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Quantum search algorithms are capable of efficiently solving large-scale quantum computing and signal processing problems, but their operation is contaminated by the decoherence of quantum circuits. This may be mitigated by quantum codes. Secure QKD is already a commercial reality in 2021.

Filtering is the fundamental operation upon which the field of signal processing is built. Loosely speaking, filtering is a mapping between signals, typically used to extract useful information (output signal) from data (input signal). Arguably, the most popular type of filter is the linear and shift-invariant (i.e. independent of the starting point of the signal) filter, which can be computed efficiently by leveraging the convolution operation. 

With the explosive growth of data, it is a heavy burden for users to store the sheer amount of data locally. Therefore, more and more organizations and individuals would like to store their data in the cloud. However, the data stored in the cloud might be corrupted or lost due to the inevitable software bugs, hardware faults and human errors in the cloud. 

Deep learning on graphs, also known as Geometric deep learning (GDL) [1], Graph representation learning (GRL), or relational inductive biases, has recently become one of the hottest topics in machine learning. While early works on graph learning go back at least a decade [2], if not two [3], it is undoubtedly the past few years’ progress that has taken these methods from a niche into the spotlight of the Machine Learning (ML) community.