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

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

Practical Bayesian Optimization for Variable Cost Objectives

We propose a novel Bayesian Optimization approach for black-box functions with an environmental variable whose value determines the tradeoff between evaluation cost and the fidelity of the evaluations. Further, we use a novel approach to sampling support points, allowing faster construction of the acquisition function. This allows us to achieve optimization with lower overheads than previous approaches and is implemented for a more general class of problem. We show this approach to be effective on synthetic and real world benchmark problems.Comment: 8 pages, 7 figure

Bounds on Information Propagation in Disordered Quantum Spin Chains

We investigate the propagation of information through the disordered XY model. We find, with a probability that increases with the size of the system, that all correlations, both classical and quantum, are suppressed outside of an effective lightcone whose radius grows at most polylogarithmically with |t|.Comment: 4 pages, pdflatex, 1 pdf figure. Corrected the bound for the localised propagator and quantified the probability it bound occur

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.

Contract Management of LHC Civil Engineering at Point 5

Civil engineering work commenced in August 1998 at LEP Point 5 for the underground and surface works necessary to accommodate the CMS detector for the LHC project. The principal underground works consist of two parallel caverns, separated by a support pillar, two new shafts, a number of smaller connection and service galleries and tunnel enlargements on the existing LEP tunnel. The surface works consist of the 140 m long SX building for the detector assembly and numerous other steel and concrete structures necessary for the installation and operation of CMS. The civil engineering design and supervision has been awarded to a joint venture of Gibb (UK), SGI (Switzerland) and Geoconsult (Austria), and the contracting to a joint venture of Dragados (Spain) and Seli (Italy) for 112 MCHF. The aim of this paper is to discuss the management of this contract and in particular how the various parties interact in order to work most efficiently