Quantum state preparation for a velocity field based on the spherical Clebsch wave function

TL;DR

This paper introduces a variational quantum algorithm to prepare quantum states representing velocity fields in fluid dynamics using spherical Clebsch wave functions, enabling accurate quantum simulations of complex fluid flows.

Contribution

It develops a novel variational ansatz and optimization method for encoding velocity fields into quantum states via SCWF, advancing quantum fluid dynamics simulations.

Findings

Validated on 1D and 2D flow fields, demonstrating accuracy and robustness.

Effectively captures flow features like sources, sinks, and saddle points.

Enables quantum simulation of multiscale, multidimensional fluid flows.

Abstract

We propose a method for preparing the quantum state for a given velocity field, e.g., in fluid dynamics, via the spherical Clebsch wave function (SCWF). Using the pointwise normalization constraint for the SCWF, we develop a variational ansatz comprising parameterized controlled rotation gates. Employing the variational quantum algorithm, we iteratively optimize the circuit parameters to transform the target velocity field into the SCWF and its corresponding discrete quantum state, enabling subsequent quantum simulation of fluid dynamics. Validations for one- and two-dimensional flow fields confirm the accuracy and robustness of our method, emphasizing its effectiveness in handling multiscale and multidimensional velocity fields. Our method is able to capture critical flow features like sources, sinks, and saddle points. Furthermore, it enables the generation of SCWFs for various vector fields, which can then be applied in quantum simulations through SCWF evolution.