Encoding Turbulent Flows into Quantum States#
Pia Siegl (DLR)
Abstract#
Structure resolving computational fluid dynamics of high-turbulent flows are often unfeasible on classical computers. It was proposed to use quantum algorithms [1] or quantum-inspired matrix product state (MPS) algorithms [2] to simulate fluid flows. With amplitude encoding, the qubit number scale logarithmically in the number of data points. We aim to introduce the ideas and potential advantages of the quantum (inspired) methods. To evaluate the potential of these algorithms for turbulent flows that are characterized by being chaotic, we study the impact of chaotic and random behavior of the classical systems on its representation as a quantum state. Using information theoretical properties, as the entropy rate, we connect the amount of randomness to the required bond dimension in the MPS representation and the entanglement behavior in the quantum state. At the example of 1D non-linear problems, we find that the amount randomness is directly related to the compression possible with an MPS. Correlations on the other hand, lead to additional structure in the data, and increase the representability. [1] M. Lubasch et al., Variational quantum algorithms for nonlinear problems, Phys. Rev. A 101, 2020 [2] N. Gourinov et al., A Quantum Inspired Approach to Exploit Turbulence Structures, Nat. Comp. Sci. 2, 30, 2022