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Quantum annealing (QA) that encodes optimization problems into Hamiltonians remains the only near-term quantum computing paradigm that provides sufficient qubits for real-world applications. To fit larger optimization instances on existing quantum annealers, reducing Hamiltonians into smaller equivalent Hamiltonians provides a promising approach. Unfortunately, existing reduction techniques are either computationally expensive or ineffective in practice. To this end, we introduce a novel notion of non-separable group, defined as a subset of qubits in a Hamiltonian that obtains the same value in optimal solutions. We develop a non-separability theory accordingly and propose FastHare, a highly efficient reduction method. FastHare, iteratively, detects and merges non-separable groups into single qubits. It does so within a provable worst-case time complexity of only O(αn^2), for some user-defined parameter α. Our extensive benchmarks for the feasibility of the reduction are done on both synthetic Hamiltonians and 3000+ instances from the MQLIB library. The results show FastHare outperforms the roof duality, the implemented reduction in D-Wave’s library. It demonstrates a high level of effectiveness with an average of 62% qubits saving and 0.3s processing time, advocating for Hamiltonian reduction as an inexpensive necessity for QA. 

Despite the great potential of Federated Learning (FL) in large-scale distributed learning, the current system is still subject to several privacy issues due to the fact that local models trained by clients are exposed to the central server. Consequently, secure aggregation protocols for FL have been developed to conceal the local models from the server. However, we show that, by manipulating the client selection process, the server can circumvent the secure aggregation to learn the local models of a victim client, indicating that secure aggregation alone is inadequate for privacy protection. To tackle this issue, we leverage blockchain technology to propose a verifiable client selection protocol. Owing to the immutability and transparency of blockchain, our proposed protocol enforces a random selection of clients, making the server unable to control the selection process at its discretion. We present security proofs showing that our protocol is secure against this attack. Additionally, we conduct several experiments on an Ethereum-like blockchain to demonstrate the feasibility and practicality of our solution.