quantum-cognition

name

quantum-cognition

description

Quantum cognition methodology for modeling cognitive processes using quantum probability theory. Combines neuroscience insights with quantum information formalism to model decision making, context-dependent reasoning, mental state dynamics, and non-classical cognitive correlations. Use when: (1) modeling cognitive phenomena that violate classical probability (order effects, conjunction fallacy), (2) building quantum-like models of decision making, (3) analyzing contextuality in mental representations, (4) designing quantum neural architectures for brain-inspired computing, (5) studying quantum effects in biological systems (radical-pair mechanism, cryptochrome), (6) implementing quantum photonic neural networks for neuromorphic computing.

Quantum Cognition

Model cognitive processes using quantum probability theory and quantum information formalism. This methodology spans two interpretations: quantum-like cognition (informational) and physical quantum brain hypotheses.

Two Paradigms

1. Quantum-Like Cognition (Informational)

Uses quantum formalism to model cognition without claiming quantum processes in the brain. Based on Khrennikov's framework: mental contexts induce non-classical correlations analogous to quantum entanglement. Key insight: incompatible measurements arise naturally from context-dependent mental representations.

When to use: decision making, judgment under uncertainty, concept combinations, cognitive biases, order effects in survey responses.

2. Physical Quantum Brain Hypotheses

Proposes actual quantum coherence in biological substrates. Wakaura (2026) evaluates CQEC (covariant quantum error correction) in radical-pair proteins MAO-A and cryptochrome. Key finding: CQEC can maintain coherence over 200ms behavioral windows, but layer-protein tradeoffs exist — no single protein optimizes all layers.

When to use: biophysical modeling of neural processes, radical-pair mechanism analysis, quantum error correction in biological systems.

Core Mathematical Framework

Quantum Probability Model

Replace classical Kolmogorov probability with quantum probability:

import numpy as np

def quantum_probability(state_vector, projector):
    """P(outcome) = |<outcome|state>|^2 = ||projector @ state||^2"""
    return np.abs(np.dot(projector, state_vector))**2

def interference_effect(p_A, p_B, theta):
    """Classical: p = p_A + p_B
       Quantum: p = p_A + p_B + 2*sqrt(p_A*p_B)*cos(theta)"""
    return p_A + p_B + 2 * np.sqrt(p_A * p_B) * np.cos(theta)

Contextuality Detection

Bell-CHSH inequality violation indicates non-classical correlations:

def chsh_inequality(E_ab, E_ab_prime, E_a_prime_b, E_a_prime_b_prime):
    """|S| = |E(ab) - E(ab') + E(a'b) + E(a'b')| <= 2 (classical)
       Quantum bound: |S| <= 2*sqrt(2) (Tsirelson bound)"""
    S = abs(E_ab - E_ab_prime + E_a_prime_b + E_a_prime_b_prime)
    return S, S > 2.0, S <= 2 * np.sqrt(2)

Cognitive State Evolution

Mental states evolve via unitary transformations (closed system) or Lindblad dynamics (open system):

from scipy.linalg import expm

def mental_state_evolution(H, psi_0, t):
    """|psi(t)> = exp(-iHt)|psi(0)> — unitary evolution"""
    U = expm(-1j * H * t)
    return U @ psi_0

Quantum Photonic Neural Networks (QPNN)

Boras Vazquez et al. (2026): time-bin-encoded QPNN for quantum information processing.

Key architectural insight: time-encoded networks use constant number of photonic elements regardless of size/depth, enabling scaling. Trained via realistic nonlinearities (quantum dot + waveguide) to achieve 0.96+ fidelity Bell-state analysis.

def qpnn_architecture(n_modes, depth, nonlinearity="kerr"):
    """Time-bin QPNN: same elements regardless of network depth.
    Layers: (1) time-delay interferometer, (2) phase shifters,
    (3) nonlinear element (Kerr or quantum dot scattering)"""
    # Each time step processes one mode through same physical elements
    # Complexity: O(n_modes * depth) elements, not O(n_modes * depth) physical components
    return {
        "encoding": "time-bin",
        "elements": "constant with depth",
        "nonlinearity": nonlinearity,
        "fidelity": ">0.96 (realistic), >0.99 (time-gated)"
    }

