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Quantum-Tunnelling Oscillators for Cognitive Modelling and Neural Computation: Foundations, Machine-Vision Realisation and Applications

The paper proposes a quantum-tunnelling oscillator model as a universal dynamical engine for cognitive systems, demonstrating how networked quantum-mechanical agents can effectively simulate complex phenomena like optical illusions and group decision-making by utilizing context-dependent transitions that surpass classical probabilistic models.

Original authors: Ivan S. Maksymov

Published 2026-04-07

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Ivan S. Maksymov

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Idea: The Human Brain as a "Quantum Radio"

Imagine your brain isn't a standard computer that processes information like a calculator (1 + 1 = 2). Instead, imagine it's more like a radio tuner trying to find a signal in a storm of static.

The author, Ivan Maksymov, proposes a new way to understand how humans make decisions, see optical illusions, and form opinions in groups. He suggests that our minds don't just flip a coin to decide; they exist in a state of "superposition" (being in two places at once) until something forces a decision.

To model this, he uses a concept from physics called Quantum Tunnelling.

1. The Problem: Why We Change Our Minds

Have you ever looked at an optical illusion, like the famous Necker Cube (a wireframe cube that looks like it's pointing up, then suddenly flips to point down)?

Classical View: A traditional computer model would say, "The cube is either pointing up OR pointing down." It's a binary choice.
The Reality: When humans look at it, our brains don't just flip instantly. We hover in a state of confusion. We see both possibilities at the same time for a split second before our brain "collapses" the image into one version.

Furthermore, if you ask someone to make a decision today, and then ask them the exact same question tomorrow, they might give a different answer. Classical theories say this is a mistake or random noise. This paper says: No, this is a feature, not a bug. Our minds are naturally fluid and uncertain until we are forced to choose.

2. The Solution: The "Quantum Tunnel"

To explain this fluidity, the author uses a physics metaphor: The Ball in the Bowl.

The Classical Ball: Imagine a ball rolling in a bowl with a small hill in the middle. If the ball doesn't have enough energy to roll over the hill, it stays stuck on one side. It can never get to the other side.
The Quantum Ball: In the quantum world, particles (like electrons) are weird. Even if they don't have enough energy to go over the hill, they can sometimes tunnel through it and appear on the other side.

The Metaphor for the Brain:
Think of your two possible choices (e.g., "I like this" vs. "I dislike this") as two valleys separated by a hill.

In a normal brain, you might get stuck in one valley.
In this Quantum-Tunnelling Model, your mind can "tunnel" through the barrier of doubt. You don't just jump from one opinion to another; you drift through the uncertainty, exploring both sides simultaneously before settling on one.

3. Real-World Application: The "Social Bubble"

The paper takes this idea and applies it to how groups of people (like on social media) think.

Imagine a Social Bubble (or Echo Chamber) as a series of connected rooms with walls between them.

Inside the Bubble: You are in a room with your friends. The walls are thick. It's hard to "tunnel" out to hear a different opinion.
The Model: The author simulates this using "potential wells" (the rooms). When people interact, the walls between their opinions get thinner or thicker.
The Result: If the walls are too thick, the group gets "polarized." They can't tunnel to the other side, so they get stuck in extreme beliefs. If the walls are thin (open to new info), opinions can flow and mix.

This explains why it's so hard to change someone's mind in a heated political debate—the "barrier" between their belief and your fact is too high for them to tunnel through.

4. The Machine Vision Test: Teaching AI to "See" Like Us

The author didn't just stop at theory; he built a Neural Network (a type of AI) that uses these quantum rules.

The Test:
He trained the AI to look at pictures of military trucks and civilian trucks. In a war zone, these can look very similar (especially in fog or smoke).

Standard AI: Tries to force a quick decision. "Is it a truck? Yes/No." It often makes mistakes because it's too rigid.
Quantum AI: This AI "hesitates." It looks at the image and says, "Hmm, it's 60% civilian and 40% military." It sits in that uncertain state, oscillating back and forth, just like a human staring at an optical illusion.

