Preparing projected entangled pair states on a quantum computer

We present a quantum algorithm to prepare injective PEPS on a quantum computer, a class of open tensor networks representing quantum states. The run-time of our algorithm scales polynomially with the inverse of the minimum condition number of the PEPS projectors and, essentially, with the inverse of the spectral gap of the PEPS' parent Hamiltonian.Comment: 5 pages, 1 figure. To be published in Physical Review Letters. Removed heuristics, refined run-time boun

Three-dimensional Heisenberg spin glass under a weak random anisotropy

We perform a finite-size scaling study of the three-dimensional Heisenberg spin glass in the presence of weak random anisotropic interactions, up to lattice sizes L = 32. Anisotropies have a major impact on the phase transition. The chiral-glass susceptibility does not diverge due to a large anomalous dimension. It follows that the anisotropic spin glass belongs to a Universality Class different from the isotropic model, which questions the applicability of the chirality scenario

A signature of quantum gravity at the source of the seeds of cosmic structure?

This article reviews a recent work by a couple of colleagues and myself about the shortcomings of the standard explanations of the quantum origin of cosmic structure in the inflationary scenario, and a proposal to address them. The point it that in the usual accounts the inhomogeneity and anisotropy of our universe seem to emerge from an exactly homogeneous and isotropic initial state through processes that do not break those symmetries. We argued that some novel aspect of physics must be called upon to able to address the problem in a fully satisfactory way. The proposed approach is inspired on Penrose's ideas regarding an quantum gravity induced, real and dynamical collapse of the wave function.Comment: LateX, (jpconference macros), Prepared for the proceedings the Third International Workshop DICE 2006, " Quantum Mechanics between decoherence and Determinism

On the regularization ambiguities in loop quantum gravity

One of the main achievements of LQG is the consistent quantization of the Wheeler-DeWitt equation which is free of UV problems. However, ambiguities associated to the intermediate regularization procedure lead to an apparently infinite set of possible theories. The absence of an UV problem is intimately linked with the ambiguities arising in the quantum theory. Among these ambiguities there is the one associated to the SU(2) unitary rep. used in the diffeomorphism covariant pointsplitting regularization of nonlinear funct. of the connection. This ambiguity is labelled by a halfinteger m and, here, it is referred to as the m-ambiguity. The aim of this paper is to investigate the important implications of this ambiguity./ We first study 2+1 gravity quantized in canonical LQG. Only when the regularization of the quantum constraints is performed in terms of the fundamental rep. of the gauge group one obtains the usual TQFT. In all other cases unphysical local degrees of freedom arise at the level of the regulated theory that conspire against the existence of the continuum limit. This shows that there is a clear cut choice in the quantization of the constraints in 2+1 LQG./ We then analyze the effects of the ambiguity in 3+1 gravity exhibiting the existence of spurious solutions for higher unit. rep. quantizations of the Hamiltonian constraint. Although the analysis is not complete in D=3+1--due to the difficulties associated to the definition of the physical inner product--it provides evidence supporting the definitions quantum dynamics of loop quantum gravity in terms of the fundamental representation of the gauge group as the only consistent possibilities. If the gauge group is SO(3) we find physical solutions associated to spin-two local excitations.Comment: 21 page

The Seeds of Cosmic structure as a door to New Physics

There is something missing in our understanding of the origin of the seeds of Cosmic Structuture. The fact that the fluctuation spectrum can be extracted from the inflationary scenario through an analysis that involves quantum field theory in curved space-time, and that it coincides with the observational data has lead to a certain complacency in the community, which prevents the critical analysis of the obscure spots in the derivation. The point is that the inhomogeneity and anisotropy of our universe seem to emerge from an exactly homogeneous and isotropic initial state through processes that do not break those symmetries. This article gives a brief recount of the problems faced by the arguments based on established physics, which comprise the point of view held by a large majority of researchers in the field. The conclusion is that we need some new physics to be able to fully address the problem. The article then exposes one avenue that has been used to address the central issue and elaborates on the degree to which, the new approach makes different predictions from the standard analyses. The approach is inspired on Penrose's proposals that Quantum Gravity might lead to a real, dynamical collapse of the wave function, a process that we argue has the properties needed to extract us from the theoretical impasse described above.Comment: Prepared for the proceedings of the conference NEBXII " Recent Developments in Gravity", Napfio Grece June 2006. LateX, 15 page

Entropy in the Classical and Quantum Polymer Black Hole Models

We investigate the entropy counting for black hole horizons in loop quantum gravity (LQG). We argue that the space of 3d closed polyhedra is the classical counterpart of the space of SU(2) intertwiners at the quantum level. Then computing the entropy for the boundary horizon amounts to calculating the density of polyhedra or the number of intertwiners at fixed total area. Following the previous work arXiv:1011.5628, we dub these the classical and quantum polymer models for isolated horizons in LQG. We provide exact micro-canonical calculations for both models and we show that the classical counting of polyhedra accounts for most of the features of the intertwiner counting (leading order entropy and log-correction), thus providing us with a simpler model to further investigate correlations and dynamics. To illustrate this, we also produce an exact formula for the dimension of the intertwiner space as a density of "almost-closed polyhedra".Comment: 24 page

One size fits ball: Macrocyclic hosts for fullerenes with micromolar affinity

Date du colloque : 25/03/2012International audienc