Multi-Partitioned Meshfree Quantum Finite Particle Method: A Hybrid Quantum Framework for Fluid Flow

This study established a quantum-classical hybrid framework that integrates quantum computing paradigm with meshfree finite particle method. By harnessing quantum superposition and entanglement, it hybridized the critical computational kernels (termed as quantum finite particle method). A resource-efficient quantum computational strategy on multi-partitioned zones was proposed, which leverages a fixed small-scale quantum circuit as a fundamental processing unit to handle inner product for arbitrarily sized arrays. This approach employs iterative nesting of the quantum-core operation to accommodate varying input dimensions while maintaining hardware feasibility throughout. Motivated with developed quantum framework, the novel numerical discretization for hybrid quantum computational particle dynamics can be derived commonly and applied in fluid flows. Through a sequence of numerical experiments purposefully, the proposed numerical model was thoroughly validated and analyzed. Results demonstrate that integrating quantum computing to hybridize conventional linear combinations of particle dynamics serves as an effective high performance computing paradigm. By further extending into the numerical investigation of viscoelastic, highly elastic, and purely elastic fluids under high Weissenberg number conditions, the applicability of quantum-hybrid framework is significantly broadened. These advances provide critical insights facilitating the transition of quantum-enhanced fluid simulation toward practical engineering applications.