The International Conference for High Performance Computing, Networking, Storage, and Analysis
The International Conference for High Performance Computing, Networking, Storage, and Analysis
Poster Type: Research Posters
Author: Manu Chaudhary (Illinois State University (ISU)), Kareem El-Araby (University of Kansas), Alvir Nobel (University of Kansas), Ishraq Islam (University of Kansas), Manish Singh (University of Kansas), Sunday Ogundele (University of Kansas), Kieran Egan (University of Kansas), Sneha Thomas (University of Kansas), Vincent Vordtriede (University of Kansas), Devon Bontrager (University of Kansas), Serom Kim (University of Kansas), Esam El-Araby (University of Kansas)
Supervisor:
Abstract: Quantum 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.
Best Poster Finalist (BP): no
Poster: PDF
Poster Summary: PDF