QAMA: Quantum annealing multi-head attention operator with classical deep learning framework

As large language models scale up, the conventional attention mechanism faces critical challenges of exponential growth in memory consumption and energy costs. Quantum annealing computing, with its inherent advantages in computational efficiency and low energy consumption, offers an innovative direction for constructing novel deep learning architectures. This study proposes the first Quantum Annealing-based Multi-head Attention (QAMA) mechanism, achieving seamless compatibility with classical attention architectures through quadratic unconstrained binary optimization (QUBO) modeling of forward propagation and energy-based backpropagation. The method innovatively leverages the quantum bit interaction characteristics of Ising models to optimize the conventional $O(n^2)$ spatiotemporal complexity into linear resource consumption. Integrated with the optical computing advantages of coherent Ising machines (CIM), the system maintains millisecond-level real-time responsiveness while significantly reducing energy consumption. Our key contributions include: Theoretical proofs establish QAMA mathematical equivalence to classical attention mechanisms; Dual optimization of multi-head specificity and long-range information capture via QUBO constraints; Explicit gradient proofs for the Ising energy equation are utilized to implement gradient conduction as the only path in the computational graph as a layer; Proposed soft selection mechanism overcoming traditional binary attention limitations to approximate continuous weights. Experiments on QBoson CPQC quantum computer show QAMA achieves comparable accuracy to classical operators while reducing inference time to millisecond level and improving solution quality. This work pioneers architectural-level integration of quantum computing and deep learning, applicable to any attention-based model, driving paradigm innovation in AI foundational computing.