Related papers: Some remarks on the effect of the Random Batch Met…
Linear mixed models with large imbalanced crossed random effects structures pose severe computational problems for maximum likelihood estimation and for Bayesian analysis. The costs can grow as fast as $N^{3/2}$ when there are N…
Quantum phase transitions (QPTs) are usually associated with many-body systems with large degrees of freedom approaching the thermodynamic limit. In such systems, the many-body ground state shows abrupt changes at zero temperature when the…
We develop an efficient numerical method to study the quantum critical behavior of disordered systems with $\mathcal{O}(N)$ order-parameter symmetry in the large$-N$ limit. It is based on the iterative solution of the large$-N$ saddle-point…
We study the dynamics of a version of the batch minority game, with random external information and with different types of inhomogeneous decision noise (additive and multiplicative), using generating functional techniques \`{a} la De…
Many-body quantum systems are notoriously hard to study theoretically due to the exponential growth of their Hilbert space. It is also challenging to probe the quantum correlations in many-body states in experiments due to their sensitivity…
In this paper, we study the phase transition behavior emerging from the interactions among multiple agents in the presence of noise. We propose a simple discrete-time model in which a group of non-mobile agents form either a fixed connected…
In this paper, a stochastic algorithm for the efficient simulation and optimal control of networked wave equations based on the random batch method is proposed and analyzed. The random approximation is constructed by dividing the time…
We consider a system of $N$ non-crossing Brownian particles in one dimension. We find the exact rate function that describes the long-time large deviation statistics of their occupation fraction in a finite interval in space. Remarkably, we…
Quantum computers promise to perform computations beyond the reach of modern computers with profound implications for scientific research. Due to remarkable technological advances, small scale devices are now becoming available for use. One…
Reduced density matrices (RDMs) are fundamental in quantum information processing, allowing the computation of local observables, such as energy and correlation functions, without the exponential complexity of fully characterizing quantum…
Modeling open quantum systems -- quantum systems coupled to a bath -- is of value in condensed matter theory, cavity quantum electrodynamics, nanosciences and biophysics. The real-time simulation of open quantum systems was advanced…
A simple statistical model for the effects of dephasing on electron transport in one-dimensional quantum systems is introduced, which allows to adjust the degree of phase and momentum randomization independently. Hence, the model is able to…
A single-sort continuum Curie-Weiss system of interacting particles is studied. The particles are placed in the space $\mathbb{R}^d$ divided into congruent cubic cells. For a region $V\subset \mathbb{R}^d$ consisting of $N\in \mathbb{N}$…
In principle a quantum system could be used to simulate another quantum system. The purpose of such a simulation would be to obtain information about problems which cannot be simulated with a classical computer due to the exponential…
The machine learning potential (MLP) based molecular dynamics (MD) method was applied for constructing the pressure-temperature phase diagram in the barium titanate (BaTiO3) crystals. The nuclear quantum effects (NQEs) on the phase…
In this paper we present a quantum algorithm that uses noise as a resource. The goal of our quantum algorithm is the calculation of operator averages of an open quantum system evolving in time. Selected low-noise system qubits and noisy…
Complex quantum simulation workflows are often hindered by incompatible wavefunction representations adopted across different algorithmic frameworks. In particular, the mismatch between the first- and second-quantization formalisms prevents…
We study an exactly solvable model of monitored dynamics in a system of $N$ spin-$1/2$ particles with pairwise all-to-all noisy interactions, where each spin is constantly perturbed by weak measurements of the spin component in a random…
In the noisy intermediate-scale quantum (NISQ) era, quantum error mitigation (QEM) is essential for producing reliable outputs from quantum circuits. We present a statistical signal processing approach to QEM that estimates the most likely…
Phase estimation is known to be a robust method for single-qubit gate calibration in quantum computers, while Bayesian estimation is widely used in devising optimal methods for learning in quantum systems. We present Bayesian phase…