- The paper introduces a quantum-tunnelling oscillator model that bridges quantum cognition and neural computation, demonstrating dynamic state transitions in ambiguous perception.
- It employs tunnelling and interference mechanisms to capture perceptual switching dynamics and biases evident in EEG and eye-tracking studies.
- The approach extends to social cognition, mapping opinion dynamics via coupled quantum states and offering improved AI models for ambiguity handling.
Quantum-Tunnelling Oscillators in Cognitive Modelling and Neural Computation
Introduction and Context
This paper proposes and analyzes a quantum-tunnelling oscillator model, presenting it as a universal dynamical engine for modelling paradigmatic phenomena in quantum cognition, including optical illusion perception and collective human decision-making. The central innovation is embedding quantum dynamical principles—specifically superposition, tunnelling, and context dependence—into physically grounded frameworks for both individual and group cognition. This model, when networked, forms quantum-cognitive neural systems capable of explaining empirical regularities and paradoxical effects unaddressed by deterministic or classical stochastic paradigms.
Theoretical Framework
The work is situated at the intersection of quantum cognition theory and neural computation. It leverages the mathematical structure of quantum mechanics, particularly the Schrödinger equation, to model cognitive state evolution, explicitly avoiding unsupported metaphysical claims about the human brain performing quantum computation. Instead, cognitive states are mapped to quantum state formalism, allowing the system to inhabit superpositions, undergo non-commutative transitions, and be sensitive to contextual measurement—features with direct empirical correlates in bistable perception, preference variability, and collective decision contexts.
The distinction from deterministic models such as EUT and CPT is emphasized, with empirical evidence compelling the inclusion of explicit stochasticity and contextual probability structures. Classical stochastic models (e.g., Fechner, Luce) are extended in the quantum-cognitive framework, enabling the description of phenomena that violate classical probabilistic calculus, such as interference effects, order dependence, and the systematic violation of the sure-thing principle.
Quantum Oscillator Model: Bistable Perception and Beyond
The construction begins with the canonical bistable perception task—the Necker cube. The model advances from previous quantum-cognitive representations (e.g., the Busemeyer-Bruza formulation), mapping ambiguous percepts to a qubit-like system evolving according to the Schrödinger equation in a parabolic potential well. Here, perceptual switching emerges naturally as the evolution and measurement-induced collapse of a quantum state, rather than as a Markovian hop between discrete attractors.
A notable refinement is the quantum tunnelling extension. This is physically instantiated as an electron in a double-well potential, with the two wells identified with distinct perceptual states. The measured probabilities of finding the electron in each well are interpreted as the probabilities for corresponding perceptual reports. Crucially, the inclusion of tunnelling and interference provides a mechanistically rigorous account of observed features: non-instantaneous (smooth) transitions detected via EEG and eye-tracking studies, variability in reversal rates, and the robust presence of unstable superposed (mixed) perceptual states. The model captures the irreducibility of perceptual switching—even with increased barrier heights (e.g., attentional modulation)—and offers a physically interpretable mechanism for perceptual bias and asymmetry.
Modelling Social Cognition and Opinion Dynamics
The oscillator formalism is generalized to the modelling of social behaviour. Here, cognitive states within individuals are represented as quantum states confined in potential wells; collective settings are modelled as networks of coupled wells and barriers, with the architecture reflecting the configuration of social influences and informational structure. The evolution from isolated, discrete energy-level spectra (representing individualized beliefs) into band structures with forbidden gaps (representing collective opinion distributions and polarization) is rigorously derived via finite-difference solutions to the Schrödinger equation.
This band-gap analogy leads to explicit, testable hypotheses: increased energetic (informational) cost is required to shift opinions entrained within forbidden ranges, corresponding to empirically observed "backfire effects" in political and risk-laden domains. This framework provides an interpretable mapping from physical parameters (e.g., barrier height, well depth, coupling strength) to behaviourally relevant phenomena such as echo chambers, group polarization, and the resilience of ideologically loaded beliefs.
A conceptual bridge is established to Khrennikov's social laser model, which treats collective amplification and coherence as quantum-like phenomena at the group scale. Here, the energy landscape of individual cognition determines microdynamics, while coupling and coherence generate macroscopic, network-level effects. The discrete oscillator and social laser frameworks are shown to be mutually compatible within a multi-scale quantum-cognitive modelling hierarchy.
Quantum-Cognitive Neural Networks and Machine Vision
A central technical contribution is the embedding of quantum-tunnelling oscillators as activation mechanisms within multilayer neural networks, resulting in an operational quantum-cognitive neural network. Unlike standard DNNs employing, e.g., ReLU or sigmoid nonlinearities, this architecture replaces the neuron’s activation function with a transmission coefficient derived from the exact tunnelling solution for a rectangular quantum barrier.
The resultant networks are trained and evaluated on both canonical bistable stimuli (Necker cube, Rubin's vase) and real-world ambiguous classification tasks (civilian versus military vehicles under adverse conditions). The output is a time-dependent probability sequence that exhibits switching dynamics and superposition in close qualitative agreement with human behavioural and neurodynamic data. Notably, the networks demonstrate robust performance on ambiguous real-world image classification tasks, with misclassification patterns that more closely match human errors compared to standard architectures. Specifically, the quantum-tunnelling networks are less prone to misclassifying clear cases and more likely to err on perceptually ambiguous examples, matching expectations from cognitive neuroscience.
Hyperparameters such as barrier height and number of training epochs modulate perceptual switching dynamics, offering a principled proxy for individual or group differences in cognitive processing (e.g., age, attention, experience).
Implications and Future Directions
The model offers concrete theoretical and practical advances. Theoretically, it demonstrates that quantum formalism provides a minimal, compact extension to existing frameworks, naturally supporting context sensitivity, superposition, and dynamic instability central to cognitive phenomena. Practically, quantum-cognitive neural networks broaden AI capabilities for uncertainty and ambiguity handling, with high interpretability and the potential for improved alignment with human-in-the-loop systems (e.g., decision-support in ambiguous real-world environments, modelling and mitigating social polarization, robust AI-human teaming in perception and classification).
The approach is directly extensible to recurrent network architectures for applications in sentiment analysis and LLMs, providing a rigorous pathway for embedding quantum-inspired mechanisms in state-of-the-art NLP systems.
A further extension is the use of physical quantum random number generators for neural weight initialization, introducing intrinsic quantum uncertainty and potentially capturing chaotic aspects of human cognitive dynamics in situations where standard pseudo-random approaches fail to produce the same variability.
Conclusion
This work articulates and operationalizes a unified quantum-tunnelling oscillator model for cognitive and social phenomena, bridging quantum cognition theory and neural computation. The approach is physically grounded and mathematically rigorous, overcoming limitations of deterministic and classical stochastic models, yielding high-fidelity reproduction of both perceptual and social regularities, and providing functional architectures for AI that effectively handle ambiguity and context dependence. The implications are both foundational for cognitive theory and immediately actionable for advanced neural computation and machine vision under uncertainty (2604.03940).