Simulation of many-qubit quantum computation with matrix product states

Matrix product states provide a natural entanglement basis to represent a quantum register and operate quantum gates on it. This scheme can be materialized to simulate a quantum adiabatic algorithm solving hard instances of a NP-Complete problem. Errors inherent to truncations of the exact action of interacting gates are controlled by the size of the matrices in the representation. The property of finding the right solution for an instance and the expected value of the energy are found to be remarkably robust against these errors. As a symbolic example, we simulate the algorithm solving a 100-qubit hard instance, that is, finding the correct product state out of ~ 10^30 possibilities. Accumulated statistics for up to 60 qubits point at a slow growth of the average minimum time to solve hard instances with highly-truncated simulations of adiabatic quantum evolution.Comment: 5 pages, 4 figures, final versio

Frustration, interaction strength and ground-state entanglement in complex quantum systems

Entanglement in the ground state of a many-body quantum system may arise when the local terms in the system Hamiltonian fail to commute with the interaction terms in the Hamiltonian. We quantify this phenomenon, demonstrating an analogy between ground-state entanglement and the phenomenon of frustration in spin systems. In particular, we prove that the amount of ground-state entanglement is bounded above by a measure of the extent to which interactions frustrate the local terms in the Hamiltonian. As a corollary, we show that the amount of ground-state entanglement is bounded above by a ratio between parameters characterizing the strength of interactions in the system, and the local energy scale. Finally, we prove a qualitatively similar result for other energy eigenstates of the system.Comment: 11 pages, 3 figure

Nonergodicity of entanglement and its complementary behavior to magnetization in infinite spin chain

We consider the problem of the validity of a statistical mechanical description of two-site entanglement in an infinite spin chain described by the XY model Hamiltonian. We show that the two-site entanglement of the state, evolved from the initial equilibrium state, after a change of the magnetic field, does not approach its equilibrium value. This suggests that two-site entanglement, like (single-site) magnetization, is a nonergodic quantity in this model. Moreover we show that these two nonergodic quantities behave in a complementary way.Comment: 4 pages, 2 eps figures, RevTeX4; v2: Published versio

Color de aceites de oliva virgen extra enriquecidos con carotenoides procedentes de microalgas: influencia de la exposición a la radiación ultravioleta y al calentamiento

A carotenoid-rich extract containing 2.5 mg/mL of lutein and 3.3 mg/mL of β-carotene from the microalga Scenedesmus almeriensis was added to ten extra virgin olive oils from four Spanish cultivars with differing degrees of ripeness, obtaining carotenoid enriched oils with lutein and β-carotene concentrations of 0.082 and 0.11 mg/mL, respectively. Extra virgin olive oils enriched with carotenoids from microalgae were studied by analyzing the effect on color of three different treatments: ultraviolet exposure, microwave heating and immersion bath heating. The methodology was designed to simulate, in controlled laboratory conditions, the effects of household treatments. Spectrophotometric color measurements were then performed to monitor color changes in the enriched and non-enriched extra virgin olive oil samples. Enriched oils are much more chromatic, darker and redder than natural oils. After 55 days UV irradiation, 40 min microwave heating, and 72 hours thermostatic heating, the average color differences for natural/enriched extra virgin olive oils were 98/117, 15/9 and 57/28 CIELAB units, respectively. In general, increasing temperature and ultraviolet exposure produced higher CIELAB color differences in the non-enriched samples. The addition of microalga extracts to extra virgin olive oils was found to induce some color stability and may constitute a future way of increasing the daily intake of beneficial bioactive compounds such as carotenoids.Añadimos un extracto rico en carotenoides, que contiene 2,5 mg/mL de luteína y 3,3 mg/mL de β-caroteno, procedente de la microalga Scenedesmus almeriensis, a diez aceites de oliva virgen extra de cuatro variedades con diferentes grados de maduración, obteniéndose aceites enriquecidos en carotenoides con concentraciones de luteína y β-caroteno de 0,082 y 0,11 mg/mL respectivamente. Se han estudiado aceites de oliva virgen extra enriquecidos con carotenoides procedentes de microalgas, estudiando el efecto producido sobre el color de los mismos como consecuencia de irradiación ultravioleta, calentamiento en microondas y en baño termostático, reproduciendo en el laboratorio los efectos de los tratamientos domésticos. Se ha determinado el color para monitorizar los cambios de las muestras control y enriquecidas de los diferentes aceites. Los aceites enriquecidos son mucho más cromáticos, oscuros y rojizos que los naturales. Tras 55 días de irradiación UV, 40 minutos de calentamiento por microondas y 72 horas de calentamiento termostático, las diferencias medias de color para los aceites de oliva virgen extra naturales/enriquecidos fueron de 98/117, 15/9 y 57/28 unidades CIELAB, respectivamente. En término generales, el incremento en la temperatura y la exposición a la radiación ultravioleta produce diferencias de color más grandes en las muestras no enriquecidas. El enriquecimiento de los aceites virgen extra con extractos procedentes de microalgas, induce estabilidad en el color y puede constituir una vía para incrementar la ingesta diaria de compuestos bioactivos beneficiosos como son los carotenoides.University of JaenCastillo de Canena Olive Juice companyMinistry of Science and Innovation of the National Government of Spain PID2019107816GB-I00 / AEI / 10.13039/50110001103

