首次在真实量子计算机上实现鲁棒拟合，突破关键算法瓶颈。
Robust Fitting on a Gate Quantum Computer
- 设计1维ℓ∞可行性测试的量子电路，解决核心计算难题。
- 在IonQ Aria量子机上首次实现实例化量子鲁棒拟合。
- 方法可扩展至高维非线性模型，适用于计算机视觉任务。
门式量子计算机因其能在多项式时间内求解如质因数分解等难题而备受关注。计算机视觉研究者长期对量子计算机潜力感兴趣。鲁棒拟合作为众多视觉流程的基础，近期被证明可适配门式量子计算。此前方案依赖量子实现ℓ∞可行性测试，但该技术尚未验证。本文迈出关键一步：提出1维ℓ∞可行性测试的量子电路，首次在真实门式量子计算机IonQ Aria上实现量子鲁棒拟合。同时展示如何将1维布尔影响累积，以计算高维非线性模型的布尔影响，并在真实基准数据集上实验验证。
原文摘要 · Abstract (English)
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.
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