Related papers: Product matrix processes for coupled multi-matrix …
Determinantal point processes (DPPs) have attracted significant attention as an elegant model that is able to capture the balance between quality and diversity within sets. DPPs are parameterized by a positive semi-definite kernel matrix.…
By combining the continuous matrix product state (cMPS) representation for quantum fields in the continuum with standard optimization techniques for matrix product states (MPS) on the lattice, we obtain an approximation $|\Psi\rangle$,…
We consider a complex-valued linear mixture model, under discrete weakly stationary processes. We recover latent components of interest, which have undergone a linear mixing. We study asymptotic properties of a classical unmixing estimator,…
Devising schemes for testing the amount of entanglement in quantum systems has played a crucial role in quantum computing and information theory. Here, we study the problem of testing whether an unknown state $|\psi\rangle$ is a matrix…
In this work, we investigate the universal representation capacity of the Matrix Product States (MPS) from the perspective of boolean functions and continuous functions. We show that MPS can accurately realize arbitrary boolean functions by…
Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…
Determinantal point processes (DPPs) are repulsive point processes where the interaction between points depends on the determinant of a positive-semi definite matrix. The contributions of this paper are two-fold. First of all, we introduce…
Here we present an efficient and numerically stable procedure for compressing a correlation matrix into a set of local unitary single-particle gates, which leads to a very efficient way of forming the matrix product state (MPS)…
The exclusive photoproduction of a pair of light mesons is studied within the framework of collinear factorisation. The amplitude factorises into a process-dependent perturbatively calculable hard part, a generalised parton distribution…
Quantum machine learning (QML) is a rapidly expanding field that merges the principles of quantum computing with the techniques of machine learning. One of the powerful mathematical frameworks in this domain is tensor networks. These…
In many real-world applications we are interested in approximating costly functions that are analytically unknown, e.g. complex computer codes. An emulator provides a fast approximation of such functions relying on a limited number of…
The similarities between Hartree-Fock (HF) theory and the density-matrix renormalization group (DMRG) are explored. Both methods can be formulated as the variational optimization of a wave-function ansatz. Linearization of the…
We study the eigenvalue correlations of random Hermitian $n\times n$ matrices of the form $S=M+\epsilon H$, where $H$ is a GUE matrix, $\epsilon>0$, and $M$ is a positive-definite Hermitian random matrix, independent of $H$, whose…
The classification of topological phases of matter is fundamental to understand and characterize the properties of quantum materials. In this paper we study phases of matter in one-dimensional open quantum systems. We define two mixed…
We design a new nonparametric method that allows one to estimate the matrix of integrated kernels of a multivariate Hawkes process. This matrix not only encodes the mutual influences of each nodes of the process, but also disentangles the…
We investigate the properties of multifractal products of geometric Gaussian processes with possible long-range dependence and geometric Ornstein-Uhlenbeck processes driven by L\'{e}vy motion and their finite and infinite superpositions. We…
The Dirichlet process (DP) is a fundamental mathematical tool for Bayesian nonparametric modeling, and is widely used in tasks such as density estimation, natural language processing, and time series modeling. Although MCMC inference…
Matrix-product states (MPS) have proven to be a versatile ansatz for modeling quantum many-body physics. For many applications, and particularly in one-dimension, they capture relevant quantum correlations in many-body wavefunctions while…
We analyze a method to produce pairs of non independent Poisson processes $M(t),N(t)$ from positively correlated, self-decomposable, exponential renewals. In particular the present paper provides the family of copulas pairing the renewals,…
Gaussian process regression is widely used because of its ability to provide well-calibrated uncertainty estimates and handle small or sparse datasets. However, it struggles with high-dimensional data. One possible way to scale this…