Related papers: Variational quantum algorithm for solving Helmholt…
We design a variational quantum algorithm to solve multi-dimensional Poisson equations with mixed boundary conditions that are typically required in various fields of computational science. Employing an objective function that is formulated…
Quantum variational optimization has been posed as an alternative to solve optimization problems faster and at a larger scale than what classical methods allow. In this paper we study systematically the role of entanglement, the structure…
Quantum optimization algorithms hold the promise of solving classically hard, discrete optimization problems in practice. The requirement of encoding such problems in a Hamiltonian realized with a finite -- and currently small -- number of…
This paper presents a quantum algorithm for the solution of prototypical second-order linear elliptic partial differential equations discretized by $d$-linear finite elements on Cartesian grids of a bounded $d$-dimensional domain. An…
A novel class of hybrid quantum-classical algorithms based on the variational approach have recently emerged from separate proposals addressing, for example, quantum chemistry and combinatorial problems. These algorithms provide an…
Universal fault-tolerant quantum computers will require error-free execution of long sequences of quantum gate operations, which is expected to involve millions of physical qubits. Before the full power of such machines will be available,…
In this work, we develop a fully implicit Hybrid High-Order algorithm for the Cahn-Hilliard problem in mixed form. The space discretization hinges on local reconstruction operators from hybrid polynomial unknowns at elements and faces. The…
The modeling of electric machines and power transformers typically involves systems of nonlinear magnetostatics or -quasistatics, and their efficient and accurate simulation is required for the reliable design, control, and optimization of…
The Helmholtz equation arises in the study of electromagnetic radiation, optics, acoustics, etc. In spherical coordinates, its general solution can be written as a spherical harmonic series which satisfies the radiation condition at…
Quantum query complexity plays an important role in studying quantum algorithms, which captures the most known quantum algorithms, such as search and period finding. A query algorithm applies $U_tO_x\cdots U_1O_xU_0$ to some input state,…
The simulation of quantum dynamics calls for quantum algorithms working in first quantized grid encodings. Here, we propose a variational quantum algorithm for performing quantum dynamics in first quantization. In addition to the usual…
This paper presents the design and analysis of a Hybrid High-Order (HHO) approximation for a distributed optimal control problem governed by the Poisson equation. We propose three distinct schemes to address unconstrained control problems…
Many standard linear algebra problems can be solved on a quantum computer by using recently developed quantum linear algebra algorithms that make use of block encodings and quantum eigenvalue/singular value transformations. A block encoding…
This work studies the variational quantum eigensolver algorithm, designed to determine the ground state of a quantum mechanical system by combining classical and quantum hardware. Methods of reducing the number of required qubit…
Recently developed quantum algorithms address computational challenges in numerical analysis by performing linear algebra in Hilbert space. Such algorithms can produce a quantum state proportional to the solution of a $d$-dimensional system…
The high-frequency Helmholtz equation on the entire space is truncated into a bounded domain using the perfectly matched layer (PML) technique and subsequently, discretized by the higher-order finite element method (FEM) and the continuous…
A semidefinite program (SDP) is a particular kind of convex optimization problem with applications in operations research, combinatorial optimization, quantum information science, and beyond. In this work, we propose variational quantum…
Identifying computational tasks suitable for (future) quantum computers is an active field of research. Here we explore utilizing quantum computers for the purpose of solving differential equations. We consider two approaches: (i) basis…
We propose a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…
We propose a variational scheme to represent composite quantum systems using multiple parameterized functions of varying accuracies on both classical and quantum hardware. The approach follows the variational principle over the entire…