Energy Scale Degradation in Sparse Quantum Solvers: A Barrier to Quantum Utility

Quantum computing offers a promising route for tackling hard optimization problems by encoding them as Ising models. However, sparse qubit connectivity requires the use of minor-embedding, mapping logical qubits onto chains of physical qubits, which necessitates stronger intra-chain coupling to maintain consistency. This elevated coupling strength forces a rescaling of the Hamiltonian due to hardware-imposed limits on the allowable ranges of coupling strengths, reducing the energy gaps between competing states, thus, degrading the solver's performance. Here, we introduce a theoretical model that quantifies this degradation. We show that as the connectivity degree increases, the effective temperature rises as a polynomial function, resulting in a success probability that decays exponentially. Our analysis further establishes worst-case bounds on the energy scale degradation based on the inverse conductance of chain subgraphs, revealing two most important drivers of chain strength, \textit{chain volume} and \textit{chain connectivity}. Our findings indicate that achieving quantum advantage is inherently challenging. Experiments on D-Wave quantum annealers validate these findings, highlighting the need for hardware with improved connectivity and optimized scale-aware embedding algorithms.

Blockchain-based Secure Client Selection in Federated Learning

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.