Presentation
An Accurate and Scalable Multidimensional Quantum Solver for Partial Differential Equations
DescriptionQuantum computing is an innovative technology that can solve certain problems faster than classical computing. One of its promising applications is in solving partial differential equations (PDEs). However, current PDE solvers that are based on variational-quantum-eigensolver (VQE) techniques suffer from low accuracy, high execution times, and low scalability on noisy-intermediate-scale-quantum (NISQ) devices, especially for multidimensional PDEs.
We introduce a highly accurate and scalable quantum algorithm for solving multidimensional PDEs and present two variants of our algorithm. The first leverages classical-to-quantum (C2Q) encoding, finite-difference-method (FDM), and numerical instantiation, while the second employs C2Q, FDM, and column-by-column decomposition (CCD). To evaluate our algorithm, we have used a multidimensional Poisson equation. Our results demonstrate higher accuracy, higher scalability, and faster execution times compared to VQE-based solvers on noise-free and noisy quantum simulators from IBM. We have also investigated our proposed algorithm on hardware emulators, employing various noise mitigation techniques with encouraging preliminary results.
We introduce a highly accurate and scalable quantum algorithm for solving multidimensional PDEs and present two variants of our algorithm. The first leverages classical-to-quantum (C2Q) encoding, finite-difference-method (FDM), and numerical instantiation, while the second employs C2Q, FDM, and column-by-column decomposition (CCD). To evaluate our algorithm, we have used a multidimensional Poisson equation. Our results demonstrate higher accuracy, higher scalability, and faster execution times compared to VQE-based solvers on noise-free and noisy quantum simulators from IBM. We have also investigated our proposed algorithm on hardware emulators, employing various noise mitigation techniques with encouraging preliminary results.
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