Figure 2

Quantum circuits using \(n=3\) qubits per spatial dimension for simulating the advection equation (a) in a Couette flow, (b) a Poiseuille (channel) flow, and (c) a boundary layer described by a third-order approximation to the Blasius solution. The top three qubits correspond to the x direction and the bottom three qubits correspond to the y direction. The phase coefficients for the Couette, Poiseuille and Blasius profiles are calculated from Eqs. (9), (10), and (11), respectively. Here, \(\alpha =2\pi U t / L\) as the variable velocity profile u(y) is encoded in the prefactors of \(\alpha\) in each gate.