As the application of Industrial Robots (IRs) scales and related participants increase, the demands for intelligent Operation and Maintenance (O&M) and multi-tenant collaboration rise. Traditional methods could no longer cover the requirements, while the Industrial Internet of Things (IIoT) has been considered a promising solution. However, there’s a lack of IIoT platforms dedicated to IR O&M, including IR maintenance, process optimization, and knowledge sharing. In this context, this paper puts forward the multi-tenant-oriented ACbot platform, which attempts to provide the first holistic IIoT-based solution for O&M of IRs. Based on an information model designed for the IR field, ACbot has implemented an application architecture with resource and microservice management across the cloud and multiple edges. On this basis, we develop four vital applications including real-time monitoring, health management, process optimization, and knowledge graph. We have deployed the ACbot platform in real-world scenarios that contain various participants, types of IRs, and processes. To date, ACbot has been accessed by 10 organizations and managed 60 industrial robots, demonstrating that the platform fulfills our expectations. Furthermore, the application results also showcase its robustness, versatility, and adaptability for developing and hosting intelligent robot applications.

In this paper, we consider the exact quantum query complexity of two fundamental symmetric functions. 1) {\mathrm{M}\mathrm{O}\mathrm{D}}_m^n, which calculates the Hamming weight of an n-bit string modulo m; 2) {\mathrm{E}\mathrm{X}\mathrm{A}\mathrm{C}\mathrm{T}}_{k,l}^n, which determines if the Hamming weight of an n-bit string is exactly k or l. Although these two symmetric functions have received considerable attention, their exact quantum query complexities have not been fully characterized. Specifically, our results are as follows:

1) We design an optimal quantum query algorithm to compute {\mathrm{M}\mathrm{O}\mathrm{D}}_m^n exactly and thus provide a tight characterization of its exact quantum query complexity, which settles a previous conjecture. Based on this algorithm, we demonstrate that a broad class of symmetric functions is not evasive in the quantum model, i.e., there exist quantum algorithms to compute these functions exactly when the number of queries is less than their input size.

2) By proposing a quantum algorithm that utilizes the minimum number of queries to compute {\mathrm{E}\mathrm{X}\mathrm{A}\mathrm{C}\mathrm{T}}_{k,l}^n exactly for some specific values of k and l, we give a tight characterization of its exact quantum query complexity in these scenarios.