FEqa: Finite Element Computations on Quantum Annealers
arXiv:2201.09743 · doi:10.1016/j.cma.2022.115014
Abstract
The solution of physical problems discretized using the finite element methods using quantum computers remains relatively unexplored. Here, we present a unified formulation (FEqa) to solve such problems using quantum annealers. FEqa is a hybrid technique in which the finite element problem is formulated on a classical computer, and the residual is minimized using a quantum annealer. The advantages of FEqa include utilizing a single qubit per degree of freedom, enforcing Dirichlet boundary conditions a priori, reaching arbitrary solution precision, and eliminating the possibility of the annealer generating invalid results. FEqa is scalable on the classical portion of the algorithm due to its Single Program Multiple Data (SPMD) nature and does not rely on ground state solutions from the annealer. The exponentially large number of collocation points used in quantum annealing are investigated for their cosine measures, and new iterative techniques are developed to exploit their properties. The quantum annealer has clear advantages in computational time over simulated annealing, for the example problems presented in this paper solved on the D-Wave machine. The presented work provides a pathway to solving physical problems using quantum annealers.
arXiv comment32 pages, 20 figures
References in corpus (22)
- Quantum Computing in the NISQ era and beyond
- Quantum algorithm for solving linear systems of equations
- Theory of Quantum Annealing of an Ising Spin Glass
- Quantum algorithm for systems of linear equations with exponentially improved dependence on precision
- Quantum Annealing: A New Method for Minimizing Multidimensional Functions
- Qudits and high-dimensional quantum computing
- High-order quantum algorithm for solving linear differential equations
- Efficient quantum algorithm for dissipative nonlinear differential equations
- Quantum algorithm for linear differential equations with exponentially improved dependence on precision
- Solving nonlinear differential equations with differentiable quantum circuits
- Quantum annealing versus classical machine learning applied to a simplified computational biology problem
- High-precision quantum algorithms for partial differential equations
- Quantum Algorithm for Simulating the Wave Equation
- A Quantum Algorithm for Solving Linear Differential Equations: Theory and Experiment
- Benchmarking a quantum annealing processor with the time-to-target metric
- Demonstration of nonstoquastic Hamiltonian in coupled superconducting flux qubits
- A quantum algorithm to solve nonlinear differential equations
- Practical Quantum Computing: solving the wave equation using a quantum approach
- Completely Quantum Neural Networks
- Box algorithm for the solution of differential equations on a quantum annealer
- Quantum annealing for systems of polynomial equations
- Quantum chemistry on quantum annealers
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