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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…
In this work we investigate the capabilities of a hybrid quantum-classical procedure to explore the solution space using the D-Wave $2000Q^{TM}$ Quantum Annealer device. Here we study the ability of the Quantum hardware to solve the Number…
We present a systematic pathway for solving differential equations within the quantum linear systems framework by combining block encoding with Quantum Singular Value Transformation (QSVT). The approach is demonstrated on a complex…
Discretizing Helmholtz problems via finite elements yields linear systems whose efficient solution remains a major challenge for classical computation. In this paper, we investigate how variational quantum algorithms could address this…
We introduce a novel approach to solving dynamic programming problems, such as those in many economic models, on a quantum annealer, a specialized device that performs combinatorial optimization. Quantum annealers attempt to solve an…
From fundamental sciences to economics and industry, discrete optimization problems are ubiquitous. Yet, their complexity often renders exact solutions intractable, necessitating the use of approximate methods. Heuristics inspired by…
Quantum annealing is a promising algorithm for solving combinatorial optimization problems. It searches for the ground state of the Ising model, which corresponds to the optimal solution of a given combinatorial optimization problem. The…
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…
With the advent of novel quantum computing technologies, and the knowledge that such technology might be used to fundamentally change computing applications, a prime opportunity has presented itself to investigate the practical application…
The quest for real-time dynamic optimization solutions in the process industry represents a formidable computational challenge, particularly within the realm of applications like model-predictive control, where rapid and reliable…
Quantum annealers manufactured by D-Wave Systems, Inc., are computational devices capable of finding high-quality solutions of NP-hard problems. In this contribution, we explore the potential and effectiveness of such quantum annealers for…
Quantum annealing is a generic solver for optimization problems that uses fictitious quantum fluctuation. The most groundbreaking progress in the research field of quantum annealing is its hardware implementation, i.e., the so-called…
Quantum annealers can be used to solve many (possibly NP-hard) combinatorial optimization problems, by formulating them as quadratic unconstrained binary optimization (QUBO) problems or, equivalently, using the Ising formulation. In this…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
We perform an in-depth comparison of quantum annealing with several classical optimisation techniques, namely thermal annealing, Nelder-Mead, and gradient descent. We begin with a direct study of the 2D Ising model on a quantum annealer,…
Quantum computation is a promising emerging technology, and by utilizing the principles of quantum mechanics, it is expected to achieve faster computations than classical computers for specific problems. There are two distinct architectures…
We present an algorithm to compute the number of solutions of the (constrained) number partitioning problem. A concrete implementation of the algorithm on an Ising-type quantum computer is given.
A particle-in-a-box model of continuous space quantum annealing is proposed and studied numerically by solving the Schr\"odinger wave equation directly. Three types of energy landscapes with multiple local minima are considered, namely a…
Ising machines are hardware solvers which aim to find the absolute or approximate ground states of the Ising model. The Ising model is of fundamental computational interest because it is possible to formulate any problem in the complexity…
Computer-aided engineering techniques are indispensable in modern engineering developments. In particular, partial differential equations are commonly used to simulate the dynamics of physical phenomena, but very large systems are often…