Computing Statistical Properties of Velocity Fields on Current Quantum Hardware

TL;DR

This paper introduces methods to efficiently extract statistical properties of velocity fields directly from quantum circuits, enabling practical quantum CFD analysis on current hardware without full state tomography.

Contribution

It presents novel techniques for measuring statistical properties of velocity fields from parameterized quantum circuits, avoiding the need for full quantum state tomography.

Findings

High accuracy achieved on IBM quantum hardware

Effective extraction of moments and structure functions

Demonstrated on sine wave and Burgers' equation data

Abstract

Quantum algorithms are gaining attention in Computational Fluid Dynamics (CFD) for their favorable scaling, as encoding physical fields into quantum probability amplitudes enables representation of two to the power of n spatial points with only n qubits. A key challenge in Quantum CFD is the efficient readout of simulation results, a topic that has received limited attention in literature. This work presents methods to extract statistical properties of spatial velocity fields, such as central moments and structure functions, directly from parameterized ansatz circuits, avoiding full quantum state tomography. As a proof of concept, we implement our approach for 1D velocity fields, encoding 16 spatial points with 4 qubits, and analyze both a sine wave signal and four snapshots from Burgers' equation evolution. Using Qedma's error mitigation software QESEM, we demonstrate that such computations achieve high accuracy on current quantum devices, specifically IBMQ's Heron2 system ibm_fez.