We review optimal quantization methods for numerically solving nonlinear problems in higher dimension associated with Markov processes. Quantization of a Markov process consists in a spatial discretization on finite grids optimally fitted to the dynamics of the process. Two quantization methods are proposed: the first one, called marginal quantization, relies on an optimal approximation of the ...

Covariant quantization of the Nambu-Goto spinning particle in 2+1-dimensions is studied. The model is relevant in the context of recent activities in non-commutative space-time. From a technical point of view also covariant quantization of the model poses an interesting problem: the set of second class constraints (in the Dirac classification scheme) is reducible. The reducibility problem is an...

We present a fast resampling scheme using vector quantiza-tion. Our method diiers from prior work applying vector quantization to speeding up image and volume processing in two essential aspects. First, our method uses blocks with overlapping rather than disjoint extents. Second, we present a means of trading oo smaller block sizes for additional computation. These two innovations allow vector ...

In this work, we present a quantum algorithm for ground-state energy calculations of periodic solids on error-corrected computers. The is based the sparse qubitization approach in second quantization and developed Bloch Wannier basis sets. We show that functions require less computational resources with respect to because: (i) L$_1$ norm Hamiltonian considerably lower (ii) translational symmetr...