Related papers: Random phase vector for calculating the trace of a…
Quantum state tomography aims to determine the state of a quantum system as represented by a density matrix. It is a fundamental task in modern scientific studies involving quantum systems. In this paper, we study estimation of…
Many models for complex phenomena use a model for strongly-interacting elements on a small scale to generate larger-scale simulations of some aspects of experimental realizations. These models may be agent-based (as in the case of discrete…
Parameter estimation in linear errors-in-variables models typically requires that the measurement error distribution be known (or estimable from replicate data). A generalized method of moments approach can be used to estimate model…
Matrix determinants play an important role in data analysis, in particular when Gaussian processes are involved. Due to currently exploding data volumes, linear operations - matrices - acting on the data are often not accessible directly…
The behavior of real quantum hardware differs strongly from the simple error models typically used when simulating quantum error correction. Error processes are far more complex than simple depolarizing noise applied to single gates, and…
In [Fleurat, Salvy 2024], we introduced a model of block-weighted random maps that undergoes a phase transition as the density of separating elements changes. The purpose of this note is to demonstrate that the methodology we developed can…
We present an efficient method for evaluating random phase errors in phase shifters within photonic integrated circuits, avoiding the computational cost of traditional Monte Carlo simulations. By modeling spatially correlated manufacturing…
Assuming the validity of random matrices for describing the statistics of a closed chaotic quantum system, we study analytically some statistical properties of the S-matrix characterizing scattering in its open counterpart. In the first…
Quantum theory predicts probabilities as well as relative phases between different alternatives of the system. A unified description of both probabilities and phases comes through a generalisation of the notion of a density matrix for…
This paper investigates the convergence of the randomized Kaczmarz algorithm for the problem of phase retrieval of complex-valued objects. While this algorithm has been studied for the real-valued case}, its generalization to the…
Large language models, like transformers, have recently demonstrated immense powers in text and image generation. This success is driven by the ability to capture long-range correlations between elements in a sequence. The same feature…
Quantum phase estimation is the workhorse behind any quantum algorithm and a promising method for determining ground state energies of strongly correlated quantum systems. Low-cost quantum phase estimation techniques make use of circuits…
We study the full counting statistics of current of large open systems through the application of random matrix theory to transition-rate matrices. We develop a method for calculating the ensemble-averaged current-cumulant generating…
Paper [1] derived the probability density function (PDF) of a sum of products of two correlated complex Gaussian zero-mean random variables (RVs) that has been applied to calculate the error probabilities of a \emph{M}-ary phase shift…
The trace $\tr(q(\ma{L} + q\ma{I})^{-1})$, where $\ma{L}$ is a symmetric diagonally dominant matrix, is the quantity of interest in some machine learning problems. However, its direct computation is impractical if the matrix size is large.…
We use multi-time correlation functions of quantum systems to construct random variables with statistical properties that reflect the degree of complexity of the underlying quantum dynamics.
We introduce a general framework of phase reduction theory for quantum nonlinear oscillators. By employing the quantum trajectory theory, we define the limit-cycle trajectory and the phase according to a stochastic Schr\"{o}dinger equation.…
We provide a graphical calculus for computing averages of tensor network diagrams with respect to the distribution of random vectors containing independent uniform complex phases. Our method exploits the order structure of the partially…
Detection of the number of signals corrupted by high-dimensional noise is a fundamental problem in signal processing and statistics. This paper focuses on a general setting where the high-dimensional noise has an unknown complicated…
Phase transitions generically occur in random matrix models as the parameters in the joint probability distribution of the random variables are varied. They affect all main features of the theory and the interpretation of statistical models…