Related papers: Nonlinear quantum input-output analysis using Volt…
Volterra series representation is a powerful mathematical model for nonlinear circuits. However, the difficulties in determining higher-order Volterra kernels limited its broader applications. In this work, a systematic approach that…
A new concept, called quasi-linear transfer functions (QLTF), which can be used to characterize the output frequency behaviour of nonlinear systems, is introduced based on the well-known Volterra series representation. By using the new…
Volterra analysis and its variants have long been prominent among methods for modeling multi-input non-linear systems. The product of Volterra analysis, the Volterra kernels, are particularly suited to quantifying intra- and inter-input…
Quantum input-output response analysis is a useful method for modeling the dynamics of complex quantum networks, such as those for communication or quantum control via cascade connections. Non-Markovian effects have not yet been studied in…
While quantum computers are naturally well-suited to implementing linear operations, it is less clear how to implement nonlinear operations on quantum computers. However, nonlinear subroutines may prove key to a range of applications of…
Explicit expressions are presented that describe the input-output behaviour of a nonlinear system in both the frequency and the time domain. The expressions are based on a set of coefficients that do not depend on the input to the system…
This paper introduces a method for the nonparametric Bayesian learning of nonlinear operators, through the use of the Volterra series with kernels represented using Gaussian processes (GPs), which we term the nonparametric Volterra kernels…
The paper presents a review of the studies that were conducted at Energy Systems Institute (ESI) SB RAS in the field of mathematical modeling of nonlinear input-output dynamic systems with Volterra polynomials. The first part presents an…
Incorporating nonlinearity into quantum machine learning is essential for learning a complicated input-output mapping. We here propose quantum algorithms for nonlinear regression, where nonlinearity is introduced with feature maps when…
Quantum computing holds great promise to accelerate scientific computations in fluid dynamics and other classical physical systems. While various quantum algorithms have been proposed for linear flows, developing quantum algorithms for…
We introduce Coarse-Grained Nonlinear Dynamics, an efficient and universal parameterization of nonlinear system dynamics based on the Volterra series expansion. These models require a number of parameters only quasilinear in the system's…
In this paper we show how nonlinear internal models can be effectively used in the design of output regulators for nonlinear systems. This result provides a significant enhancement of the non-equilibrium theory for output regulation, which…
The promising performance increase offered by quantum computing has led to the idea of applying it to neural networks. Studies in this regard can be divided into two main categories: simulating quantum neural networks with the standard…
The paper introduces a non-linear version of the process convolution formalism for building covariance functions for multi-output Gaussian processes. The non-linearity is introduced via Volterra series, one series per each output. We…
Recurrent neural networks (RNNs) are brain-inspired models widely used in machine learning for analyzing sequential data. The present work is a contribution towards a deeper understanding of how RNNs process input signals using the response…
Input-output theory is a well-known tool in quantum optics and ubiquitous in the description of quantum systems probed by light. Owing to the generality of the setup it describes, the theory finds application in a wide variety of…
As quantum machine-learning architectures mature, a central challenge is no longer their construction, but identifying the regimes in which they offer practical advantages over classical approaches. In this work, we introduce a framework…
The power and expressivity of deep classical neural networks can be attributed to non-linear input-output relations. Such non-linearities are at the heart of many computational tasks, such as data classification and pattern recognition.…
This paper presents detailed insights of embedding Carleman linearization into nonlinear systems for designing Volterra model-based control technique. Volterra series method is a competent mathematical tool, which extends the convolution…
This paper presents a novel framework for high-dimensional nonlinear quantum computation that exploits tensor products of amplified vector and matrix encodings to efficiently evaluate multivariate polynomials. The approach enables the…