Why is this better?
When the AI finally makes a decision, it's often more accurate in ambiguous situations. It mimics the human ability to say, "I'm not sure yet, let me look closer," rather than guessing immediately.

5. The Personal Motivation

The author mentions a deeply personal reason for this work. He is from Ukraine and is watching the war from Australia. He noticed how the "cognitive environment" of his country changed so drastically that friends and family became unrecognizable in their views.

He wanted to build a mathematical model that could explain why people change their minds so drastically under pressure, and how to build machines that understand human uncertainty, rather than just treating humans as error-prone robots.

Summary: The "Takeaway"

This paper argues that to truly understand human thinking (and to build better AI), we need to stop treating the brain like a calculator and start treating it like a quantum wave.

Uncertainty is normal: It's okay to be in two minds at once.
Decisions are tunnels: We don't just jump; we drift through barriers of doubt.
AI needs to hesitate: The best AI for complex, real-world problems might be the one that isn't afraid to be unsure for a moment.

By using the physics of particles tunneling through walls, the author gives us a new lens to see why we argue, why we see illusions, and how we can build machines that think more like us.

1. Problem Statement

The paper addresses the limitations of classical deterministic decision theories (such as Expected Utility Theory and Cumulative Prospect Theory) in explaining human behavior under uncertainty. Classical models assume stable preferences, yet empirical evidence shows that individuals often exhibit:

Choice variability: Revising decisions when identical problems are repeated.
Context dependence: Choices shifting based on framing or prior exposure.
Bistable perception: Ambiguous figures (e.g., Necker cube) inducing spontaneous, seemingly random perceptual reversals.
Social polarization: The formation of "social bubbles" where beliefs become entrenched and resistant to contradictory information.

The author argues that these phenomena are better modeled using Quantum Cognition Theory, which utilizes the mathematical formalism of quantum mechanics (superposition, interference, and context-dependent transitions) rather than physical claims that the brain is a quantum computer. Specifically, the paper seeks to bridge the gap between abstract quantum cognitive models and physically grounded, computationally tractable systems that can be implemented in machine learning.

2. Methodology

The author develops a multi-layered framework progressing from physical modeling to neural network implementation:

A. The Quantum-Tunnelling Oscillator Model

Physical Basis: The model treats cognitive states as a quantum particle (electron) evolving in a potential well governed by the Schrödinger equation.
Single vs. Double Well:
- A single parabolic well models harmonic oscillation between states.
- A double parabolic potential well with a central barrier is introduced to model bistable perception (e.g., the Necker cube).
Quantum Tunnelling: Unlike classical particles that require energy to cross a barrier, the quantum particle can tunnel through the barrier. This creates a continuous, probabilistic transition between states $|0\rangle$ and $|1\rangle$ (representing two perceptual interpretations).
Simulation: The author uses the Finite-Difference Time-Domain (FDTD) method to numerically solve the Schrödinger equation, simulating the wave packet's evolution, probability density, and tunneling rates.

B. Social Network Modelling

Tabula Rasa to Structure: The model conceptualizes an individual's mind as a "blank slate" (continuous spectrum) that becomes structured into discrete belief states when confined by social environments (potential wells).
Network Dynamics: A social network is modeled as a sequence of coupled potential wells. Interactions between individuals modify the energy levels (beliefs) of the system.
Opinion Polarization: The emergence of forbidden energy gaps in the collective spectrum is used to model opinion polarization, where certain belief states become energetically "forbidden" or resistant to change, mimicking the "backfire effect."

