量子计算和注意力机制结合的新思路，把softmax映射到量子测量，数学上还挺严谨，搞量子ML的可以看看。
该论文提出软注意力机制在概率单纯形上的精确量子实现方案。注意力分数通过Hadamard测试统计获得，指数softmax与Born规则测量存在精确双射。温度参数对应重复测量次数，值聚合通过确定性列加载通道实现。所有可学习参数均为旋转门角度，组合层在无限射击极限下精确。代数核心已用Lean 4形式化验证。
A Quantum Roadmap for Softmax Attention: Exact Born-Rule Analogs for Softmax Attention on the Probability Simplex
The attention mechanism forms the foundation of many modern AI models such as the Transformer. In one subclass of problems where attention is used, inputs and outputs are bound to the probability simplex so that all outputs sum to one. In this setting, softmax attention admits an exact, component-by-component quantum realization. Attention scores are Hadamard-test statistics on block-encoded projections of amplitude-encoded inputs. The exponential softmax is the interior of a cosine-squared family generated by Born-rule measurement under an exact bijection, whose boundary expresses sparse attention with exact zeros at finite parameter values. The softmax temperature is a repetition count where post-selected measurement rounds realize discretized inverse temperature exactly. Value aggregation is a deterministic column-loading channel that dilates the column-stochastic value matrix. The gated residual is the preparation angle of a single ancilla, with the additive identity at a mixing angle of π/2. Every learnable parameter is a rotation-gate angle. The composed layer is exact in the infinite-shot limit with one measure-and-reload step per attention score; a fully-coherent variant is ε-approximate via quantum singular value transformation in the infinite depth limit. The algebraic core is machine-checked in Lean 4.