Connecting the generalized robustness and the geometric measure of entanglement

The main goal of this paper is to provide a connection between the generalized robustness of entanglement ($R_g$) and the geometric measure of entanglement ($E_{GME}$). First, we show that the generalized robustness is always higher than or equal to the geometric measure. Then we find a tighter lower bound to $R_g(\rho)$ based only on the purity of $\rho$ and its maximal overlap to a separable state. As we will see it is also possible to express this lower bound in terms of $E_{GME}$.Comment: 4 pages, 2 figures. Comments welcome. v2: text improved - some completely symmetric states were used to illustrate the results. Comments are always welcome! v3: minor changes. Accepted by Phys. Rev. A. v4: results on symmetric states fixe

Modelling and analysing the relationship between innovation and the European Regulations on hazardous waste shipments

In Europe, there are different regulations regarding hazardous waste management with which European Union Member States must comply. On the one hand, Member States must meet the recovery targets that are set in the different waste Directives, and they have two options here: material recovery facilities in the country of origin, or recovery through the shipment of waste. In addition, EU Member States must comply with the regulations governing the shipment of hazardous waste (HW), that is, the Basel Convention and the European Regulation on the shipment of waste. Two main questions arise: where is hazardous waste sent, and why? We analyse the European regulation on the shipment of waste, and we consider the above questions by combining network analysis methodology, to examine which countries in the network can be grouped in HW-trading communities, and ANOVA technique to study how the groups created in the network behave in different contexts. These HW-trading communities can be assessed according to European Innovation Indicators, GDP, and other variables. The results allow us to understand the drivers behind the shipment of HW for recovery in Europe. First, this study provides a descriptive overview of the relationships between European countries, the way in which they cooperate and describes how each country is positioned in the joint network. Second, the study is able to identify the most relevant countries in the network. Third, the HW-trading communities are analysed to discover whether they behave differently from the other groups according to GDP and other variables, amongst which we have included the following Europe Innovation Indicators: innovation index, research systems, innovation friendly environment, or innovators. The results show that the Nordic countries are outstanding in the way in which their waste is managed with other countries and reveal a community that works both in the context of hazardous waste shipment and innovation

Understanding hazardous waste exports for disposal in europe: A contribution to sustainable development

The concept of sustainable development was introduced in Europe by the Treaty of Amsterdam (1997) and was extended to waste management in the Waste Framework Directive. In order to achieve sustainable development, hazardous waste (HW) must be managed safely and in accordance with regulations. This also applies to worldwide HW transport, especially when HW is shipped for disposal. The United Nations, through the Basel Convention, aims to prevent the export of HW from developed countries to developing countries for disposal. In Europe, HW shipments are regulated by Regulation (EC) No. 1013/2006 of the European Parliament and by the Council of 14 June 2006 on shipments of waste. Additionally, all HW shipments must be in accordance with two principles contained in the Waste Framework Directive: proximity and self-sufficiency. Using data from 2014 and network analysis methodology, this paper fills the gaps in the scientific literature by looking at how shipments of HW travel for disposal in Europe, how the regulations affect these shipments and how GDP per capita influences the shipment of waste. The results show that countries with a high GDP per capita play an important role in the network (having the highest in-degree) and that the absence of landfill taxes for HW does not influence HW shipments for disposal. Therefore, countries in the EU act in accordance with the proximity and self-sufficiency principles. © 2021 by the authors. Licensee MDPI, Basel, Switzerland

The mutual assessment system in teamwork: The value of the individual grade

Teaching-learning based on cooperative learning is grounded on a methodology that is currently one of the most widely used within formal education classrooms. Recently, special attention has begun to be paid to a fundamentally relevant aspect of the assessment of the learning of university students within their group performance: their individual grades obtained from teamwork. In addition to describing the individual grading system that is used to assess individual contributions, this study analyses the perceptions of 99 university students regarding the benefits that the system has for students’ learning process. A system of evaluation based on self-assessment, co-assessment and peer-assessment was implemented in a Spanish university. The results collected using a specially designed questionnaire led to the conclusion that improvements were achieved in the teaching-learning process, in manifesting positive attitudes and in improving students’ ability to learn to learn. In conclusion, students feel that they are granted greater control over their final grade and, as a result, perceive that their involvement in the task increases and their capacity for self-criticism develops

Phase transitions, entanglement and quantum noise interferometry in cold atoms

We show that entanglement monotones can characterize the pronounced enhancement of entanglement at a quantum phase transition if they are sensitive to long-range high order correlations. These monotones are found to develop a sharp peak at the critical point and to exhibit universal scaling. We demonstrate that similar features are shared by noise correlations and verify that these experimentally accessible quantities indeed encode entanglement information and probe separability.Comment: 4 pages 4 figure

Entanglement of indistinguishable particles in condensed matter physics

The concept of entanglement in systems where the particles are indistinguishable has been the subject of much recent interest and controversy. In this paper we study the notion of entanglement of particles introduced by Wiseman and Vaccaro [Phys. Rev. Lett. 91, 097902 (2003)] in several specific physical systems, including some that occur in condensed matter physics. The entanglement of particles is relevant when the identical particles are itinerant and so not distinguished by their position as in spin models. We show that entanglement of particles can behave differently to other approaches that have been used previously, such as entanglement of modes (occupation-number entanglement) and the entanglement in the two-spin reduced density matrix. We argue that the entanglement of particles is what could actually be measured in most experimental scenarios and thus its physical significance is clear. This suggests entanglement of particles may be useful in connecting theoretical and experimental studies of entanglement in condensed matter systems.Comment: 13 pages, 6 figures, comments welcome, published version (minor changes, added references