在门量子计算机上的鲁棒拟合
Robust Fitting on a Gate Quantum Computer
AI总结：
本文提出一维 $\ell_\infty$ 可行性测试的量子电路，首次在 IonQ Aria 门量子计算机上实现量子鲁棒拟合，并通过累积一维布尔影响力扩展到高维非线性模型，在真实基准数据集上验证有效。
摘要：
门量子计算机因其在多项式时间内解决某些难题（如质因数分解）的潜力而引起了广泛关注。计算机视觉研究者长期以来一直被量子计算机的能力所吸引。鲁棒拟合对许多计算机视觉流程具有根本性的重要意义，最近已被证明适用于门量子计算。此前提出的解决方案是利用 Bernstein-Vazirani 量子电路计算布尔影响力，作为离群程度的度量。然而，该方法假设了一个 $\ell_\infty$ 可行性测试的量子实现，而这一实现尚未被展示。在本文中，我们向量子鲁棒拟合迈出了一大步：我们提出了一个量子电路，用于在一维情形下求解 $\ell_\infty$ 可行性测试，从而首次在真实门量子计算机 IonQ Aria 上展示了量子鲁棒拟合。我们还展示了如何累积一维布尔影响力，以计算更高维非线性模型的布尔影响力，并在真实基准数据集上进行了实验验证。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
