Speaker
Description
This work presents a hybrid quantum-classical framework for solving the linear systems arising from discretised unsteady magnetohydrodynamic (MHD) nanofluid Couette flow equations. The classical component employs a Bivariate Spectral Quasilinearisation Method (BI-SQLM) and Crank-Nicolson finite difference scheme to solve the coupled momentum and energy equations with partial slip and convective boundary conditions. The discretised linear systems are then solved using two quantum linear solvers: the Harrow-Hassidim-Lloyd (HHL) algorithm and the Variational Quantum Linear Solver (VQLS).
We present results for Pure Water, Cu-Water, and Al₂O₃-Water nanofluids across seven parameter variations. The Hartmann number dominates velocity suppression and entropy amplification, while velocity slip reduces upper-wall entropy generation by more than nine-fold. VQLS achieves 0.007% solution error with a transpiled circuit depth of only 5 gates, confirming NISQ-device compatibility, while HHL shows theoretical advantage at larger problem sizes (∼18,000× speedup at n=1024) but remains hardware-infeasible at its current transpiled depth of 43,127 gates.
This is the first exploratory application of quantum linear solvers to a discretised MHD nanofluid system, establishing a foundation for future full quantum computational fluid dynamics treatments. The framework demonstrates that near-term quantum devices can contribute to thermo-fluid simulations while highlighting the resource trade-offs between variational and phase-estimation-based approaches.
| Topic | Quantum variational circuits and their applications |
|---|---|
| Additional Topic | Hybrid quantum-classical approaches for learning and optimization |