Quantum Computing

VQA_POISSON : Efficient and Scalable Library Solving 2D Poisson Equations

Quantum computing represents a transformative direction in scientific computing, offering potential breakthroughs in solving large-scale numerical problems that are computationally prohibitive on classical hardware. While classical High-Performance Computing (HPC) has continuously advanced our ability to solve complex partial differential equations (PDEs), the required computational cost scales dramatically with increasing spatial resolution and physical complexity. This poses fundamental limitations for multi-physics simulations such as incompressible fluid dynamics, electrochemical transport, and high-fidelity battery modeling. 

In the Noisy Intermediate-Scale Quantum (NISQ) era, our laboratory explores hybrid quantum–classical algorithms that aim to bridge the gap between theoretical quantum speedups and practical scientific applications. We focus particularly on Variational Quantum Algorithms (VQAs), which are designed to operate efficiently on current hardware with limited qubit counts and connectivity constraints. These approaches leverage parameterized quantum circuits optimized through classical feedback loops to approximate the solutions of linear systems and PDEs, enabling reduced circuit depth and improved noise tolerance. 

A key research direction in our group is the development of quantum solvers for the Poisson and Navier–Stokes equations, which appear as core components in numerical methods including projection-based incompressible flow solvers. Our recent work introduces a VQA-based Poisson solver that integrates hardware-efficient ansätze with Quantum Fourier Transform (QFT)–based diagonalization schemes, significantly reducing computational cost by minimizing operator decomposition overhead. This capability opens the door to hybrid projection methods where quantum hardware accelerates the pressure-Poisson subsystem, enabling faster time-marching simulations in large-scale CFD workflows.