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DTSTART;TZID=America/Chicago:20251121T080000
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UID:submissions.supercomputing.org_SC25_sess620_post141@linklings.com
SUMMARY:A Quantum Solver for Multidimensional Partial Differential Equatio
 ns: Practical Case Studies
DESCRIPTION:Manu Chaudhary (Illinois State University (ISU)) and Kareem El
 -Araby, Alvir Nobel, Ishraq Islam, Manish Singh, Sunday Ogundele, Kieran E
 gan, Sneha Thomas, Vincent Vordtriede, Devon Bontrager, Serom Kim, and Esa
 m El-Araby (University of Kansas)\n\nQuantum computing is consistently bec
 oming transformational for computational problem-solving. This capability 
 appears particularly suited for numerical solution of multidimensional par
 tial-differential-equations (PDEs). Although many quantum techniques are c
 urrently available for solving PDEs, these algorithms, particularly the on
 es based on variational-quantum-algorithms (VQAs), suffer from low accurac
 y, high execution times, and low scalability. In this work, we propose an 
 efficient and scalable algorithm targeting multidimensional PDEs. We prese
 nt two variants of the algorithm, that differ on how the final quantum cir
 cuit is generated. While both utilize finite-difference-method (FDM) and c
 lassical-to-quantum (C2Q) encoding as the initial steps, the first variant
  uses numerical-instantiation and the second uses column-by-column-decompo
 sition (CCD) for quantum-circuit-synthesis. Our proposed algorithm has bee
 n validated by various case studies such as Poisson, Heat, Black-Scholes, 
 and Navier-Stokes equations. The results demonstrate better accuracy and s
 calability with faster execution times compared to VQA-based solvers on no
 ise-free and noisy quantum simulators and promising results on real-quantu
 m-hardware.\n\nTag: Research & ACM SRC Posters\n\nRegistration Category: T
 echnical Program Reg Pass\n\nSession Chairs: Kento Sato (RIKEN Center for 
 Computational Science (R-CCS)); Anja Gerbes (Georg-August-Universität Gött
 ingen); and Chris Schlipalius (Pawsey Supercomputing Research Centre; Comm
 onwealth Scientific and Industrial Research Organisation (CSIRO), Australi
 a)\n\n
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