Classical simulation of quantum many-body systems with a tree tensor network

We show how to efficiently simulate a quantum many-body system with tree structure when its entanglement (Schmidt number) is small for any bipartite split along an edge of the tree. As an application, we show that any one-way quantum computation on a tree graph can be efficiently simulated with a classical computer.

Optimal unravellings for feedback control in linear quantum systems

For quantum systems with linear dynamics in phase space much of classical feedback control theory applies. However, there are some questions that are sensible only for the quantum case: Given a fixed interaction between the system and the environment what is the optimal measurement on the environment for a particular control problem? We show that for a broad class of optimal (state- based) control problems ( the stationary linear-quadratic-Gaussian class), this question is a semidefinite program. Moreover, the answer also applies to Markovian (current-based) feedback.

Improvement of the Derjaguin-Broekhoff-de Boer theory for capillary condensation/evaporation of nitrogen in mesoporous systems and its implications for pore size analysis of MCM-41 silicas and related materials

In this work, we propose an improvement of the classical Derjaguin-Broekhoff-de Boer (DBdB) theory for capillary condensation/evaporation in mesoporous systems. The primary idea of this improvement is to employ the Gibbs-Tolman-Koenig-Buff equation to predict the surface tension changes in mesopores. In addition, the statistical film thickness (so-called t-curve) evaluated accurately on the basis of the adsorption isotherms measured for the MCM-41 materials is used instead of the originally proposed t-curve (to take into account the excess of the chemical potential due to the surface forces). It is shown that the aforementioned modifications of the original DBdB theory have significant implications for the pore size analysis of mesoporous solids. To verify our improvement of the DBdB pore size analysis method (IDBdB), a series of the calcined MCM-41 samples, which are well-defined materials with hexagonally ordered cylindrical mesopores, were used for the evaluation of the pore size distributions. The correlation of the IDBdB method with the empirically calibrated Kruk-Jaroniec-Sayari (KJS) relationship is very good in the range of small mesopores. So, a major advantage of the IDBdB method is its applicability for small mesopores as well as for the mesopore range beyond that established by the KJS calibration, i.e., for mesopore radii greater than similar to4.5 nm. The comparison of the IDBdB results with experimental data reported by Kruk and Jaroniec for capillary condensation/evaporation as well as with the results from nonlocal density functional theory developed by Neimark et al. clearly justifies our approach. Note that the proposed improvement of the classical DBdB method preserves its original simplicity and simultaneously ensures a significant improvement of the pore size analysis, which is confirmed by the independent estimation of the mean pore size by the powder X-ray diffraction method.

Logic of Violations: A gentzen systems for reasoning with contrary-to-duty obligations

In this paper we present a Gentzen system for reasoning with contrary-to-duty obligations. The intuition behind the system is that a contrary-to-duty is a special kind of normative exception. The logical machinery to formalise this idea is taken from substructural logics and it is based on the definition of a new non-classical connective capturing the notion of reparational obligation. Then the system is tested against well-known contrary-to-duty paradoxes.