Related papers: Classical Shadows with Improved Median-of-Means Es…

For many inference problems in statistics and econometrics, the unknown parameter is identified by a set of moment conditions. A generic method of solving moment conditions is the Generalized Method of Moments (GMM). However, classical GMM…

Stein operators allow to characterise probability distributions via differential operators. Based on these characterisations, we develop a new method of point estimation for marginal parameters of strictly stationary and ergodic processes,…

Advances in quantum technology require scalable techniques to efficiently extract information from a quantum system, such as expectation values of observables or its entropy. Traditional tomography is limited to a handful of qubits and…

Mutual information (MI) is a fundamental measure of statistical dependence between two variables, yet accurate estimation from finite data remains notoriously difficult. No estimator is universally reliable, and common approaches fail in…

(Abridged) We develop median statistics that provide powerful alternatives to chi-squared likelihood methods and require fewer assumptions about the data. Applying median statistics to Huchra's compilation of nearly all estimates of the…

Dynamic circuits use real-time outcomes of mid-circuit measurements, processed by a classical controller, to adapt subsequent operations during circuit execution. This additional flexibility over static circuits comes at a price.…

We provide a new perspective on shadow tomography by demonstrating its deep connections with the general theory of measurement frames. By showing that the formalism of measurement frames offers a natural framework for shadow tomography --…

Shadow estimation is a method for deducing numerous properties of an unknown quantum state through a limited set of measurements, which suffers from noises in quantum devices. In this paper, we introduce an error-mitigated shadow estimation…

The Median-of-Means (MoM) is a robust estimator widely used in machine learning that is known to be (minimax) optimal in scenarios where samples are i.i.d. In more grave scenarios, samples are contaminated by an adversary that can inspect…

Shadow tomography protocols have recently emerged as powerful tools for efficient quantum state learning, aiming to reconstruct expectation values of observables with fewer resources than traditional quantum state tomography. For the…

This paper introduces a new version of the smoothly trimmed mean with a more general version of weights, which can be used as an alternative to the classical trimmed mean. We derive its asymptotic variance and to further investigate its…

Higher-order clustering statistics, like the galaxy bispectrum, can add complementary cosmological information to what is accessible with two-point statistics, like the power spectrum. While the standard way of measuring the bispectrum…

Shadow tomography is a scalable technique to characterise the quantum state of a quantum computer or quantum simulator. The protocol is based on the transformation of the outcomes of random measurements into the so-called classical shadows,…

Spurious couplings and decoherence degrade the performance of solid-state quantum processors, demanding careful design, calibration, and mitigation protocols. These strategies often rely on characterization of the idling processor, but…

Many hybrid quantum-classical algorithms for the application of ground state energy estimation in quantum chemistry involve estimating the expectation value of a molecular Hamiltonian with respect to a quantum state through measurements on…

Shadow estimation is a sample-efficient protocol for learning the properties of a quantum system using randomized measurements, but the current understanding of qudit shadow estimation is quite limited compared with the qubit setting. Here…

Accurately estimating the properties of quantum systems is a central challenge in quantum computing and quantum information. We propose a method to obtain unbiased estimators of multiple observables with low statistical error by…

Classical shadow tomography serves as a potent tool for extracting numerous properties from quantum many-body systems with minimal measurements. Nevertheless, prevailing methods yielding optimal performance for few-body operators…

We study sequential quantum changepoint detection in settings where the pre- and post-change regimes are specified through constraints on the expectation values of a finite set of observables. We consider an architecture with separate…

Estimating predictive uncertainty is crucial for many computer vision tasks, from image classification to autonomous driving systems. Hamiltonian Monte Carlo (HMC) is an sampling method for performing Bayesian inference. On the other hand,…