量子逻辑Tsetlin机：具有对易投影算子子句的可解释量子机器学习
Quantum-Logic Tsetlin Machines: Interpretable Quantum Machine Learning with Commuting Projector Clauses
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中文总结 AI 辅助
该研究提出量子逻辑Tsetlin机（QL-TM），将Tsetlin子句学习与量子逻辑关联，经实验验证其在合适语境下可恢复有物理意义的子句，不涉及量子优势宣称。
中文摘要 AI 辅助
Tsetlin机（TMs）利用有限状态自动机学习可解释的布尔子句。我们提出量子逻辑Tsetlin机（QL-TM），其用由投影算子表示的量子命题替代布尔文字，同时保留经典的包含/排除自动机。子句被限制在对易测量语境中，并通过其联合投影算子的玻恩概率激活。我们证明在对角计算基语境下，QL-TM可精确归约为普通布尔TM子句，并将泡利投影算子子句与稳定子及症候语义关联。针对贝尔态、相位翻转症候、随机16类稳定子任务、混合文字池、语境预算消融实验及有限 shot 噪声的受控实验表明，正确的非对角语境可恢复具有物理意义的子句，而对角或错误语境会丢失相关相位/症候信息。语境预算结果与预测的可分性阶梯2^(b-k)高度吻合，其中b为语境预算，k为移除的真实稳定子生成元数量。本研究的贡献是在Tsetlin子句学习与量子逻辑之间建立了可控桥梁，并非宣称量子优势。
英文摘要
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.
发表机构
- Fractal Analytics（分形分析公司）
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