Quantum-Logic Tsetlin Machines: Interpretable Quantum Machine Learning with Commuting Projector Clauses

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.

Quantum Logic as the Logic of Contexts

Quantum logic is usually presented as a non-classical departure from ordinary reasoning forced on us by quantum mechanics, with classical logic kept as the secure starting point. We argue for the opposite order of explanation in a finite and fully computable setting. The free orthomodular lattice on two generators has ninety-six elements, the direct product of a six-element non-distributive factor and a sixteen-element Boolean factor. Reading the first factor as a register of contexts and the second as Boolean content, we obtain a calculus whose elements are context--bit-vector pairs and whose operations act component by component. With this calculus we establish three results. First, we classify the six layers by commutativity, identifying the central kernel of context-neutral propositions together with a dual central layer in which all complementary contexts are present. Second, we show that orthocomplementation rearranges the layers exactly as the complementation of the small factor rearranges its elements, which makes the duality among the layers rigid rather than accidental. Third, we prove that the operation forgetting the context is a surjective homomorphism of orthocomplemented lattices whose quotient is the classical Boolean algebra, so that classical logic is a six-to-one, information-losing image of the contextual calculus.