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We propose a distinct approach to solving linear and nonlinear differential equations (DEs) on quantum computers by encoding the problem into ground states of effective Hamiltonian operators. Our algorithm relies on constructing such…
We present a quantum algorithm to solve systems of linear equations of the form $A\mathbf{x}=\mathbf{b}$, where $A$ is a tridiagonal Toeplitz matrix and $\mathbf{b}$ results from discretizing an analytic function, with a circuit complexity…
In this work, we present scalable balancing domain decomposition by constraints methods for linear systems arising from arbitrary order edge finite element discretizations of multi-material and heterogeneous 3D problems. In order to enforce…
We present a novel variational quantum framework for nonlinear partial differential equation (PDE) constrained optimization problems. The proposed work extends the recently introduced bi-level variational quantum PDE constrained…
Quantum computing presents a promising avenue for solving complex problems, particularly in quantum chemistry, where it could accelerate the computation of molecular properties and excited states. This work focuses on hybrid…
This paper explores the use of quantum computing, specifically the use of HHL and VQLS algorithms, to solve optimal power flow problem in electrical grids. We investigate the effectiveness of these quantum algorithms in comparison to…
Classical-quantum hybrid algorithms have recently garnered significant attention, which are characterized by combining quantum and classical computing protocols to obtain readout from quantum circuits of interest. Recent progress due to…
Recent studies on quantum computing algorithms focus on excavating features of quantum computers which have potential for contributing to computational model enhancements. Among various approaches, quantum annealing methods effectively…
Solving a quadratic nonlinear system of equations (QNSE) is a fundamental, but important, task in nonlinear science. We propose an efficient quantum algorithm for solving $n$-dimensional QNSE. Our algorithm embeds QNSE into a…
Variational quantum algorithms are a promising tool for solving partial differential equations. The standard approach for its numerical solution are finite difference schemes, which can be reduced to the linear algebra problem. We consider…
Despite extensive research efforts, few quantum algorithms for classical optimization demonstrate realizable quantum advantage. The utility of many quantum algorithms is limited by high requisite circuit depth and nonconvex optimization…
Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…
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…
This paper presents an iterative method suitable for inverting semilinear problems which are important kernels in many numerical applications. The primary idea is to employ a parametrization that is able to reduce semilinear problems into…
Partial differential equation solvers are required to solve the Navier-Stokes equations for fluid flow. Recently, algorithms have been proposed to simulate fluid dynamics on quantum computers. Fault-tolerant quantum devices might enable…
Variational quantum algorithms have emerged as a powerful tool for harnessing the potential of near-term quantum devices to address complex challenges across quantum science and technology. Yet, the robust and scalable quantification of…
Decomposing unitary operations into native gates is an essential step for implementing quantum algorithms. For qubit-based devices, where native gates are typically single- and two-qubit operations, a range of decomposition techniques have…
The variational quantum eigensolver (VQE), a type of variational quantum algorithm, is a hybrid quantum-classical algorithm to find the lowest-energy eigenstate of a particular Hamiltonian. We investigate ways to optimize the VQE solving…
A variational quantum algorithm for numerically solving partial differential equations (PDEs) on a quantum computer was proposed by Lubasch et al. In this paper, we generalize the method introduced by Lubasch et al. to cover a broader class…
Recently, it is shown that quantum computers can be used for obtaining certain information about the solution of a linear system Ax=b exponentially faster than what is possible with classical computation. Here we first review some key…