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 $I(V)$ 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