Robust Fitting on a Gate Quantum Computer

TL;DR

This paper introduces a quantum circuit for 1D $ ext{l}_ ext{infty}$ feasibility testing, enabling the first demonstration of quantum robust fitting on a real gate quantum computer and extending influence computation to higher dimensions.

Contribution

It presents a novel quantum circuit for 1D $ ext{l}_ ext{infty}$ feasibility testing and demonstrates quantum robust fitting on IonQ Aria, advancing quantum computer applications in computer vision.

Findings

Successful implementation of quantum robust fitting on IonQ Aria.

Validated influence computation for higher-dimensional models.

Demonstrated potential of quantum algorithms in computer vision pipelines.

Abstract

Gate quantum computers generate significant interest due to their potential to solve certain difficult problems such as prime factorization in polynomial time. Computer vision researchers have long been attracted to the power of quantum computers. Robust fitting, which is fundamentally important to many computer vision pipelines, has recently been shown to be amenable to gate quantum computing. The previous proposed solution was to compute Boolean influence as a measure of outlyingness using the Bernstein-Vazirani quantum circuit. However, the method assumed a quantum implementation of an $\ell_\infty$ feasibility test, which has not been demonstrated. In this paper, we take a big stride towards quantum robust fitting: we propose a quantum circuit to solve the $\ell_\infty$ feasibility test in the 1D case, which allows to demonstrate for the first time quantum robust fitting on a real gate quantum computer, the IonQ Aria. We also show how 1D Boolean influences can be accumulated to compute Boolean influences for higher-dimensional non-linear models, which we experimentally validate on real benchmark datasets.