Related papers: Asymptotically optimal quantization schemes for Ga…
Asymptotic solutions to the quantized Knizhnik-Zamolodchikov equation associated with $\frak{gl}_{N+1}$ are constructed. The leading term of an asymptotic solution is the Bethe vector -- an eigenvector of the transfer-matrix of a quantum…
We present a new quantum algorithm for estimating the mean of a real-valued random variable obtained as the output of a quantum computation. Our estimator achieves a nearly-optimal quadratic speedup over the number of classical i.i.d.…
For a large class of variational quantum circuits, we show how arbitrary-order derivatives can be analytically evaluated in terms of simple parameter-shift rules, i.e., by running the same circuit with different shifts of the parameters. As…
Quantization is a fundamental optimization for many machine-learning use cases, including compressing gradients, model weights and activations, and datasets. The most accurate form of quantization is \emph{adaptive}, where the error is…
Optimized, necessary and sufficient conditions for the identification of the Schmidt number will be derived in terms of general Hermitian operators. These conditions apply to arbitrary mixed quantum states. The optimization procedure…
We consider the problem of estimating a smooth functional of an unknown signal with discontinuity from Gaussian observations. The signal is a known function that depends on an unknown parameter. This problem is closely related to the famous…
Gaussian process regression is used throughout statistics and machine learning for prediction and uncertainty quantification. A Gaussian process is specified by its mean and covariance functions. Many covariance functions, including…
We analyze a stochastic approximation algorithm for decision-dependent problems, wherein the data distribution used by the algorithm evolves along the iterate sequence. The primary examples of such problems appear in performative prediction…
Quantum computing may speed up numerical problems involving large matrices that are demanding for classical computers, and active research on this possibility is ongoing. In this work, we propose quantum algorithms for the exact simulation…
Complex-valued signals are used in the modeling of many systems in engineering and science, hence being of fundamental interest. Often, random complex-valued signals are considered to be proper. A proper complex random variable or process…
This article provides an introduction to the asymptotic analysis of covariance parameter estimation for Gaussian processes. Maximum likelihood estimation is considered. The aim of this introduction is to be accessible to a wide audience and…
Quantum process characterization is a fundamental task in quantum information processing, yet conventional methods, such as quantum process tomography, require prohibitive resources and lack scalability. Here, we introduce an efficient…
Quantum Variational Circuits (QVCs) are often claimed as one of the most potent uses of both near term and long term quantum hardware. The standard approaches to optimizing these circuits rely on a classical system to compute the new…
This paper considers the problem of reconstructing missing parts of functions based on their observed segments. It provides, for Gaussian processes and arbitrary bijective transformations thereof, theoretical expressions for the…
Starting from a characterization of holomorphic functions in terms of a suitable mean value property, we build some nonlinear asymptotic characterizations for complex-valued solutions of certain nonlinear systems, which have to do with the…
Optimization of quadratic functions and the quotient of those are relevant in subspace and iterative optimization methods. In this paper, the calculation of the generalized operator norm and extremal generalized Rayleigh quotient is…
The estimation of signal parameters using quantized data is a recurrent problem in electrical engineering. As an example, this includes the estimation of a noisy constant value and of the parameters of a sinewave, that is, its amplitude,…
This paper investigates the performance of the Generalized Covariance estimator (GCov) in estimating and identifying mixed causal and noncausal models. The GCov estimator is a semi-parametric method that minimizes an objective function…
In this paper, we consider asymptotics of the optimal value and the optimal solutions of parametric minimax estimation problems. Specifically, we consider estimators of the optimal value and the optimal solutions in a sample minimax problem…
We describe a self-consistent canonical quantization of Liouville theory in terms of canonical free fields. In order to keep the non-linear Liouville dynamics, we use the solution of the Liouville equation as a canonical transformation.…