Related papers: Improved power-series method for confined one-dime…
We present a method of concatenated quantum error correction in which improved classical processing is used with existing quantum codes and fault-tolerant circuits to more reliably correct errors. Rather than correcting each level of a…
This article is concerned with the numerical solution of convex variational problems. More precisely, we develop an iterative minimisation technique which allows for the successive enrichment of an underlying discrete approximation space in…
The development of quantum computational techniques has advanced greatly in recent years, parallel to the advancements in techniques for deep reinforcement learning. This work explores the potential for quantum computing to facilitate…
This paper develops an enhanced finite element method for approximating a class of variational problems which exhibit the \textit{Lavrentiev gap phenomenon} in the sense that the minimum values of the energy functional have a nontrivial gap…
In this work, we focus on on the approach by noncommutative formal power series to study the combinatorial aspects of the renormalization at the singularities in $\{0,1,+\infty\}$ of the solutions of nonlinear differential equations…
In this paper, we consider a modified projected Gauss-Newton method for solving constrained nonlinear least-squares problems. We assume that the functional constraints are smooth and the the other constraints are represented by a simple…
In this work, the power series solutions are given around a regular-singular point, in the case of variable coefficients for homogeneous sequential linear conformable fractional differential equations of order 2{\alpha}.
Mindlins systematic procedure of power series expansion for deriving one and two dimensional equations of elastic beams and plates is extended to layered beams and plates with interface slips by adding a step function term to the power…
Currently, dynamics of a massive macroparticle is given by classical analytical mechanics (CM), while that of a massive micro one is given by quantum mechanics (QM). We propose a mechanics effective for both: We transform, under coordinate…
We describe an improved version of the quantum simulation method based on the implementation of a truncated Taylor series of the evolution operator. The idea is to add an extra step to the previously known algorithm which implements an…
We propose a new method to accelerate the convergence of optimization algorithms. This method simply adds a power coefficient $\gamma\in[0,1)$ to the gradient during optimization. We call this the Powerball method and analyze the…
We propose new algorithms for the computation of the first N terms of a vector (resp. a basis) of power series solutions of a linear system of differential equations at an ordinary point, using a number of arithmetic operations which is…
Quantum mechanics is well known to accelerate statistical sampling processes over classical techniques. In quantitative finance, statistical samplings arise broadly in many use cases. Here we focus on a particular one of such use cases,…
A unitary coupled-cluster (UCC) form for the wavefunction in the variational quantum eigensolver has been suggested as a systematic way to go beyond the mean-field approximation and include electron correlation in solving quantum chemistry…
In this paper a unifying energy-based approach is provided to the modeling and stability analysis of power systems coupled with market dynamics. We consider a standard model of the power network with a third-order model for the synchronous…
Variational quantum algorithms are a promising tool for solving partial differential equations. The standard approach for its numerical solution are finite difference schemes, which can be reduced to the linear algebra problem. We consider…
Standard variational methods tend to obtain upper bounds on the ground state energy of quantum many-body systems. Here we study a complementary method that determines lower bounds on the ground state energy in a systematic fashion, scales…
A variational technique is established to deal with the Schrodinger equation with parity-time(PT) symmetric Gaussian complex potential. The method is extended to the linear and self-focusing and defocusing nonlinear cases. Some unusual…
Quantum computing, leveraging principles of quantum mechanics, represents a transformative approach in computational methodologies, offering significant enhancements over traditional classical systems. This study tackles the complex and…
Force-based multiphysics coupling methods have become popular since they provide a simple and efficient coupling mechanism, avoiding the difficulties in formulating and implementing a consistent coupling energy. They are also the only known…