High-fidelity simulation of complex transport phenomena remains a central challenge in computational fluid dynamics. Direct Numerical Simulation (DNS) can resolve fluid behaviour with high accuracy, but its extremely large computational and memory requirements make it impractical for large-scale or industrial applications on classical hardware.
Quantum Computing is a potential way to reduce computational cost while keeping accuracy. However, quantum-assisted fluid dynamics still faces hardware limits, shallow circuit depths, and difficulty in representing nonlinear physical effects within quantum circuits. Consequently, many current methods must simplify physics, use fixed or constrained parameters, or remain limited to low-complexity flow regimes, which reduces their practical applicability.
The Lattice Boltzmann Method (LBM) is promising for quantum implementation due to its structured, locally defined update rules. Despite this, a major bottleneck arises with the collision operator. This component is inherently nonlinear and non-unitary, making it hard to implement directly on gate-based quantum computers.
The core challenge is both computational and physical. Efficiently and accurately capturing nonlinear fluid interactions at scale within a quantum framework is very difficult. Addressing this challenge has significant practical value: it would enable more efficient and accurate simulation of complex flows in engineering and science. For this reason, quantum-assisted formulations are motivated by the need to overcome the limits of classical computation while remaining compatible with near-term quantum hardware. This represents a key step toward practical quantum advantage in fluid dynamics simulation.
