The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently

In this Letter we show that an arbitrarily good approximation to the propagator e^{itH} for a 1D lattice of n quantum spins with hamiltonian H may be obtained with polynomial computational resources in n and the error \epsilon, and exponential resources in |t|. Our proof makes use of the finitely correlated state/matrix product state formalism exploited by numerical renormalisation group algorithms like the density matrix renormalisation group. There are two immediate consequences of this result. The first is that the Vidal's time-dependent density matrix renormalisation group will require only polynomial resources to simulate 1D quantum spin systems for logarithmic |t|. The second consequence is that continuous-time 1D quantum circuits with logarithmic |t| can be simulated efficiently on a classical computer, despite the fact that, after discretisation, such circuits are of polynomial depth.Comment: 4 pages, 2 figures. Simplified argumen

Entanglement, quantum phase transitions, and density matrix renormalization

We investigate the role of entanglement in quantum phase transitions, and show that the success of the density matrix renormalization group (DMRG) in understanding such phase transitions is due to the way it preserves entanglement under renormalization. We provide a reinterpretation of the DMRG in terms of the language and tools of quantum information science which allows us to rederive the DMRG in a physically transparent way. Motivated by our reinterpretation we suggest a modification of the DMRG which manifestly takes account of the entanglement in a quantum system. This modified renormalization scheme is shown,in certain special cases, to preserve more entanglement in a quantum system than traditional numerical renormalization methods.Comment: 5 pages, 1 eps figure, revtex4; added reference and qualifying remark

MEASUREMENT AND TESTING FOR NEUTRALITY OF FOREIGN PRICE AND CPI TRANSMISSION IN RUSSIA

This paper examines domestic and international food market integration in Russia before and after the financial crisis of 1998. Using monthly prices of bread, pork, and beef in 80 regions of Russia from 1994 to 1999, we measure the short-run response of regional prices to changes in foreign prices and domestic inflation. We find that both changes in foreign prices and domestic inflation have distinct impacts on the prices of these commodities in different Russian markets, indicating poor market integration in the short run. An analysis of the effect of the financial crisis shows that market integration for bread and beef deteriorated after the crisis. However, integration improved for pork in some parts of Russia, and the integration of Siberian pork markets with Chinese pork markets also improved after the crisis.International Relations/Trade,

How are topics born? Understanding the research dynamics preceding the emergence of new areas

The ability to promptly recognise new research trends is strategic for many stake- holders, including universities, institutional funding bodies, academic publishers and companies. While the literature describes several approaches which aim to identify the emergence of new research topics early in their lifecycle, these rely on the assumption that the topic in question is already associated with a number of publications and consistently referred to by a community of researchers. Hence, detecting the emergence of a new research area at an embryonic stage, i.e., before the topic has been consistently labelled by a community of researchers and associated with a number of publications, is still an open challenge. In this paper, we begin to address this challenge by performing a study of the dynamics preceding the creation of new topics. This study indicates that the emergence of a new topic is anticipated by a significant increase in the pace of collaboration between relevant research areas, which can be seen as the ‘parents’ of the new topic. These initial findings (i) confirm our hypothesis that it is possible in principle to detect the emergence of a new topic at the embryonic stage, (ii) provide new empirical evidence supporting relevant theories in Philosophy of Science, and also (iii) suggest that new topics tend to emerge in an environment in which weakly interconnected research areas begin to cross-fertilise

Fingerprint Policy Optimisation for Robust Reinforcement Learning

Policy gradient methods ignore the potential value of adjusting environment variables: unobservable state features that are randomly determined by the environment in a physical setting, but are controllable in a simulator. This can lead to slow learning, or convergence to suboptimal policies, if the environment variable has a large impact on the transition dynamics. In this paper, we present fingerprint policy optimisation (FPO), which finds a policy that is optimal in expectation across the distribution of environment variables. The central idea is to use Bayesian optimisation (BO) to actively select the distribution of the environment variable that maximises the improvement generated by each iteration of the policy gradient method. To make this BO practical, we contribute two easy-to-compute low-dimensional fingerprints of the current policy. Our experiments show that FPO can efficiently learn policies that are robust to significant rare events, which are unlikely to be observable under random sampling, but are key to learning good policies.Comment: ICML 201

Probabilistic Numerics and Uncertainty in Computations

We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such uncertainties, arising from the loss of precision induced by numerical calculation with limited time or hardware, are important for much contemporary science and industry. Within applications such as climate science and astrophysics, the need to make decisions on the basis of computations with large and complex data has led to a renewed focus on the management of numerical uncertainty. We describe how several seminal classic numerical methods can be interpreted naturally as probabilistic inference. We then show that the probabilistic view suggests new algorithms that can flexibly be adapted to suit application specifics, while delivering improved empirical performance. We provide concrete illustrations of the benefits of probabilistic numeric algorithms on real scientific problems from astrometry and astronomical imaging, while highlighting open problems with these new algorithms. Finally, we describe how probabilistic numerical methods provide a coherent framework for identifying the uncertainty in calculations performed with a combination of numerical algorithms (e.g. both numerical optimisers and differential equation solvers), potentially allowing the diagnosis (and control) of error sources in computations.Comment: Author Generated Postprint. 17 pages, 4 Figures, 1 Tabl