Quantum-assisted Lagrangian tracer dispersion in turbulent shear flow

We present a quantum-assisted generative algorithm for synthetic tracks of Lagrangian tracer particles in a simple turbulent shear flow. The parallelism, a result of the underlying tensor product structure of an n-qubit quantum register, and the sampling properties of quantum algorithms are used to build and optimize a parametric quantum circuit, which generates a quantum state that corresponds to the joint probability density function of the classical turbulent velocity components, p(u1′,u2′,u3′). Velocity samples are drawn by one-shot measurements on the quantum circuit. The hybrid quantum-classical algorithm is validated with two classical methods, a standard stochastic Lagrangian model and a classical sampling scheme in the form of a Markov-chain Monte Carlo approach. In detail, we consider a homogeneous turbulent shear flow with a constant shear rate S as a proof of concept for which the velocity fluctuations are Gaussian. The generation of the joint probability density function is also tested on a real quantum device, the 20-qubit IQM Resonance quantum computing platform for cases of up to 10 qubits. Our study paves the way to applications of Lagrangian small-scale parameterizations of turbulent transport in complex turbulent flows with quantum computers. A quantum advantage is possible by the efficient reconstruction of high-dimensional probability density functions, which can be sampled efficiently.