Related papers: Classical and Quantum Ensembles via Multiresolutio…
The structure of covariant instruments is studied and a general structure theorem is derived. A detailed characterization is given to covariant instruments in the case of an irreducible representation of a locally compact group.
We construct a general quantization procedure for square integrable functions on well-behaved connected exponential Lie groups. The Lie groups in question should admit at least one co-adjoint orbit of maximal possible dimension. The…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider variational wavelet approach for loops,…
A successful approach to understand field theories is to resolve the physics into different length or energy scales using the renormalization group framework. We propose a quantum simulation of quantum field theory which encodes field…
A simple method has been introduced to furnish the equilibrium solution of the Wigner equation for all order of the quantum correction. This process builds up a recursion relation involving the coefficients of the different power of the…
A variational framework for structural topology optimization is developed, integrating quantum and classical latent encoding strategies within a coordinate-based neural decoding architecture. In this approach, a low-dimensional latent…
Quantum machine learning witnesses an increasing amount of quantum algorithms for data-driven decision making, a problem with potential applications ranging from automated image recognition to medical diagnosis. Many of those algorithms are…
We show convexity of solutions to a class of convex variational problems in the Gauss and in the Wiener space. An important tool in the proof is a representation formula for integral functionals in this infinite dimensional setting, that…
Variational quantum eigensolver (VQE), which combines quantum systems with classical computational power, has been arisen as a promising candidate for near-term quantum computing applications. However, the experimental resources such as the…
We consider the problem of estimating the density of observations taking values in classical or nonclassical spaces such as manifolds and more general metric spaces. Our setting is quite general but also sufficiently rich in allowing the…
We construct a non-perturbative approach based on quantum averaging combined with resonant transformations to detect the resonances of a given Hamiltonian and to treat them. This approach, that generalizes the rotating-wave approximation,…
Wavelet Transforms are a widely used technique for decomposing a signal into coefficient vectors that correspond to distinct frequency/scale bands while retaining time localization. This property enables an adaptive analysis of signals at…
We review the Weyl-Wigner formulation of quantum mechanics in phase space. We discuss the concept of Narcowich-Wigner spectrum and use it to state necessary and sufficient conditions for a phase space function to be a Wigner distribution.…
A consistent description of interactions between classical and quantum systems is relevant to quantum measurement theory, and to calculations in quantum chemistry and quantum gravity. A solution is offered here to this longstanding problem,…
In this paper, we address the challenge of multivariate time-series forecasting using quantum machine learning techniques. We introduce adaptation strategies that extend variational quantum circuit models, traditionally limited to…
The representation of discrete, compact wavelet transformations (WTs) as circuits of local unitary gates is discussed. We employ a similar formalism as used in the multi-scale representation of quantum many-body wavefunctions using unitary…
Capturing solution near the singular point of any nonlinear SBVPs is challenging because coefficients involved in the differential equation blow up near singularities. In this article, we aim to construct a general method based on…
This Ph.D. thesis provides a comprehensive review of the state-of-the-art in the field of Variational Quantum Algorithms and Quantum Machine Learning, including numerous original contributions. The first chapters are devoted to a brief…
The use of orthonormal wavelet basis functions for solving singular integral scattering equations is investigated. It is shown that these basis functions lead to sparse matrix equations which can be solved by iterative techniques. The…
We provide an alternative approach to the decoherence-by-environment paradigm in the field of the quantum measurement process and the appearance of a classical world. In contrast to the decoherence approach we argue that the transition from…