Related papers: Asymptotically optimal quantization schemes for Ga…
Bayesian quantum estimation provides a robust framework for quantum technologies, especially in scenarios with limited data and minimal prior information. Yet, its application to continuous-variable Gaussian systems has remained limited and…
A new technique towards finding asymptotic normalization coefficients in the complex-ranged Gaussian basis is presented. It is shown that a diagonalisation procedure for the total Hamiltonian matrix in the given basis results in…
We investigate optimal subsampling for quantile regression. We derive the asymptotic distribution of a general subsampling estimator and then derive two versions of optimal subsampling probabilities. One version minimizes the trace of the…
We compute the exact asymptotics for the cumulants of linear statistics associated with the zeros counting measure of a large class of real Gaussian processes. Precisely, we show that if the underlying covariance function is regular and…
The construction of synthetic complex-valued signals from real-valued observations is an important step in many time series analysis techniques. The most widely used approach is based on the Hilbert transform, which maps the real-valued…
Although complete randomization ensures covariate balance on average, the chance for observing significant differences between treatment and control covariate distributions increases with many covariates. Rerandomization discards…
We derive the path-integral representation of the fractional Ornstein-Uhlenbeck process driven by Riemann-Liouville fractional Gaussian noise, for both the subdiffusive and superdiffusive regimes. We express the corresponding action, which…
In networked control systems, often the sensory signals are quantized before being transmitted to the controller. Consequently, performance is affected by the coarseness of this quantization process. Modern communication technologies allow…
This paper proposes feasible asymptotically efficient estimators for a certain class of Gaussian noises with self-similar and stationary properties, which includes the fractional Gaussian noise, under high frequency observations. In this…
The problem of finding the large order asymptotics for the eigenfunction perturbation theory in quantum mechanics is studied. The relation between the wave function argument x and the number of perturbation theory order k that allows us to…
Variational quantum algorithms involve training parameterized quantum circuits using a classical co-processor. An important variational algorithm, designed for combinatorial optimization, is the quantum approximate optimization algorithm.…
We consider the problem of minimizing a continuous function given quantum access to a stochastic gradient oracle. We provide two new methods for the special case of minimizing a Lipschitz convex function. Each method obtains a dimension…
Motivated by practical applications, I present a novel and comprehensive framework for operator-valued positive definite kernels. This framework is applied to both operator theory and stochastic processes. The first application focuses on…
We consider the estimation of quadratic functionals in a Gaussian sequence model where the eigenvalues are supposed to be unknown and accessible through noisy observations only. Imposing smoothness assumptions both on the signal and the…
We propose to quantify the complexity of non-equilibrium steady state density operators, as well as of long-lived Liouvillian decay modes, in terms of level spacing distribution of their spectra. Based on extensive numerical studies in a…
An exact invariant operator of time-dependent coupled oscillators is derived using the Liouville-von Neumann equation. The unitary relation between this invariant and the invariant of two uncoupled simple harmonic oscillators is…
This paper establishes optimal convergence rates for estimation of structured covariance operators of Gaussian processes. We study banded operators with kernels that decay rapidly off-the-diagonal and $L^q$-sparse operators with an…
Quantization is essential for reducing the computational cost and memory usage of deep neural networks, enabling efficient inference on low-precision hardware. Despite the growing adoption of uniform and floating-point quantization schemes,…
We consider an unknown multivariate function representing a system-such as a complex numerical simulator-taking both deterministic and uncertain inputs. Our objective is to estimate the set of deterministic inputs leading to outputs whose…
We present optimal schemes, based on photon number measurements, for Gaussian state tomography and for Gaussian process tomography. An $n$-mode Gaussian state is completely specified by $2 n^2+3n$ parameters. Our scheme requires exactly $2…