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We present a novel technique for tailoring Bayesian quadrature (BQ) to model selection. The state-of-the-art for comparing the evidence of multiple models relies on Monte Carlo methods, which converge slowly and are unreliable for…
We consider the problem of estimating a random state vector when there is information about the maximum distances between its subvectors. The estimation problem is posed in a Bayesian framework in which the minimum mean square error (MMSE)…
Conventional Monte Carlo simulations are stochastic in the sense that the acceptance of a trial move is decided by comparing a computed acceptance probability with a random number, uniformly distributed between 0 and 1. Here we consider the…
We demonstrate that the task of determining an unknown quantum state can be accomplished efficiently by making a sequential measurement of two observables $\hat{A}$ and $\hat{B}$, provided that the two observables are chosen in such a way…
Uncertainty quantification (UQ) is essential for deploying machine learning models in safety-critical physical systems, yet classical Bayesian approaches incur substantial computational overhead. We establish a formal connection between…
An important problem in statistics is the construction of confidence regions for unknown parameters. In most cases, asymptotic distribution theory is used to construct confidence regions, so any coverage probability claims only hold…
The tomographic reconstruction of the state of a quantum-mechanical system is an essential component in the development of quantum technologies. We present an overview of different tomographic methods for determining the quantum-mechanical…
We analyze mean fidelity between random density matrices of size N, generated with respect to various probability measures in the space of mixed quantum states: Hilbert-Schmidt measure, Bures (statistical) measure, the measures induced by…
Quantum state tomography is a fundamental tool in quantum information processing. It allows us to estimate the state of a quantum system by measuring different observables on many identically prepared copies of the system. This is, in…
Multimode Gaussian states are a versatile resource for quantum information technologies and have been realized across a wide range of physical platforms. Recent progress in the large-scale generation of such states provides a key ingredient…
Models of stochastic processes are widely used in almost all fields of science. Theory validation, parameter estimation, and prediction all require model calibration and statistical inference using data. However, data are almost always…
A promising use of quantum computers is to prepare quantum states that model complex domains, such as correlated electron wavefunctions or the underlying distribution of a complex dataset. Such states need to be verified in view of…
The Markov chain Monte Carlo method (MCMC), especially the Metropolis-Hastings (MH) algorithm, is a widely used technique for sampling from a target probability distribution $P$ on a state space $\Omega$ and applied to various problems such…
This paper is on Bayesian inference for parametric statistical models that are defined by a stochastic simulator which specifies how data is generated. Exact sampling is then possible but evaluating the likelihood function is typically…
We give bounds on the average fidelity achievable by any quantum state estimator, which is arguably the most prominently used figure of merit in quantum state tomography. Moreover, these bounds can be computed online---that is, while the…
Measuring the distinguishability between quantum states is a basic problem in quantum information theory. In this paper, we develop optimal quantum algorithms that estimate both the trace distance and the (square root) fidelity between pure…
Quantum tomography is the main method used to assess the quality of quantum information processing devices, but its complexity presents a major obstacle for the characterization of even moderately large systems. The number of experimental…
We present a new procedure for quantum state reconstruction based on weak continuous measurement of an ensemble average. By applying controlled evolution to the initial state new information is continually mapped onto the measured…
Sliced Wasserstein distances preserve properties of classic Wasserstein distances while being more scalable for computation and estimation in high dimensions. The goal of this work is to quantify this scalability from three key aspects: (i)…
Approximate Bayesian computation (ABC) is a widely used inference method in Bayesian statistics to bypass the point-wise computation of the likelihood. In this paper we develop theoretical bounds for the distance between the statistics used…