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This paper introduces the Quantum-Logic Tsetlin Machine (QL-TM), which innovatively integrates quantum propositions into Tsetlin Machines by replacing Boolean literals with commuting projector clauses while preserving classical automata. The authors demonstrate that QL-TMs can recover meaningful quantum clauses in non-diagonal contexts, while diagonal contexts fail to retain essential phase information, thus establishing a clear connection between quantum logic and classical clause learning. Experimental results validate the theoretical framework, showing that as stabilizer generators are removed, the performance aligns with the predicted separability ladder, emphasizing the utility of QL-TMs in bridging quantum and classical machine learning paradigms.
Non-diagonal contexts in Quantum-Logic Tsetlin Machines can recover meaningful quantum clauses, while diagonal contexts lose critical phase information, revealing the intricate relationship between quantum logic and classical learning.
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.
