Related papers: Efficient Variational Quantum Linear Solver for St…
Variational quantum eigensolver (VQE) is demonstrated to be the promising methodology for quantum chemistry based on near-term quantum devices. However, many problems are yet to be investigated for this methodology, such as the influences…
In this paper, we aim to introduce a new perspective when comparing highly parallelized algorithms on GPU: the energy consumption of the GPU. We give an analysis of the performance of linear algebra operations, including addition of…
We propose a cost-efficient measurement scheme of the variational quantum eigensolver (VQE) for atomistic simulations of electronic structures based on a tight-binding (TB) theory. Leveraging the lattice geometry of a material domain, the…
We present a method to split quantum circuits of variational quantum algorithms (VQAs) to allow for parallel training and execution, that maximally exploits the limited number of qubits in hardware to solve large problem instances. We apply…
Some important applicative problems require the evaluation of functions $\Psi$ of large and sparse and/or \emph{localized} matrices $A$. Popular and interesting techniques for computing $\Psi(A)$ and $\Psi(A)\mathbf{v}$, where $\mathbf{v}$…
L-QLES is an open source python code for generating 1D, 2D and 3D Laplacian operators and associated Poisson equations and their classical solutions. Its goal is to provide quantum algorithm developers with a flexible test case framework…
Pole Expansion and Selected Inversion (PEXSI) is an efficient scheme for evaluating selected entries of functions of large sparse matrices as required e.g. in electronic structure algorithms. We show that the triangular factorizations…
In recent years, the fervent demand for computational power across various domains has prompted hardware manufacturers to introduce specialized computing hardware aimed at enhancing computational capabilities. Particularly, the utilization…
Pauli Correlation Encoding (PCE) is as a qubit-efficient variational approach to combinatorial optimization problems. The method offers a polynomial reduction in qubit count and a super-polynomial suppression of barren plateaus. Here, we…
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…
Quantum annealing is a promising approach for solving combinatorial optimization problems. However, its performance is often limited by the overhead of additional qubits required for embedding logical QUBO models onto quantum annealers.…
For the solution of time-dependent nonlinear differential equations, we present variational quantum algorithms (VQAs) that encode both space and time in qubit registers. The spacetime encoding enables us to obtain the entire time evolution…
In this paper we investigate the linear and nonlinear models of optical quantum computation and discuss their scalability and efficiency. We show how there are significantly different scaling properties in single photon computation when…
We provide novel linear combination of unitaries decompositions for a class of discrete elliptic differential operators. Specifically, Poisson problems augmented with periodic, Dirichlet, Neumann, Robin, and mixed boundary conditions are…
Variational quantum algorithms (VQAs), as one of the most promising routes in the noisy intermediate-scale quantum (NISQ) era, offer various potential applications while also confront severe challenges due to near-term quantum hardware…
Circulant matrices are an important family of operators, which have a wide range of applications in science and engineering related fields. They are in general non-sparse and non-unitary. In this paper, we present efficient quantum circuits…
The equivalent split-circuit formulation is a novel approach that has recently been applied to a range of power system related problems. As a result, a linear and a nonlinear method for power system state estimation with simultaneous…
The linearity inherent in quantum mechanics limits current quantum hardware from directly solving nonlinear systems governed by nonlinear differential equations. One can opt for linearization frameworks such as Carleman linearization, which…
Key properties of physical systems can be described by the eigenvalues of matrices that represent the system. Computational algorithms that determine the eigenvalues of these matrices exist, but they generally suffer from a loss of…
Lattice systems and discrete networks with dissipative interactions are successfully employed as meso-scale models of heterogeneous solids. As the application scale generally is much larger than that of the discrete links, physically…