Quantum-enhanced Markov chain Monte Carlo sampling to model Lagrangian tracer dispersion in turbulent boundary layer

We present a quantum-enhanced Markov chain Monte Carlo (QE-MCMC) method to sample turbulent acceleration vectors from a joint target distribution that depends on all three components and height to model the transport and dispersion of massless Lagrangian tracer particles in two different turbulent shear flows. A homogeneous shear flow, which is characterized by a uniform shear rate $S$, is considered as the starting point. Secondly, a turbulent boundary layer, which forms in both halves of a plane turbulent channel flow (TCF) at a friction Reynolds number of $Re_{\tau}=1000$, is considered. Then the mean shear rate $S(y)$ varies with distance from the wall $y$. In this hybrid quantum-classical method, the proposal distribution $Q$ for the first of the two Metropolis-Hastings sampling substeps is constructed by a parametric quantum circuit. The algorithm generates synthetic tracer particle tracks. The resulting scaling laws for the tracer particle pair dispersion, a central quantity to probe the turbulent mixing properties of the shear flow from a Lagrangian perspective, are found to agree with a stochastic transport model consisting of a set of coupled Langevin equations and the classical MCMC counterpart. Differently to the classical sampling method, QE-MCMC takes to this end a tempered target distribution. Due to the height-dependence of the tracer dynamics in TCF, an effective height-weighted spectral gap between the first and second eigenvalue of the Markov chain transition matrix is introduced. The latter is found to significantly exceed the one of classical MCMC when the sampling is done from a multivariate distribution with cross correlations at the highest qubit numbers and thus resolutions. Consequently, our results support the applicability of this one-shot algorithm as a generative Lagrangian quantum computing module, possibly embedded in a complex fluid flow problem. Our module is found to work reliably for a relatively small number of qubits per spatial dimension of $N_q\le 6$.  

This repository contains Python scripts implementing a quantum-enhanced Markov chain Monte Carlo sampling method to model Lagrangian tracer dispersion in homogeneous shear flows and turbulent boundary layers.

The paper related to the data in this repository will be published in Physical Review Research with DOI number 10.1103/5qcg-fhk1