将量子逻辑引入可解释机器学习，用投影算子构建新型判别规则
Quantum-Logic Tsetlin Machines: Interpretable Quantum Machine Learning with Commuting Projector Clauses
- 用投影算子替代传统布尔量词，保持经典状态机学习机制
- 非对角基下能恢复物理上意义明确的量子纠缠与纠错信息
- 适合研究量子逻辑与可解释性结合的学者，尤其关注量子纠错
Tsetlin Machines（TMs）通过有限状态自动机学习可解释的布尔命题。本文提出量子逻辑Tsetlin机（QL-TM），将布尔文字替换为由投影算符表示的量子命题，同时保留经典的包含/排除自动机机制。命题受限于可交换测量上下文，通过联合投影算符的玻恩概率激活。我们证明在对角计算基上下文中，该模型精确还原为普通布尔TM命题，并建立泡利投影算符命题与稳定子及纠偏语义的联系。在贝尔态、相位翻转纠偏、16类随机稳定子任务、混合文字池、上下文预算消融实验及有限采样噪声测试中，正确非对角上下文可恢复具有物理意义的命题，而对角或错误上下文会丢失相关相位/纠偏信息。上下文预算结果与预测的可分性阶梯2^(b-k)高度吻合，随着真实稳定子生成元被移除而衰减。本工作是将Tsetlin命题学习与量子逻辑可控衔接的桥梁，不主张量子优势。
原文摘要 · Abstract (English)
Tsetlin Machines (TMs) learn interpretable Boolean clauses using finite-state automata. We introduce the Quantum-Logic Tsetlin Machine (QL-TM), which replaces Boolean literals with quantum propositions represented by projectors while retaining classical include/exclude automata. Clauses are restricted to commuting measurement contexts and activate through the Born probability of their joint projector. We prove an exact reduction to ordinary Boolean TM clauses in diagonal computational-basis contexts and connect Pauli-projector clauses to stabilizer and syndrome semantics. Controlled experiments on Bell states, phase-flip syndromes, randomized 16-class stabilizer tasks, mixed literal pools, context-budget ablations, and finite-shot noise show that correct non-diagonal contexts recover physically meaningful clauses, while diagonal or wrong contexts lose the relevant phase/syndrome information. The context-budget results closely follow the predicted separability ladder 2^(b-k) as true stabilizer generators are removed. The contribution is a controlled bridge between Tsetlin clause learning and quantum logic, not a claim of quantum advantage.
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