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Approximate Bayesian computation (ABC) methods, which are applicable when the likelihood is difficult or impossible to calculate, are an active topic of current research. Most current ABC algorithms directly approximate the posterior…
We study the internal dynamics of an elementary quantum system placed close to a body held at a temperature different from that of the surrounding radiation. We derive general expressions for lifetime and density matrix valid for bodies of…
We apply Quantum Monte Carlo technique to analyze the non equlibrium state of a trapped 1d Bose gas just after the quenching of the confining potential. As a matter of fact we solve the time dependent Schroedinger equation for the system of…
Variational algorithms have particular relevance for near-term quantum computers but require non-trivial parameter optimisations. Here we propose Analytic Descent: Given that the energy landscape must have a certain simple form in the local…
We present BAE, a problem-tailored and noise-aware Bayesian algorithm for quantum amplitude estimation. In a fault tolerant scenario, BAE is capable of saturating the Heisenberg limit; if device noise is present, BAE can dynamically…
The random matrix ensembles (RME), especially Gaussian random matrix ensembles GRME and Ginibre random matrix ensembles, are applied to following quantum systems: nuclear systems, molecular systems, and two-dimensional electron systems…
One of the fundamental problems of quantum statistical physics is how an ideally isolated quantum system can ever reach thermal equilibrium behavior despite the unitary time evolution of quantum-mechanical systems. Here, we study, via…
We consider a randomised implementation of the finite element method (FEM) for elliptic partial differential equations on high-dimensional models. This is motivated by applications where model predictions are essential for real-time process…
Searching large and complex design spaces for a global optimum can be infeasible and unnecessary. A practical alternative is to iteratively refine the neighborhood of an initial design using local optimization methods such as gradient…
We develop randomized matrix-free algorithms for estimating partial traces, a generalization of the trace arising in quantum physics and chemistry. Our algorithm improves on the typicality-based approach used in [T. Chen and Y-C. Cheng,…
We investigate the Bose-Einstein Condensation on non homogeneous non amenable networks for the model describing arrays of Josephson junctions on perturbed Cayley Trees. The resulting topological model has also a mathematical interest in…
We introduce a method for computing corrections to Bethe approximation for spin models on arbitrary lattices. Unlike cluster variational methods, the new approach takes into account fluctuations on all length scales. The derivation of the…
We introduce an algorithm for estimating the entropy of pairwise, probabilistic graph models by leveraging bridges between social communities and an accurate entropy estimator on sparse samples. We propose using a measure of investment from…
Dynamical response functions are fundamental quantities to describe the excited-state properties in quantum many-body systems. Quantum algorithms have been proposed to evaluate these quantities by means of quantum phase estimation (QPE),…
This thesis synthesizes probability and entropic inference with Quantum Mechanics (QM) and quantum measurement [1-6]. It is shown that the standard and quantum relative entropies are tools designed for the purpose of updating probability…
Quantum thermalization is well understood via the Eigenstate Thermalization Hypothesis (ETH). The general form of ETH, describing all the relevant correlations of matrix elements, may be derived on the basis of a `typicality' argument of…
We present a novel approach for computing reduced density matrices for superpositions of eigenstates of a Bethe-ansatz solvable model by direct integration of the wave function in coordinate representation. A diagrammatic approach is…
We consider the energy-driven stochastic state vector reduction equation for the density matrix, which for pure state density matrices can be written in two equivalent forms. We use these forms to discuss the decoupling of the noise terms…
Density matrix embedding theory (DMET) describes finite fragments in the presence of a surrounding environment. In contrast to most embedding methods, DMET explicitly allows for quantum entanglement between both. In this chapter, we discuss…
We develop a model based on the fractional exclusion statistics (FES) applicable to non-homogeneous interacting particle systems. Here the species represent elementary volumes in an (s+1)-dimensional space, formed by the direct product…