Related papers: Bayesian error regions in quantum estimation II: r…
We introduce a Bayesian method for the estimation of single qubit errors in quantum devices, and use it to characterize these errors on three 27-qubit superconducting qubit devices. We self-consistently estimate up to seven parameters of…
We address estimation of one-parameter unitary gates for qubit systems and seek for optimal probes and measurements. Single- and two-qubit probes are analyzed in details focusing on precision and stability of the estimation procedure.…
This review aims at gathering the most relevant quantum multi-parameter estimation methods that go beyond the direct use of the Quantum Fisher Information concept. We discuss in detail the Holevo Cram\'er-Rao bound, the Quantum Local…
We consider nonparametric Bayesian estimation inference using a rescaled smooth Gaussian field as a prior for a multidimensional function. The rescaling is achieved using a Gamma variable and the procedure can be viewed as choosing an…
We derive a necessary and sufficient condition for the possibility of achieving the Heisenberg scaling in general adaptive multi-parameter estimation schemes in presence of Markovian noise. In situations where the Heisenberg scaling is…
A theory of superefficiency and adaptation is developed under flexible performance measures which give a multiresolution view of risk and bridge the gap between pointwise and global estimation. This theory provides a useful benchmark for…
We analyse and explain the increased generalisation performance of iterate averaging using a Gaussian process perturbation model between the true and batch risk surface on the high dimensional quadratic. We derive three phenomena…
In quantum metrology, one of the major applications of quantum technologies, the ultimate precision of estimating an unknown parameter is often stated in terms of the Cram\'er-Rao bound. Yet, the latter is no longer guaranteed to carry an…
A central challenge in quantum metrology is identifying optimal measurements that saturate the quantum Cramer-Rao bound under realistic constraints, e.g., local measurements. We show that symmetries of the probe state provide a general…
Bayesian experimental design is a technique that allows to efficiently select measurements to characterize a physical system by maximizing the expected information gain. Recent developments in deep neural networks and normalizing flows…
This is a tutorial aimed at illustrating some recent developments in quantum parameter estimation beyond the Cram\`er-Rao bound, as well as their applications in quantum metrology. Our starting point is the observation that there are…
We analyze the performance of a generalized Kitaev's phase estimation algorithm where N phase gates, acting on $M$ qubits prepared in a product state, may be distributed in an arbitrary way. Unlike the standard algorithm, where the mean…
This paper develops new insights into quantitative methods for the validation of computational model prediction. Four types of methods are investigated, namely classical and Bayesian hypothesis testing, a reliability-based method, and an…
Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…
Bayesian Model Calibration is used to revisit the problem of scaling factor calibration for semi-empirical correction of ab initio harmonic properties (e.g. vibrational frequencies and zero-point energies). A particular attention is devoted…
A major obstacle to attain the fundamental precision limit of the phase estimation in an interferometry is the identification and implementation of the optimal measurement. Here we demonstrate that this can be accomplished by the use of…
The Bayesian uncertainty quantification technique has become well established in turbulence modeling over the past few years. However, it is computationally expensive to construct a globally accurate surrogate model for Bayesian inference…
Layer potentials represent solutions to partial differential equations in an integral equation formulation. When numerically evaluating layer potentials at evaluation points close to the domain boundary, specialized quadrature techniques…
The estimation of parameters characterizing dynamical processes is central to science and technology. The estimation error changes with the number N of resources employed in the experiment (which could quantify, for instance, the number of…
We identify the critical deviation scale governing Bayesian evidence accumulation in regular parametric testing. Under integrated Bayes risk with zero-one loss, the risk-optimal rejection boundary lies in a moderate deviation regime, with a…