Bosonic Quantum Computing in Computational Fluid Dynamics

Quantum computing has the potential to efficiently perform massive calculations in several fields of science and engineering. In particular, applications for problems in computational fluid dynamics have recently gained wide attention. However, state-of-the-art quantum computers are strongly limited by noise and their small number of qubits, making them ineffective for solving the highly nonlinear governing equations of turbulent flows. In this work, a framework for using bosonic quantum computers to simulate nonlinear equations is presented. This approach efficiently addresses nonlinearities by encoding the flow fields as coherent states of photonic degrees of freedom of an optical system, utilizing their infinite-dimensional Hilbert space. Using photonic creation and annihilation operators, finite-difference algorithms can be written as a Hamiltonian describing the dynamics of the coherent state. To benchmark the proposed methodology, the 1D Burgers equation and the 2D Navier-Stokes equation for a lid-driven cavity are solved for varying Reynolds numbers. The complexity of the calculations is characterized and compared with that of classical computations. The effects of environmental noise such as photon loss and dephasing are explored, showing the ability to perform error correction for the flow variables. The results demonstrate that the analog quantum computer is a handy tool for computational fluid dynamics, opening new possibilities for outperforming classical numerical simulations.