Related papers: Solving oscillations problems through affine quant…
Quantum annealing is a method developed to solve combinatorial optimization problems by utilizing quantum bits. Solving such problems corresponds to minimizing a cost function defined over binary variables. However, in many practical cases,…
Semiclassical quantization is exact only for the so called \emph{solvable} potentials, such as the harmonic oscillator. In the \emph{nonsolvable} case the semiclassical phase, given by a series in $\hbar$, yields more or less approximate…
Multi-frequency, highly-oscillatory Hamiltonian problems derive from the mathematical modelling of many real life applications. We here propose a variant of Hamiltonian Boundary Value Methods (HBVMs), which is able to efficiently deal with…
In this paper, we study the affine phase retrieval problem, which aims to recover signals from the magnitudes of affine measurements. We develop second-order optimization methods based on Newton and Gauss-Newton iterations and establish…
Quantum annealing (QA) has the potential to significantly improve solution quality and reduce time complexity in solving combinatorial optimization problems compared to classical optimization methods. However, due to the limited number of…
Applications such as simulating complicated quantum systems or solving large-scale linear algebra problems are very challenging for classical computers due to the extremely high computational cost. Quantum computers promise a solution,…
We present a methodology for numerically integrating ordinary differential equations containing rapidly oscillatory terms. This challenge is distinct from that for differential equations which have rapidly oscillatory solutions: here the…
Solving continuous variable optimization problems by factorization machine quantum annealing (FMQA) demonstrates the potential of Ising machines to be extended as a solver for integer and real optimization problems. However, the details of…
We present a collection of well-conditioned integral equation methods for the solution of electrostatic, acoustic or electromagnetic scattering problems involving anisotropic, inhomogeneous media. In the electromagnetic case, our approach…
We consider many-body problems in classical mechanics where a wide range of time scales limits what can be computed. We apply the method of optimal prediction to obtain equations which are easier to solve numerically. We demonstrate by…
I investigate a new idea of perturbation theory in covariant canonical quantization. I present preliminary results for a toy model of a harmonic oscillator with a quartic perturbation, and show that this method reproduces the quantized…
Traditional quantum field theory can lead to enormous zero-point energy, which markedly disagrees with experiment. Unfortunately, this situation is built into conventional canonical quantization procedures. For identical classical theories,…
The use of entangled light to illuminate objects is shown to provide significant enhancements over unentangled light for detecting and imaging those objects in the presence of high levels of noise and loss. Each signal sent out is entangled…
This paper introduces a robust and scalable framework for implementing nested affine transformations in quantum circuits. Utilizing Hadamard-supported conditional initialization and block encoding, the proposed method systematically applies…
Using stochastic quantization method we derive equations for correlators of quantum fluctuations around the classical solution in the massless phi^4 theory. The obtained equations are then solved in the lowest orders of perturbation theory,…
We approximate an elliptic problem with oscillatory coefficients using a problem of the same type, but with constant coefficients. We deliberately take an engineering perspective, where the information on the oscillatory coefficients in the…
Other than scattering problems where perturbation theory is applicable, there are basically two ways to solve problems in physics. One is to reduce the problem to harmonic oscillators, and the other is to formulate the problem in terms of…
This paper considers a version of the Wiener filtering problem for equalization of passive quantum linear quantum systems. We demonstrate that taking into consideration the quantum nature of the signals involved leads to features typically…
Problems concerning with application of quantum rules on classical phenomena have been widely studied, for which lifted up the idea about quantization and uncertainty principle. Energy quantization on classical example of simple harmonic…
Representation of the quantum measurement with the help of non-orthogonal decomposition of unit is presented in the paper for the first time. Methods for solution of the quantum detection and measurement problems based on the suggested…