Related papers: Finding Hadamard matrices by a quantum annealing m…
Quantum annealing has shown promise for finding solutions to difficult optimization problems, including protein folding. Recently, we used the D-Wave Advantage quantum annealer to explore the folding problem in a coarse-grained lattice…
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…
Beam Placement (BP) is a well-known problem in Low-Earth Orbit (LEO) satellite communication (SatCom) systems, which can be modelled as an NP-hard clique cover problem. Recently, quantum computing has emerged as a novel technology which…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
The Fermi-Hubbard model is a plausible target to be solved by a quantum computer using the variational quantum eigensolver algorithm. However, problem sizes beyond the reach of classical exact diagonalisation are also beyond the reach of…
The Fermi-Hubbard model (FHM) on a two dimensional square lattice has long been an important testbed and target for simulating fermionic Hamiltonians on quantum hardware. We present an alternative for quantum simulation of FHMs based on an…
With the advent of quantum computers, researchers are exploring if quantum mechanics can be leveraged to solve important problems in ways that may provide advantages not possible with conventional or classical methods. A previous work by…
Efficient production planning is essential in modern manufacturing to improve performance indicators such as lead time and to reduce reliance on human intuition. While mathematical optimization approaches, formulated as job shop scheduling…
We consider the time and space required for quantum computers to solve a wide variety of problems involving matrices, many of which have only been analyzed classically in prior work. Our main results show that for a range of linear algebra…
We investigate the use of quantum computing algorithms on real quantum hardware to tackle the computationally intensive task of feature selection for light-weight medical image datasets. Feature selection is often formulated as a k of n…
In this paper we present a novel strategy to solve optimization problems within a hybrid quantum-classical scheme based on quantum annealing, with a particular focus on QUBO problems. The proposed algorithm is based on an iterative…
We present two new algebraic multilevel hierarchical matrix algorithms to perform fast matrix-vector product (MVP) for $N$-body problems in $d$ dimensions, namely efficient $\mathcal{H}^2_{*}$ (fully nested algorithm, i.e., $\mathcal{H}^2$…
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…
Quantum annealing solves combinatorial optimization problems by finding the energetic ground states of an embedded Hamiltonian. However, quantum annealing dynamics under the embedded Hamiltonian may violate the principles of adiabatic…
Quantum machine learning (QML) is a discipline that seeks to transfer the advantages of quantum computing to data-driven tasks. However, many studies rely on toy datasets or heavy feature reduction, raising concerns about their scalability.…
The Hamiltonian cycle problem (HCP), which is an NP-complete problem, consists of having a graph G with n nodes and m edges and finding the path that connects each node exactly once. In this paper we compare some algorithms to solve a…
Systems of linear equations are employed almost universally across a wide range of disciplines, from physics and engineering to biology, chemistry and statistics. Traditional solution methods such as Gaussian elimination become very time…
This is a presentation of recent work on quantum permutation groups, complex Hadamard matrices, and the connections between them. A long list of problems is included. We include as well some conjectural statements, about matrix models.
An important yet challenging problem in numerical linear algebra is finding a principal submatrix with maximum determinant from a given symmetric positive semidefinite matrix. This problem arises in experimental design, statistics, and…
We show how to visualize the process of diagonalizing the Hamiltonian matrix to find the energy eigenvalues and eigenvectors of a generic one-dimensional quantum system. Starting in the familiar sine-wave basis of an embedding infinite…