C. Quantum-Cognitive Neural Networks (QT-NN)

Architecture: A deep neural network is constructed where the activation function of hidden neurons is replaced by the quantum tunneling transmission coefficient ( $T$ ) derived from the Schrödinger equation.
Mechanism: Instead of standard non-linearities like ReLU, neuron activation is determined by the probability of an electron tunneling through a potential barrier. This introduces intrinsic non-linearity and stochasticity.
Training: The network uses standard backpropagation with cross-entropy loss, but the gradient calculation involves the derivative of the tunneling transmission coefficient.
Initialization: The author proposes using quantum random number generators to initialize weights, introducing genuine chaotic dynamics to avoid periodic repetition in predictions.

3. Key Contributions

Unified Physical Framework: The paper provides a rigorous physical derivation (via the Schrödinger equation) for quantum cognitive models, moving beyond abstract probability axioms to a dynamical systems approach.
Tunneling as a Cognitive Mechanism: It explicitly links quantum tunneling to the mechanism of perceptual switching and decision reversal, offering a mathematical explanation for the smooth, continuous dynamics observed in eye-tracking and neural data during ambiguity resolution.
Social Bubble Simulation: It demonstrates how coupled quantum wells can simulate the formation of social bubbles and the hardening of opinions (polarization) through the creation of energy gaps in the belief spectrum.
Novel Neural Architecture: The introduction of a Quantum-Tunnelling Neural Network where the activation function is physically grounded in quantum mechanics, bridging quantum cognition theory with deep learning.
Application to Real-World Ambiguity: The model is tested not just on optical illusions but on a custom dataset of ambiguous military vs. civilian vehicles in conflict zones, demonstrating practical utility in high-stakes machine vision.

4. Results

Optical Illusions (Necker Cube & Rubin's Vase):
- The QT-NN successfully reproduces the time-dependent switching between perceptual states observed in humans.
- The network outputs oscillate between $|0\rangle$ and $|1\rangle$ , passing through intermediate superposition states, rather than making abrupt binary switches.
- Increasing the "barrier thickness" (simulating attention or aging) slows the switching rate, mimicking human perceptual latency.
Social Network Dynamics:
- Simulations show that as individuals interact (wells couple), their discrete energy levels evolve into quasi-continuous bands with forbidden gaps.
- Introducing a "perturbed" well (conflicting information) fails to bridge these gaps easily, modeling the resistance to changing entrenched opinions.
Machine Vision (Military vs. Civilian Trucks):
- The QT-NN was trained to classify trucks in combat zones (fog, smoke, ambiguity).
- Error Analysis: The QT-NN made "human-like" errors. It misclassified civilian trucks with ambiguous features (e.g., dark cabins, missile-like cargo) as military, whereas traditional networks misclassified obvious civilian trucks.
- The model's behavior suggests it captures the contextual uncertainty and "reasonable doubt" inherent in human decision-making under stress, rather than just pattern matching.

5. Significance

Theoretical Advancement: The paper validates quantum cognition theory by grounding it in a solvable physical model (quantum oscillators) and demonstrating its equivalence to observed psychological phenomena.
AI and Human-Machine Teaming: The proposed QT-NN offers a new class of AI that mimics human cognitive flexibility and ambiguity handling. This is crucial for applications like drone warfare, where distinguishing between civilian and military targets in ambiguous conditions requires a "human-like" ability to weigh uncertainty rather than rigid binary classification.
Social Science Implications: The model provides a quantitative tool for understanding the mechanics of polarization and echo chambers, suggesting that breaking these cycles requires "energy" (information diversity) sufficient to overcome the quantum-like energy barriers of social belief systems.
Interdisciplinary Bridge: It successfully integrates physics (quantum mechanics), psychology (cognitive theory), and computer science (deep learning), offering a compact, physically grounded framework for modeling complex cognitive and social systems.

In conclusion, Maksymov presents a robust framework where quantum tunneling serves as the dynamical engine for cognitive switching. By translating this into a neural network architecture, the paper demonstrates that quantum-inspired models can outperform or better align with human behavior in tasks involving ambiguity, social influence, and high-stakes decision-making.