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This research introduces the Quantum-Logic Tsetlin Machine (QL-TM), a framework that integrates quantum propositions with classical automata to learn interpretable clauses from commuting measurement contexts. By demonstrating an exact reduction to Boolean logic in specific bases and validating performance on stabilizer tasks, the study establishes a rigorous bridge between Tsetlin clause learning and quantum mechanics without claiming immediate computational advantage. The work provides critical insights into how context budgets affect the recovery of physically meaningful information versus noise in non-diagonal settings.
Quantum-Logic Tsetlin Machines: Interpretable Quantum Machine Learning with Commuting Projector Clauses
arXiv:2608.18659v1 Announce Type: cross Abstract: 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.
Abstract: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.
8 pages, 5 figures. Accepted at the Fifth International Symposium on the Tsetlin Machine (ISTM 2026), Indian Institute of Science, Bangalore, India, 12-14 October 2026
Quantum Physics (quant-ph); Machine Learning (cs.LG); Logic in Computer Science (cs.LO)
arXiv:2608.18659 [quant-ph]
(or arXiv:2608.18659v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2608.18659 arXiv-issued DOI via DataCite (pending registration)
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