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Efficient quantum Monte Carlo update schemes called directed loops have recently been proposed, which improve the efficiency of simulations of quantum lattice models. We propose to generalize the detailed balance equations at the local…
Mutual information is a measure of the dependence between random variables that has been used successfully in myriad applications in many fields. Generalized mutual information measures that go beyond classical Shannon mutual information…
Entanglement is a distinguishing feature of quantum many-body systems, and uncovering the entanglement structure for large particle numbers in quantum simulation experiments is a fundamental challenge in quantum information science. Here we…
Scalable Gaussian process (GP) inference is essential for sequential decision-making tasks, yet improving GP scalability remains a challenging problem with many open avenues of research. This paper focuses on iterative GPs, where iterative…
The efficiency of statistical sampling in broad-histogram Monte Carlo simulations can be considerably improved by optimizing the simulated extended ensemble for fastest equilibration. Here we describe how a recently developed feedback…
Belonging to the family of Bayesian nonparametrics, Gaussian process (GP) based approaches have well-documented merits not only in learning over a rich class of nonlinear functions, but also in quantifying the associated uncertainty.…
In this work, we investigate quantum phase transition (QPT) in a generic family of spin chains using the ground-state energy, the energy gap, and the geometric measure of entanglement (GE). In many of prior works, GE per site was used.…
The connection between the non-equilibrium dynamics of isolated quantum many-body systems and statistical mechanics is a fundamental open question. It is generally believed that the unitary quantum evolution of a sufficiently complex system…
Consider solving large sparse range symmetric singular linear systems $ A {\bf x}= {\bf b} $ which arise, for instance, in the discretization of convection diffusion equations with periodic boundary conditions, and partial differential…
We explore the link between deep ensembles and Gaussian processes (GPs) through the lens of the Neural Tangent Kernel (NTK): a recent development in understanding the training dynamics of wide neural networks (NNs). Previous work has shown…
The cumulative shrinkage process is an increasing shrinkage prior that can be employed within models in which additional terms are supposed to play a progressively negligible role. A natural application is to Gaussian factor models, where…
Finite mixture models are frequently used to uncover latent structures in high-dimensional datasets (e.g.\ identifying clusters of patients in electronic health records). The inference of such structures can be performed in a Bayesian…
In this PhD thesis we investigate some properties of one-dimensional quantum systems, focusing on two important aspects of integrable models: Their entanglement properties at equilibrium and their dynamical correlators after a quantum…
Quantifying quantum entanglement is a pivotal challenge in quantum information science, particularly for high-dimensional systems, due to its computational complexity. This thesis extends the geometric measure of entanglement (GME) to…
A quasi-complementary sequence set (QCSS) refers to a set of two-dimensional matrices with low non-trivial aperiodic auto- and cross- correlation sums. For multicarrier code-division multiple-access applications, the availability of large…
In biomolecular systems (especially all-atom models) with many degrees of freedom such as proteins and nucleic acids, there exist an astronomically large number of local-minimum-energy states. Conventional simulations in the canonical…
The integrable system is constrained strictly by the conservation law during the time evolution, and the nearly integrable system or nonintegrable system is also constrained by the conserved parameters (like the constants of motion) with…
In this work, we propose a novel framework for large-scale Gaussian process (GP) modeling. Contrary to the global, and local approximations proposed in the literature to address the computational bottleneck with exact GP modeling, we employ…
When a generic quantum system is prepared in a simple initial condition, it typically equilibrates toward a state that can be described by a thermal ensemble. A known exception are localized systems which are non-ergodic and do not…
Gaussian elimination (GE) is the archetypal direct algorithm for solving linear systems of equations and this has been its primary application for thousands of years. In the last decade, GE has found another major use as an iterative…