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

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

Advanced study of video signal processing in low signal to noise environments Quarterly progress report, Oct. 1969 - Jan. 1970

Video signal processing in low signal to noise environment

Cost benefit analysis vs. referenda

We consider a planner who chooses between two possible public policies and ask whether a referendum or a cost benefit analysis leads to higher welfare. We find that a referendum leads to higher welfare than a cost benefit analyses in "common value" environments. Cost benefit analysis is better in "private value" environments.Cost benefit analysis, elections, referenda, project evaluation

Information geometric approach to the renormalisation group

We propose a general formulation of the renormalisation group as a family of quantum channels which connect the microscopic physical world to the observable world at some scale. By endowing the set of quantum states with an operationally motivated information geometry, we induce the space of Hamiltonians with a corresponding metric geometry. The resulting structure allows one to quantify information loss along RG flows in terms of the distinguishability of thermal states. In particular, we introduce a family of functions, expressible in terms of two-point correlation functions, which are non increasing along the flow. Among those, we study the speed of the flow, and its generalization to infinite lattices.Comment: Accepted in Phys. Rev.

2100 AI: Reflections on the mechanisation of scientific discovery

The pace of research is nowadays extremely intensive, with datasets and publications being published at an unprecedented rate. In this context data science, artificial intelligence, machine learning and big data analytics are providing researchers with new automatic techniques which not only help them to manage this flow of information but are also able to identify automatically interesting patterns and insights in this vast sea of information. However, the emergence of mechanised scientific discovery is likely to dramatically change the way we do science, thus introducing and amplifying serious societal implications on the role of researchers themselves, which need to be analysed thoroughly