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UID:submissions.supercomputing.org_SC24_sess533_post192@linklings.com
SUMMARY:An Accurate and Scalable Multidimensional Quantum Solver for Parti
 al Differential Equations
DESCRIPTION:Manu Chaudhary, Ishraq Islam, Alvir Nobel, Dylan Kneidel, Vina
 yak Jha, Ben Phillips, Kareem El-Araby, Manish Singh, and Esam El-Araby (U
 niversity of Kansas)\n\nQuantum computing is an innovative technology that
  can solve certain problems faster than classical computing. One of its pr
 omising applications is in solving partial differential equations (PDEs). 
 However, current PDE solvers that are based on variational-quantum-eigenso
 lver (VQE) techniques suffer from low accuracy, high execution times, and 
 low scalability on noisy-intermediate-scale-quantum (NISQ) devices, especi
 ally for multidimensional PDEs. \n\nWe introduce a highly accurate and sca
 lable 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, whi
 le the second employs C2Q, FDM, and column-by-column decomposition (CCD). 
 To evaluate our algorithm, we have used a multidimensional Poisson equatio
 n. Our results demonstrate higher accuracy, higher scalability, and faster
  execution times compared to VQE-based solvers on noise-free and noisy qua
 ntum simulators from IBM. We have also investigated our proposed algorithm
  on hardware emulators, employing various noise mitigation techniques with
  encouraging preliminary results.\n\nRegistration Category: Tech Program R
 eg Pass, Exhibits Reg Pass\n\nSession Chairs: Ayesha Afzal (Friedrich-Alex
 ander University, Erlangen-Nuremberg; Erlangen National High Performance C
 omputing Center); Sally Ellingson (University of Kentucky); and Alan Sussm
 an (University of Maryland)\n\n
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