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: Sangwon Kim (RIKEN Center for Computational Science (R-CCS)), Junya Onishi (RIKEN Center for Computational Science (R-CCS)), Ayato Takii (Kobe University, Japan), Younghwa Cho (Hokkaido University, Japan), Tsubokura Makoto (RIKEN Center for Computational Science (R-CCS); Kobe University, Japan)
Supervisor:
Abstract: This work presents a time-stepping Hamiltonian simulation framework for nonlinear PDEs on a hybrid quantum–classical approach. Using warped phase transform (WPT)–based Schrödingerization, spatial discretizations are reformulated as Hermitian/anti-Hermitian operators for Schrödinger-type equations, enabling unitary propagation even for dissipative systems. In contrast to traditional linearizations (Carleman, KvN) that cause exponential statevector growth and truncation errors on NISQ hardware, we update nonlinear terms classically at each step, incorporate into the Hamiltonian, and calculate it by unitary evolution on the quantum circuit. This local linear approximation over small time intervals prevents dimensional inflation while securing calculation accuracy. We implement the framework in Qiskit and evaluate it with the Qiskit Aer statevector simulator on linear advection–diffusion and nonlinear problems including Burgers and Allen–Cahn phase field models. The results show good agreement with classical solutions, highlighting its potential for efficiently simulating nonlinear dynamics without dimensional inflation.
Best Poster Finalist (BP): no
Poster: PDF
Poster Summary: PDF