An efficient quantum approach for solving the collisionless Boltzmann equation in qiskit

  • Schalkers, Merel (Delft University of Technology)
  • Möller, Matthias (Delft University of Technology)

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Quantum computing is an emerging technology that has the potential to radically change the way we will be solving computational problems in the future. Computational fluid dynamics (CFD) belongs to the disciplines that are constantly pushing the capabilities of modern high-performance computing systems to their limits. This has lead early adopters in the CFD community to explore the potential advantage of quantum computing for this discipline. The potential of quantum computers comes in the form of exploiting properties such as quantum superposition, quantum parallelism and entanglement of quantum states. However, in contrast to classical computers that process data deterministically and allow to read-out the solution 'as is', quantum computing requires to retrieve information via measurements that lead to results being represented as a probability distribution. The probabilistic nature of measurement suggests the Boltzmann equation as a natural framework for formulating quantum CFD algorithm. In this presentation we present a novel quantum approach to solve the collisionless Boltzmann equation. Next to a rigorous complexity analysis of the different algorithmic building blocks we introduce a new formulation of the reflection step that enables the accurate simulation of arbitrary flow fields. We furthermore propose a novel encoding of data that improves the efficiency of the resulting quantum circuits both in terms of gate count and gate complexity. We demonstrate the correct functioning and the smooth interplay of all novel components with a start-to-end implementation in the quantum computing programming and simulation framework qiskit, applied to open domain fluid flow around various obstacles.