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.
Comments
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
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.
Machine learning is typically described in terms of deterministic logical operations, whereas physical systems generally operate in the presence of noise, dissipation and irreversibility. Here, we turn these physical effects into computational resources for an autonomous, interpretable learning architecture. We develop a classifier based on thermodynamic neurons, which are autonomous quantum thermal machines that implement logical operations through heat flow, and use these to construct a stochastic version of the Tsetlin machine, an interpretable rule-based learning architecture. By combining thermodynamic AND, NOT and OR gates with an autonomous coupling mechanism, we realise a learning system whose computation unfolds without the need for external time-dependent control. Despite its noisy components, the resulting classifier achieves classification accuracy that is statistically comparable to that of the standard Tsetlin machine. Reliability arises from architectural mechanisms such as thresholding and redundancy, rather than exact logical operations. Our results highlight that accurate and interpretable learning can emerge from autonomous stochastic dynamics, and establish thermodynamic computation as a viable framework for physical machine learning.
According to quantum mechanics, the pure states of a microsystem are represented by vectors in a Hilbert Space. Sentences of the form, "x є L" (where x is the state vector for a system, L a subspace of the appropriate Hilbert space), may be called Q-propositions: such sentences serve to summarise our information about the results of possible experiments on the system. Quantum logic investigates the relations which hold among the Q-propositions about a given physical sys tem. These logical relations correspond to algebraic relations among the subspaces of Hilbert space. The algebra of this set of subspaces is non-Boolean, and may be regarded either as an orthomodular lattice or as a partial Boolean algebra. With each type of structure we can associate a logic. A general approach to the semantics for such a logic is provided in terms of interpretations of a formal language within an algebraic structure; an interpretation maps sentences of the language homomorphically onto elements of the structure. When the structure in question is a Boolean algera, the resulting logic is classical; here we develop a semantics for the logic associated with partial Boolean algebras. Two systems of proof, based on the natural deduction systems of Gentzen, are shown for this logic. With respect to the given sematics, these calculi are sound and weakly complete. Strong completeness is conjectured. Quantum logic deals with the logical relations between sentences, and so is properly called a logic. However, it is the logic appropriate to a limited class of sentences: proposals that it should replace classical logic wherever the latter is used should be viewed with suspicion.
Quantum language models have shown competitive performance on sequential tasks, yet whether trained quantum circuits exploit genuinely quantum resources -- or merely embed classical computation in quantum hardware -- remains unknown. Prior work has evaluated these models through endpoint metrics alone, without examining the memory strategies they actually learn internally. We introduce the first mechanistic interpretability study of quantum language models, combining causal gate ablation, entanglement tracking, and density-matrix interchange interventions on a controlled long-range dependency task. We find that single-qubit models are exactly classically simulable and converge to the same geometric strategy as matched classical baselines, while two-qubit models with entangling gates learn a representationally distinct strategy that encodes context in inter-qubit entanglement -- confirmed by three independent causal tests (p < 0.0001, d = 0.89). On real quantum hardware, only the classical geometric strategy survives device noise; the entanglement strategy degrades to chance. These findings open mechanistic interpretability as a tool for the science of quantum language models and reveal a noise-expressivity tradeoff governing which learned strategies survive deployment.
In our previous work we described quantized computation using Horn clauses and based the semantics, dubbed as entanglement semantics as a generalization of denotational and distribution semantics, and founded it on quantum probability by exploiting the key insight classical random variables have quantum decompositions. Towards this end we built a Hilbert space of H-interpretations and a corresponding non commutative von Neumann algebra of bounded linear operators. In this work we extend the formalism using second-quantized Horn clauses that describe processes such as Heisenberg evolutions in optical circuits, quantum walks, and quantum filters in a formally verifiable way. Our goal is to build a model of computation based on logic via Currry-Howard correspondence. Towards this end we can think of completely positive *-unital maps of Horn clauses as function types representing modus ponens (equation (19)). Recursions that result from inductive reasoning has a quantum analogue in terms of sequence of *-homomorphisms induced by completely positive *-unital maps (equation (18)). We base our system on a measure theoretic approach to handle infinite dimensional systems and demonstrate the expressive power of the formalism by casting an algebra used to describe interconnected quantum systems (QNET) in this language. The variables of a Horn clause bounded by universal or existential quantifiers can be used to describe parameters of optical components such as beam splitter scattering paths, cavity detuning from resonance, strength of a laser beam, or input and output ports of these components. Prominent clauses in this non commutative framework are Weyl predicates, that are operators on a Boson Fock space in the language of quantum stochastic calculus, martingales and conjugate Brownian motions compactly representing statistics of quantum field fluctuations. We formulate theorem proving as a quantum stochastic process in Heisenberg picture of quantum mechanics, a sequence of goals to be proved, using backward chaining.
Single Flux Quantum (SFQ) circuits provide ultrafast operation and low power consumption, making them attractive candidates for machine learning accelerators. The Tsetlin Machine (TM) is a low-complexity and highly interpretable architecture, organized as a voting system of propositional clauses. In the TM, an ensemble of finite-state automata (FSAs), called Tsetlin automata, independently decides whether to include or exclude specific literals. The chosen literals are assembled into propositional clauses that collectively form the voting system, while each FSA updates its state based on rewards or penalties determined by the prediction outcome. However, existing FSA designs for TM based on SFQ circuits still suffer from either a narrow margin or excessive circuit area. To achieve compact and stable state transitions using SFQ circuits, we designed High-Capacity Resettable D Flip-Flop (HC-RDFF) cells by cascading storage loops. The proposed FSA was implemented using two HC-RDFFs to store the include and exclude states, respectively. The FSA with 16 states requires only 395 Josephson junctions with a static power of approximately 128 μW, exhibiting a bias margin of −21% to +25% at low speed and a maximum operating frequency of 20 GHz in simulation. We fabricated the HC-RDFF and the FSA using a 10 kA/cm² Nb four-layer superconducting process and verified their correct operation through low-speed measurements. The number of FSA states can be increased simply by extending the cascaded storage loops in the HC-RDFFs. We expect the proposed FSA to be suitable for constructing stable TM systems based on SFQ circuits with reduced hardware costs.
Two commuting channels yield the same composite channel in either fixed order, yet their quantum switch can alter information preservation. We study how this effect depends on the input state, retaining the joint output of the control and target. Exact Kraus commutator identities determine overlap and squared fidelity gaps. Fixed order preserves product inputs at least as well as the switch in fidelity. The reverse inequality holds for pure states of two qubits whose control Schmidt basis can be chosen to coincide with the order basis. A commutator matrix determines the target basis that maximizes the squared fidelity gap at fixed entanglement within this aligned family. For Pauli X and Y channels with equal error probabilities, the switch replaces a logical phase flip with an operator that stabilizes a joint code. At fixed noise, the switch preserves at least as much distinguishability and quantum Fisher information as fixed order for every state family in this code. For the pure encoded family studied here, exact formulas connect the phase information gain to the squared fidelity gap and quantify the reduction in information about the noise probability. Optimizing the probes yields equal maximal quantum Fisher information for noise estimation under both joint channels. These results connect commutator geometry and logical error structure to state preservation and the retention of encoded information.