Related papers: Problems with using separated variables for comput…
We consider the problem of estimating the ensemble average of an observable on an ensemble of equally prepared identical quantum systems. We show that, among all kinds of measurements performed jointly on the copies, the optimal unbiased…
We study the average rank of elliptic curves $E_{A,B} : y^2 = x^3 + Ax + B$ over $\mathbb{Q}$, ordered by the height function $h(E_{A,B}) := \text{max}(|A|, |B|)$. Understanding this average rank requires estimating the number of…
The classification of big data usually requires a mapping onto new data clusters which can then be processed by machine learning algorithms by means of more efficient and feasible linear separators. Recently, Lloyd et al. have advanced the…
In this paper we introduce a measure of genuine quantum incompatibility in the estimation task of multiple parameters, that has a geometric character and is backed by a clear operational interpretation. This measure is then applied to some…
In this Letter, we strengthen and extend the connection between simulation and estimation to exploit simulation routines that do not exactly compute the probability of experimental data, known as the likelihood function. Rather, we provide…
It is well known that individual parameters of strongly correlated predictor variables in a linear model cannot be accurately estimated by the least squares regression due to multicollinearity generated by such variables. Surprisingly, an…
The purpose of this paper is to use semiclassical analysis to unify and generalize Lp estimates on high energy eigenfunctions and spectral clusters. In our approach these estimates do not depend on ellipticity and order, and apply to…
Motivated by applications to stochastic programming, we introduce and study the expected-integral functionals, which are mappings given in an integral form depending on two variables, the first a finite dimensional decision vector and the…
During the recent developments of quantum theory it has been clarified that the observable quantities (like energy or position) may be represented by operators (with real spectra) which are manifestly non-Hermitian. The mathematical…
An important application for near-term quantum computing lies in optimization tasks, with applications ranging from quantum chemistry and drug discovery to machine learning. In many settings --- most prominently in so-called parametrized or…
Causal inference with observational studies often relies on the assumptions of unconfoundedness and overlap of covariate distributions in different treatment groups. The overlap assumption is violated when some units have propensity scores…
A generic non-integrable (unitary) out-of-equilibrium quantum process, when interrogated across many times, is shown to yield the same statistics as an (non-unitary) equilibrated process. In particular, using the tools of quantum stochastic…
This paper focuses on the computational complexity of computing empirical plug-in estimates for causal effect queries. Given a causal graph and observational data, any identifiable causal query can be estimated from an expression over the…
A reduced-rank mixed effects model is developed for robust modeling of sparsely observed paired functional data. In this model, the curves for each functional variable are summarized using a few functional principal components, and the…
We compare classical and quantum query complexities of total Boolean functions. It is known that for worst-case complexity, the gap between quantum and classical can be at most polynomial. We show that for average-case complexity under the…
Parameterized quantum circuits have been extensively used as the basis for machine learning models in regression, classification, and generative tasks. For supervised learning, their expressivity has been thoroughly investigated and several…
Recently, a classical algorithm for estimating the normalized Betti number of an arbitrary simplicial complex was proposed. Motivated by a quantum algorithm with a similar Monte Carlo structure and improved sample complexity, we give a more…
Construction of explicit quantum circuits follows the notion of the "standard circuit model" introduced in the solid and profound analysis of elementary gates providing quantum computation. Nevertheless the model is not always optimal (e.g.…
Hidden-variable models aim to reproduce the results of quantum theory and to satisfy our classical intuition. Their refutation is usually based on deriving predictions that are different from those of quantum mechanics. Here instead we…
We consider the problem of predicting a real random variable from a functional explanatory variable. The problem is attacked by mean of nonparametric kernel approach which has been recently adapted to this functional context. We derive…