Resource-efficient quantum simulation of transport phenomena via Hamiltonian embedding

This project looks at using quantum computing to solve transport‑phenomena equations, which are central to chemical‑engineering processes and dynamic simulations. Classical numerical methods for these complex transport partial‑differential equations (PDEs) become much slower as the system’s dimensionality grows. Quantum algorithms promise speedups, but they usually need a lot of hardware, making practical use difficult. To tackle this, we develop a resource‑efficient quantum‑simulation framework based on the Hamiltonian‑embedding technique. The method gives a systematic, hardware‑friendly way to simulate sparse Hamiltonians from start to finish, avoiding abstract query models while keeping near‑optimal asymptotic complexity. We apply the framework to both linear and nonlinear transport PDEs, including the multi‑dimensional advection equation. By mapping

these equations onto quantum platforms such as trapped‑ion systems, we achieve a large reduction in circuit depth. The project also provides implementation support and guidance for dynamic simulations, helping evaluate quantum‑classical hybrid workflows. This offers a path toward scalable, high‑fidelity simulation of chemical transport processes on near‑term quantum hardware.

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