Spectral quantum algorithm for passive scalar transport in shear flows

Area of Science:

• Quantum Computing
• Computational Fluid Dynamics
• Chemical Engineering

Background:

• Scalar mixing via stirring and diffusion is fundamental in natural phenomena, chemical engineering, and microfluidic applications.
• Simulating the advection-diffusion equation is crucial for understanding and predicting these mixing processes.

Purpose of the Study:

• To present a novel spectral quantum algorithm for simulating scalar mixing.
• To solve the advection-diffusion equation within a quantum computational fluid dynamics framework.

Main Methods:

• Derived exact gate decompositions for advection and diffusion operators in spectral space.
• Employed operator splitting to construct quantum circuits for simulating multi-dimensional polynomial velocity profiles.
• Implemented quantum spectral transforms to impose various boundary conditions (Periodic, Neumann, Dirichlet).

Main Results:

• Successfully simulated Couette flow, plane Poiseuille flow, and a polynomial Blasius profile approximation.
• Compared ideal quantum simulations with real quantum computer implementations (superconducting and trapped-ion qubits).
• Determined that the number of two-qubit gates scales logarithmically with grid points, dependent on velocity profile order.

Conclusions:

• The spectral quantum algorithm provides an efficient method for simulating scalar mixing in fluid flows.
• The approach is versatile, capable of handling complex velocity profiles and boundary conditions.
• This quantum simulation framework shows promise for advancing fluid dynamics research and applications.