A Flexible Quantum Lattice-Boltzmann Algorithm for the 3-D Linear Advection-Diffusion Equation with Spatially and Temporally Variable Velocity Field

  • Wawrzyniak, David (Technical University Munich)
  • Winter, Josef (Technical University Munich)
  • Schmidt, Steffen (Technical University Munich)
  • Indinger, Thomas (Technical University Munich)
  • Janßen, Christan (Altair Engineering Inc.)
  • Schramm, Uwe (Altair Engineering Inc.)
  • Adams, Nikolaus (Technical University Munich)

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The Lattice-Boltzmann method offers versatility and high parallel efficiency for simulating fluid mechanical phenomena that even enables interactive design analysis today. However, the required computing power increases proportionally to finer resolution and larger domain size. Due to its potential exponential efficiency scales, quantum computers are attracting more and more interest. Technical as well as algorithmic development are progressing fast towards universal functionality. Therefore, the potential of quantum computing in computational fluid dynamic applications needs to be researched. We demonstrate the first general discretization strategy of the Lattice-Boltzmann method as a quantum algorithm. Starting on the ideas of Budinski (2021), we propose general quantum building blocks for the algorithmic steps of the Lattice-Boltzmann method for the linear advection-diffusion equations: collision, streaming, and calculation of the macroscopic quantities. All proposed building blocks apply for arbitrary (spatially and temporally dependent) velocity fields and are valid for one-, two-, and three-dimensional problems with arbitrary stencils. In our test cases, we find significant speedup potential for the streaming operator, which is unattainable on classical (digital) computer systems. We base our implementation on the open-source software development kit Qiskit, that allows simulating quantum computers using different backends. An analytic simulator shows exact agreement between the quantum and classical algorithm. Solutions generated using a sampling-based simulator mimicking a noise-free quantum computer agree with classical results superposed by oscillations due to the stochastic nature of the problem. We analyze the implementation strategies and discuss the hardware-related challenges of a Lattice-Boltzmann simulation run on quantum computers.