Hamiltonian Simulation for Advection-Diffusion Equation with arbitrary transport field

• URL: http://arxiv.org/abs/2508.16728v1
• Date: Fri, 22 Aug 2025 18:02:08 GMT
• Title: Hamiltonian Simulation for Advection-Diffusion Equation with arbitrary transport field
• Authors: Niladri Gomes, Gautam Sharma, Jay Pathak,
• Abstract summary: We present a novel approach to solve the advection-diffusion equation under arbitrary transporting fields using a quantum-inspired 'Schrodingerisation' technique for Hamiltonian simulation.<n>Building on this potential, our quantum algorithm is designed to accommodate non-trivial, spatially varying transport fields.<n>We demonstrate the algorithm's effectiveness on benchmark scenarios involving coupled rotational, shear, and diffusive transport in two and three dimensions.
• Score: 0.6608945629704324
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a novel approach to solve the advection-diffusion equation under arbitrary transporting fields using a quantum-inspired 'Schrodingerisation' technique for Hamiltonian simulation. Although numerous methods exist for solving partial differential equations (PDEs), Hamiltonian simulation remains a relatively underexplored yet promising direction-particularly in the context of long-term, fault-tolerant quantum computing. Building on this potential, our quantum algorithm is designed to accommodate non-trivial, spatially varying transport fields and is applicable to both 2D and 3D advection-diffusion problems. To ensure numerical stability and accuracy, the algorithm combines an upwinding discretization scheme for the advective component and the central differencing for diffusion, adapted for quantum implementation through a tailored mix of approximation and optimization techniques. We demonstrate the algorithm's effectiveness on benchmark scenarios involving coupled rotational, shear, and diffusive transport in two and three dimensions. Additionally, we implement the 2D advection-diffusion equation using 16 qubits on IBM Quantum hardware, validating our method and highlighting its practical applicability and robustness.

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