Related papers: Variational quantum algorithm for solving Helmholt…
Recently J. M. Arrazola et al. [Phys. Rev. A 100, 032306 (2019)] proposed a quantum algorithm for solving nonhomogeneous linear partial differential equations of the form $A\psi(\textbf{r})=f(\textbf{r})$. Its nonhomogeneous solution is…
We present an efficient procedure for computing resonances and resonant modes of Helmholtz problems posed in exterior domains. The problem is formulated as a nonlinear eigenvalue problem (NEP), where the nonlinearity arises from the use of…
Quantum computers promise to revolutionize our ability to simulate molecules, and cloud-based hardware is becoming increasingly accessible to a wide body of researchers. Algorithms such as Quantum Phase Estimation and the Variational…
We develop a sparse hierarchical $hp$-finite element method ($hp$-FEM) for the Helmholtz equation with variable coefficients posed on a two-dimensional disk or annulus. The mesh is an inner disk cell (omitted if on an annulus domain) and…
Differential equations are ubiquitous in models of physical phenomena. Applications like steady-state analysis of heat flow and deflection in elastic bars often admit to a second order differential equation. In this paper, we discuss the…
A rapid algorithm is derived for the Helmholtz--Hodge decomposition on the surface of the sphere in spherical coordinates. The algorithm uncouples modes of spherical harmonics with different absolute order, writes the conversion as…
We introduce a new efficient algorithm for Helmholtz problems in perforated domains with the design of the scheme allowing for possibly large wavenumbers. Our method is based upon the Wavelet-based Edge Multiscale Finite Element Method…
Block encoding is a successful technique used in several powerful quantum algorithms. In this work we provide an explicit quantum circuit for block encoding a sparse matrix with a periodic diagonal structure. The proposed methodology is…
Quantum variational circuits have gained significant attention due to their applications in the quantum approximate optimization algorithm and quantum machine learning research. This work introduces a novel class of classical probabilistic…
In this paper we extend analysis of the WaveHoltz iteration -- a time-domain iterative method for the solution of the Helmholtz equation. We expand the previous analysis of energy conserving problems and prove convergence of the WaveHoltz…
A broad class of hybrid quantum-classical algorithms known as "variational algorithms" have been proposed in the context of quantum simulation, machine learning, and combinatorial optimization as a means of potentially achieving a quantum…
We solve the one-dimensional Helmholtz equation in several scenarios using the quantum annealer provided by the D-Wave systems within a pseudospectral scheme, where its solution is encoded into certain set of suitable basis functions. We…
Quantum algorithms are typically understood in terms of the evolution of a multi-qubit quantum system under a prescribed sequence of unitary transformations. The input to the algorithm prescribes some of the unitary transformations in the…
Quantum computers promise a great computational advantage over classical computers, yet currently available quantum devices have only a limited amount of qubits and a high level of noise, limiting the size of problems that can be solved…
We propose quantum algorithms, purely quantum in nature, for calculating the determinant and inverse of an $(N-1)\times (N-1)$ matrix (depth is $O(N^2\log N)$) which is a simple modification of the algorithm for calculating the determinant…
Although quantum computing holds promise for solving Combinatorial Optimization Problems (COPs), the limited qubit capacity of NISQ hardware makes large-scale instances intractable. Conventional methods attempt to bridge this gap through…
Implementing variational quantum algorithms with noisy intermediate-scale quantum machines of up to a hundred qubits is nowadays considered as one of the most promising routes towards achieving a quantum practical advantage. In multiqubit…
The data input model is a fundamental component of every quantum algorithm, as its efficiency is crucial for achieving potential speed-ups over classical methods. For quantum linear algebra tasks that utilize quantum eigenvalue or singular…
The Helmholtz equation is notoriously difficult to solve with standard numerical methods, increasingly so, in fact, at higher frequencies. Controllability methods instead transform the problem back to the time-domain, where they seek the…
The finite element method can be viewed as a machine that automates the discretization of differential equations, taking as input a variational problem, a finite element and a mesh, and producing as output a system of discrete equations.…