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

Recent evidence on the impact of electricity liberalisation on consumer prices

This report reviews recent evidence on the impact of the Electricity Directive on prices

Sustainability and the Development of an Energy Efficient Housing Stock: a review of some theoretical issues

Global stabilisation of carbon emissions may require emission reductions of 60 percent in the first half of the next century and governments are placing increasing importance on energy efficiency in carbon abatement policies. However a large gap exists between what is possible and what has been achieved to date. This paper seeks to discuss the fundamental issues which should be addressed in the definition and application of energy efficiency policy designed to close the gap. It also addresses the likely impact of take-back effects (the Brookes-Khazzom postulate). The paper argues that despite the considerable work on the problem, the mechanisms which determine the propensity of individuals and organisations to invest in efficiency improvements are not well understood and that greater attention should be paid to motivational factors if a more complete understanding is to emerge

The Business Guide to the Low Carbon Economy: California

Outlines California's climate change policy and offers a detailed framework for calculating and reducing greenhouse gas emissions and purchasing offsets. Includes focus areas for each sector, reference lists, and profiles of successful strategies

Reductions for Frequency-Based Data Mining Problems

Studying the computational complexity of problems is one of the - if not the - fundamental questions in computer science. Yet, surprisingly little is known about the computational complexity of many central problems in data mining. In this paper we study frequency-based problems and propose a new type of reduction that allows us to compare the complexities of the maximal frequent pattern mining problems in different domains (e.g. graphs or sequences). Our results extend those of Kimelfeld and Kolaitis [ACM TODS, 2014] to a broader range of data mining problems. Our results show that, by allowing constraints in the pattern space, the complexities of many maximal frequent pattern mining problems collapse. These problems include maximal frequent subgraphs in labelled graphs, maximal frequent itemsets, and maximal frequent subsequences with no repetitions. In addition to theoretical interest, our results might yield more efficient algorithms for the studied problems.Comment: This is an extended version of a paper of the same title to appear in the Proceedings of the 17th IEEE International Conference on Data Mining (ICDM'17

Geometries in perturbative quantum field theory

In perturbative quantum field theory one encounters certain, very specific geometries over the integers. These `perturbative quantum geometries' determine the number contents of the amplitude considered. In the article `Modular forms in quantum field theory' F. Brown and the author report on a first list of perturbative quantum geometries using the `$c_2$-invariant' in $\phi^4$ theory. A main tool was `denominator reduction' which allowed the authors to examine graphs up to loop order (first Betti number) 10. We introduce an improved `quadratic denominator reduction' which makes it possible to extend the previous results to loop order 11 (and partially orders 12 and 13). For comparison, also 'non-$\phi^4$' graphs are investigated. Here, we were able to extend the results from loop order 9 to 10. The new database of 4801 unique $c_2$-invariants (previously 157)---while being consistent with all major $c_2$-conjectures---leads to a more refined picture of perturbative quantum geometries.Comment: 35 page