Modeling Noise in Quantum Computing of Scalar Convection

TL;DR

This paper investigates how quantum noise affects scalar convection simulations on quantum computers, revealing that errors can be modeled as deterministic physical effects like artificial diffusion.

Contribution

It introduces a theoretical model predicting spectral decay due to noise and demonstrates that quantum errors act as effective physical terms in the simulation.

Findings

Quantum noise causes spectral decay predictable by a Hamming-distance-based transition matrix.

Noise manifests as artificial diffusion and nonlinear source terms in the effective PDE.

Model validated through simulations and experiments on superconducting quantum processors.

Abstract

Quantum computing holds potential for accelerating the simulation of fluid dynamics. However, hardware noise in the noisy intermediate-scale quantum era significantly distorts simulation accuracy. Although error magnitudes are frequently quantified, the specific physical effects of quantum noise on flow simulation results remain largely uncharacterized. We investigate the influence of gate noise on the quantum simulation of one-dimensional scalar convection. By employing a quantum spectral algorithm where ideal time advancement affects only Fourier phases, we isolate and analyze noise-induced artifacts in spectral magnitudes. We derive a theoretical transition matrix based on Hamming distances between computational basis states to predict spectral decay, and then validate this model against density-matrix simulations and experiments on a superconducting quantum processor. Furthermore, using data-driven sparse regression, we demonstrate that quantum noise manifests in the effective partial differential equation primarily as artificial diffusion and nonlinear source terms. These findings suggest that quantum errors can be modeled as deterministic physical terms rather than purely stochastic perturbations.