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

The U(1) Lattice Gauge Theory Universally Connects All Classical Models with Continuous Variables, Including Background Gravity

We show that the partition function of many classical models with continuous degrees of freedom, e.g. abelian lattice gauge theories and statistical mechanical models, can be written as the partition function of an (enlarged) four-dimensional lattice gauge theory (LGT) with gauge group U(1). This result is very general that it includes models in different dimensions with different symmetries. In particular, we show that a U(1) LGT defined in a curved spacetime can be mapped to a U(1) LGT with a flat background metric. The result is achieved by expressing the U(1) LGT partition function as an inner product between two quantum states.Comment: Published version, 31 pages, 12 figures; references update

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

Uso de SAAC en el autismo: una revisión bibliográfica

Según el DSM V el autismo se define como un trastorno del desarrollo neurológico causado por una disfunción prenatal del Sistema Nervioso Central caracterizado por la presencia de otros síntomas como: comunicación e interacción social deficitaria, etc., además, es común la afectación del lenguaje. Debido a esta razón es importante el uso de herramientas para combatir esta carencia, es por ello que utilizamos los SAAC. Los resultados indican que efectivamente el uso de los SAAC en el autismo es beneficioso y eficaz, mostrando una evidente mejora en estas personas después de su implantación. Por otra parte, cabe añadir la poca información disponible sobre el tema y la necesidad de más investigaciones que respalden lo anteriormente expuesto.According to DSM V, autism is defined as a neurodevelopmental disorder caused by a prenatal dysfunction of the Central Nervous System characterized by the presence of other symptoms such as communication and deficit social interaction, etc. In addition, language involvement is common. Due to this reason it is important the use of tools to combat this lack, that is why we use the SAAC. The results indicate that indeed the use of SAAC in autism is beneficial and effective, showing an evident improvement in these people after its implantation. On the other hand, we should add the Little information available on the subject and the need for more research to support the above

On polynomials associated to Voronoi diagrams of point sets and crossing numbers

Three polynomials are defined for sets S of n points in general position in the plane: The Voronoi polynomial with coefficients the numbers of vertices of the order-k Voronoi diagrams of S, the circle polynomial with coefficients the numbers of circles through three points of S enclosing k points, and the E=k polynomial with coefficients the numbers of (at most k)-edges of S. We present several formulas for the rectilinear crossing number of S in terms of these polynomials and their roots. We also prove that the roots of the Voronoi polynomial lie on the unit circle if and only if S is in convex position. Further, we present bounds on the location of the roots of these polynomials.Postprint (published version

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

Las criptomonedas como medio de pago y su influencia en el comercio electrónico

Conocer y explicar la influencia de las criptomonedas como medio de pago en el comercio electrónico es el objetivo principal de la investigación, por ello la metodología utilizada es de nivel descriptivo-explicativo con un enfoque cualitativo y un diseño no experimental-longitudinal. Así mismo, mediante una guía de entrevista elaborada a tres especialistas en criptomonedas y comercio electrónico se permitió obtener diversos resultados, entre ellos, conocer las características principales de las criptomonedas como el uso de la criptografía, su valor volátil y su descentralización. También, se determinaron sus funcionalidades más importantes como su capacidad de ser utilizada como reserva de valor, permitir el anonimato y realizar transacciones transfronterizas. Además, se identificó la existencia de tendencias en el comercio electrónico como la utilización marketplaces para vender y ofrecer productos o servicios, la implementación de sistemas de seguridad y el crecimiento del uso de integraciones de plataformas de pagos para adquirir productos y/o servicios mediante dinero de curso legal o criptomonedas. Los resultados nos permitieron cumplir con el objetivo general de la investigación, concluyendo que actualmente las criptomonedas utilizadas como medio de pago no generan una gran influencia en el comercio electrónico, debido a las características y funcionalidades actuales que poseen, entre ellas, el valor volátil y la capacidad de servir como una reserva de valor, lo cual resulta en su uso reducido por parte de las personas y una baja implementación como medio de pago en las empresas. Sin embargo, una pequeña parte del mercado digital, entre ellas, el consumidor y las empresas, ya utilizan las criptomonedas como medio de pago, pero su uso todavía no está popularizado

Measuring cocircularity in a point set

In a given set S of n points in the plane, how close are four points of S to be cocircular? We define several measures to study this question, and present bounds on this almost-cocircularity in a point set. Algorithms for cocircularity are presented as well.Peer ReviewedPostprint (published version

Productivity of the English National Health Service: 2015/16 update

This report updates the Centre for Health Economics’ time series of National Health Service (NHS) productivity growth for the period 2014/15 to 2015/16. It also reports trends in output, input and productivity since 2004/05. NHS productivity growth is measured by comparing growth in the outputs produced by the NHS to growth in the inputs used to produce them. NHS outputs include all the activities undertaken for NHS patients wherever they are treated in England and accounts for changes in the quality of care provided to those patients. NHS inputs include the number of doctors, nurses and support staff providing care, the equipment and clinical supplies used, and the facilities of hospitals and other premises where care is provided