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Spectral quantum algorithm for passive scalar transport in shear flows.

Philipp Pfeffer1, Peter Brearley2,3, Sylvain Laizet2

  • 1Institute of Thermodynamics and Fluid Mechanics, Technische Universität Ilmenau, 98684, Ilmenau, Germany. philipp.pfeffer@tu-ilmenau.de.

Scientific Reports
|November 21, 2025
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Summary
This summary is machine-generated.

We developed a quantum algorithm to simulate scalar mixing in fluid dynamics by solving the advection-diffusion equation. This quantum computational fluid dynamics approach efficiently handles complex flows and boundary conditions.

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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.