Metrological comparison between a generalised N-dimensional classical and quantum point cloud Phase 2 Continuation

物联网数据的大规模多模态传感器融合可以转化为n维经典点云。例如，转换可能是LiDAR（光成像、检测和测距）、一组RGB图像和一组热图像等三种不同性质的成像模式的融合。然而，处理一个点云并不容易，因为它可以有数百万甚至数亿个点。因此，传统计算机在操作多模态传感器数据的点云时经常崩溃。新兴的量子计算技术可以帮助用户更高效地解决多模态传感器点云处理问题。量子计算硬件的发展速度很快，目前的量子计算机已经存在，每台计算机的量子比特（量子位）数量稳步增加。因此，量子计算有望成为克服高实时性计算要求的重要而有效的工具。为了在量子计算机中运行点云，需要解决两个问题，即量子点云表示和量子点云处理。二维图像的量子表示比比皆是。然而，使用量子表示来表达三维图像的方法明显缺乏。此外，为了提供基于量子计算的融合多模态传感器数据解决方案，需要进一步推广到n维量子点云的表示和处理。我们已经从理论上证明，如果量子计算机没有固有误差，量子计算机的表示和处理是可能的。现有的和近期的量子计算硬件是嘈杂的，因此任何提出的量子算法都需要测试其对这种噪音的恢复能力。因此，在这个项目中，我们也将在真实的噪声量子硬件上执行QPC处理。我们将首先模拟包括噪声的qpc，并进行不确定性量化以了解其对qpc的影响。本文将在噪声量子计算机上对CPC和QPC进行系统的计量比较。这包括定义量子点计算结果的效率和准确性，例如在准备和处理量子点云时由噪声硬件引起的不确定性，以及评估量子点计算结果的统计变化。

The large-scale multimodal sensor fusion of internet of things (loT) data can be transformed into a N-dimensional classical point cloud. For example, the transformation may be the fusion of three imaging modalities of different natures such as LiDAR (light imaging, detection, and ranging), a set of RGB images, and a set of thermal images. However, it is not easy to process a point cloud because it can have millions or even hundreds of millions of points. Classical computers therefore often crash when operating a point cloud of multimodal sensor data.The emerging quantum computing technology can help users to solve the multimodal sensor point cloud processing problem more efficiently.The development of the quantum computing hardware is proceeding at a fast pace, and current quantum computers exist, with the number of quantum-bits (qubits) per computer steadily increasing. Quantum computation is therefore expected to become an important and effective tool to overcome the high real-time computational requirements. In order to operate point clouds in quantum computers, there are two problems to be solved, and these are quantum point cloud representation and quantum point cloud processing. Quantum representations of two-dimensional images abound. However, there is a distinct paucity of methods to express a three-dimensional image using quantum representation. Furthermore, to provide a quantum computing based solution for fused multimodal sensor data the representation and processing needs to be further generalized to N-dimensional quantum point clouds.We have theoretically demonstrated that representation and processing of QPCs is possible if the quantum computers have no inherent errors. Existing and near-term quantum computing hardware is noisy, so that any proposed quantum algorithm needs to be tested for its resilience to this noise. In this project we will therefore perform QPC processing also on real noisy quantum hardware. We will first simulate QPCs including noise and perform uncertainty quantification to understand its effects on QPCs. A systematic metrological comparison between CPC and QPC on noisy quantum computers will be performed. This includes definitions of measures for the efficiency and accuracy of QPC results, such as the uncertainty induced by the noisy hardware when preparing and processing the quantum point cloud, and the evaluation of the statistical variations of QPC outcomes.