Presentation
A Quantum Solver for Multidimensional Partial Differential Equations: Practical Case Studies
DescriptionQuantum computing is consistently becoming transformational for computational problem-solving. This capability appears particularly suited for numerical solution of multidimensional partial-differential-equations (PDEs). Although many quantum techniques are currently available for solving PDEs, these algorithms, particularly the ones based on variational-quantum-algorithms (VQAs), suffer from low accuracy, high execution times, and low scalability. In this work, we propose an efficient and scalable algorithm targeting multidimensional PDEs. We present two variants of the algorithm, that differ on how the final quantum circuit is generated. While both utilize finite-difference-method (FDM) and classical-to-quantum (C2Q) encoding as the initial steps, the first variant uses numerical-instantiation and the second uses column-by-column-decomposition (CCD) for quantum-circuit-synthesis. Our proposed algorithm has been validated by various case studies such as Poisson, Heat, Black-Scholes, and Navier-Stokes equations. The results demonstrate better accuracy and scalability with faster execution times compared to VQA-based solvers on noise-free and noisy quantum simulators and promising results on real-quantum-hardware.
Authors
Event Type
Research and ACM SRC Posters
TimeThursday, 20 November 20258:00am - 5:00pm CST
LocationSecond Floor Atrium
Archive
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