Related papers: Optimal Scalar Quantization for Matrix Multiplicat…
The Quark Meson Coupling Model which describes nuclear matter as a collection of non-overlapping MIT bags interacting by the self-consistent exchange of scalar and vector mesons is used to study nuclear matter at finite temperature. In its…
In this paper, we demonstrate how a class of advanced matrix concentration inequalities, introduced in \cite{brailovskaya2024universality}, can be used to eliminate the dimensional factor in the convergence rate of matrix completion. This…
In this paper,a systematic study of quantum phase transition within U(5) \leftrightarrow SO(6) limits is presented in terms of infinite dimensional Algebraic technique in the IBM framework. Energy level statistics are investigated with…
We investigate the phase diagram at the boundary of an infinite two-dimensional cluster state subject to bulk measurements using tensor network methods. The state is subjected to uniform measurements $M = \cos{\theta}Z+\sin{\theta}X$ on the…
In this paper we propose a method to estimate the density matrix \rho of a d-level quantum system by measurements on the N-fold system. The scheme is based on covariant observables and representation theory of unitary groups and it extends…
Quantum Monte Carlo methods are powerful tools for studying quantum many-body systems but face difficulties in accessing excited states and in treating sign problems. We present a continuous-time path-integral Monte Carlo method for…
Non-local properties of ensembles of quantum gates induced by the Haar measure on the unitary group are investigated. We analyze the entropy of entanglement of a unitary matrix U equal to the Shannon entropy of the vector of singular values…
We present error mitigation (EM) techniques for noisy intermediate-scale quantum computers (QC) based on density matrix purification and perturbative corrections to the target energy. We incorporate this scheme into the variational quantum…
In the context of entanglement in relativistic $2\to 2$ scattering described by a perturbative $S$-matrix, we derive analytically the concurrence for a mixed final state of two qubits corresponding to a discrete quantum number of the…
We report the development of a scalar quantization approach that helps build tables of decision and reconstruction levels for any probability density function (pdf). Several example pdf's are used for illustration: Uniform, Gaussian,…
A numerical method based on Matrix Product Formalism is proposed to study the phase transitions and shock formation in the Asymmetric Simple Exclusion Process with open boundaries and parallel dynamics. By working in a canonical ensemble,…
We investigate the ultimate precision achievable in Gaussian quantum metrology. We derive general analytical expressions for the quantum Fisher information matrix and for the measurement compatibility condition, ensuring asymptotic…
We present a novel method for approximately equilibrating a matrix $A \in {\bf R}^{m \times n}$ using only multiplication by $A$ and $A^T$. Our method is based on convex optimization and projected stochastic gradient descent, using an…
Uniform sampling on implicitly defined manifolds is a core primitive in motion planning, constrained simulation, and probabilistic machine learning. MASEM addresses this problem by entropy-maximizing resampling, but its resampling weights…
We analyze the properties of entangled random pure states of a quantum system partitioned into two smaller subsystems of dimensions $N$ and $M$. Framing the problem in terms of random matrices with a fixed-trace constraint, we establish,…
We propose a method for strict error control in sparse approximate matrix-matrix multiplication. The method combines an error bound and a parameter sweep to select an appropriate threshold value. The scheme for error control and the sparse…
In this paper, we consider an image coding process consisting of the following four steps: a direct transformation, a direct quantization, an inverse quantization, and an inverse transformation, where Hadamard transforms are used for the…
Planar nanostructures allow near-ideal extraction of emission from a quantum emitter embedded within, thereby realizing deterministic single-photon sources. Such a source can be transformed into M single-photon sources by implementing…
Stochastic quantization provides an alternate approach to the computation of quantum observables, by stochastically sampling phase space in a path integral. Furthermore, the stochastic variational method can provide analytical control over…
Matrix square roots and their inverses arise frequently in machine learning, e.g., when sampling from high-dimensional Gaussians $\mathcal{N}(\mathbf 0, \mathbf K)$ or whitening a vector $\mathbf b$ against covariance matrix $\mathbf K$.…