of systemic inflammation (IL-6, IL-8, and tumor necrosis factor-α), Th2-related markers (periostin, IL-5, and IL-13), and IL-17 in asthma, COPD, and ACO. This is a cross-sectional study of patients aged ≥40 years with a post-bronchodilator forced expiratory volume in the first second/forced vital capacity 10 pack-years in a patient with a previous diagnosis of asthma or by the presence of eosinophilia in a patient with a previous diagnosis of COPD. Clinical, functional, and inflammatory parameters were compared between categories using discriminant and network analysis. In total, 109 ACO, 89 COPD, and 94 asthma patients were included. Serum levels (median [interquartile range]) of IL-5 were higher in asthma patients than in COPD patients (2.09 [0.61-3.57] vs 1.11 [0.12-2.42] pg/mL, respectively; p =0.03), and IL-8 levels (median [interquartile range]) were higher in COPD patients than in asthma patients (9.45 [6.61-13.12] vs 7.03 [4.69-10.44] pg/mL, respectively; p <0.001). Their values in ACO were intermediate between those in asthma and in COPD. Principal component and network analysis showed a mixed inflammatory pattern in ACO in between asthma and COPD. IL-13 was the most connected node in the network, with different weights among the three conditions. Asthma and COPD are two different inflammatory conditions that may overlap in some patients, leading to a mixed inflammatory pattern. IL-13 could be central to the regulation of inflammation in these conditions
Digital Quantum Simulation of the Statistical Mechanics of a Frustrated Magnet
Many interesting problems in physics, chemistry, and computer science are
equivalent to problems of interacting spins. However, most of these problems
require computational resources that are out of reach by classical computers. A
promising solution to overcome this challenge is to exploit the laws of quantum
mechanics to perform simulation. Several "analog" quantum simulations of
interacting spin systems have been realized experimentally. However, relying on
adiabatic techniques, these simulations are limited to preparing ground states
only. Here we report the first experimental results on a "digital" quantum
simulation on thermal states; we simulated a three-spin frustrated magnet, a
building block of spin ice, with an NMR quantum information processor, and we
are able to explore the phase diagram of the system at any simulated
temperature and external field. These results serve as a guide for identifying
the challenges for performing quantum simulation on physical systems at finite
temperatures, and pave the way towards large scale experimental simulations of
open quantum systems in condensed matter physics and chemistry.Comment: 7 pages for the main text plus 6 pages for the supplementary
material
Horizontal low gradient magnetophoresis behaviour of iron oxide nanoclusters at the different steps of the synthesis route
In this work the use of Horizontal Low Gradient Magnetic Field (HLGMF) (<100T/m) for filtration, control and separation of synthesized magnetic nanoparticles (NPs) is investigated. The characteristics of the suspension, size and type of the NPs are considered and discussed. For these purposes, Fe2O3 silica coated nanoclusters of about 150 nm are synthesized by co-precipitation, monodispersion and silica coating. SQUID, TEM, XRD, and z potential techniques were used to characterize the synthesized nanoclusters. An extensive magnetophoresis study was performed at different magnetophoretical conditions. Different reversible aggregation times were observed at different HLGMF, at each step of the synthesis route. In particular, differences of several orders of magnitude were observed when comparing citric acid modified NPs with silica coated nanoclusters . Reversible aggregation times are correlated to the properties of the NPs at different steps of synthesis route.Fundação para a Ciência e a Tecnologia (FCT) - Bolsa NANO/NMed-SD/0156/2007, PTCD/CTM/69316/2006
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