Quantum Error Correction in Biological Systems

CQEC protocol for radical-pair proteins:

1. Three-layer architecture: nuclear spin memory → electron spin interface → electrochemistry
2. Coherence preservation: CQEC extends T2 coherence beyond decoherence rate
3. Layer-protein tradeoff: CRY has longer T2 (52ms) but shorter T1 (0.53ns); MAO-A has opposite
4. Behavioral threshold: 200ms Schultze-Kraft veto window is the minimum coherence requirement

Decision Making Patterns

Order Effects

P(A then B) ≠ P(B then A) — classical commutativity violation
Quantum: P(A then B) = ||P_B P_A |psi>||^2 ≠ ||P_A P_B |psi>||^2

Conjunction Fallacy

Linda problem: P(bank teller AND feminist) > P(bank teller) Explained by quantum interference between mental representations.

Disjunction Effect

Violation of sure-thing principle in decision making under uncertainty. Traditionally modeled via quantum interference term in probability calculation.

Updated (2026-06-29): arXiv:2603.23233 proves that a classical probability model with continuous expectation parameter partitioning reproduces the disjunction effect exactly. Classical and quantum-like models have identical observable expressiveness — their substantive difference is ambiguity representation (expectation partitions vs quantum superposition states), not probability law violation. Key insight: when comparing classical vs quantum-like decision models, the disjunction effect alone cannot distinguish them; look for structural differences in event semantics instead.

See classical-disjunction-effect-model skill for the full classical model.

Application Workflow

1. Identify classical probability violation in cognitive data
2. Construct quantum state space (Hilbert space dimension = number of distinguishable outcomes)
3. Define mental state vector and measurement projectors
4. Fit interference parameters to empirical data
5. Validate with contextuality tests (Bell-CHSH, Leggett-Garg inequalities)
6. Predict novel effects (order reversal, compatibility effects)

Key Findings from Literature

• CQEC coherence: 0.83 at decoherence rate 0.19 (6.9x improvement over uncorrected)
• QPNN fidelity: 0.96 with realistic nonlinearity, 0.99+ with time gating
• Contextuality: Mental markers exhibit quantum-like incompatibility without physical quantum processes
• Layer tradeoff: No single radical-pair protein optimizes both T1 and T2 coherence times

References

See references/ for detailed mathematical derivations and implementation guides.

Confirmation Bias as Optimal Evidence (arXiv:2606.23325)

• Skill: confirmation-bias-quantum-probability
• Confirmation bias emerges from optimal evidence selection on square-root probability space
• Sequential hypothesis testing: minimum memory capacity + exponential error reduction
• Active inference (max info) = error-minimizing evidence choice

Classical Disjunction Effect Model (arXiv:2603.23233)

• Skill: classical-disjunction-effect-model
• Classical model reproduces disjunction effect without violating law of total probability
• Introduces continuous expectation parameter replacing certainty-only premise
• Classical and quantum-like models have equal observable expressiveness

Recent Papers (2026)

• arXiv:2601.10588 - Searching for Quantum Effects in the Brain: A Bell-Type Test for Nonclassical Latent Representations in Autoencoders → See quantum-nonclassicality-latent-test skill
• arXiv:2605.23943 - Spacetime Formation under Requirements: Contextual Realization and Form-Dependent Probability (quantum cognition as fixed-spacetime projection)
• arXiv:2605.29877 - Verifying Adversarial Robustness in QML → See qml-adversarial-robustness-verification skill
• arXiv:2605.29557 - Quantum Subliminal Learning → See quantum-subliminal-learning skill
• arXiv:2605.24152 - Neuro-Inspired Inverse Learning for Planning and Control → See neuro-inspired-inverse-learning skill

Overlap alerts:

• confirmation-bias-quantum-probability (2606.23325) and quantum-like-associative-benchmark-adaptive (2606.12449) both address quantum probability models of cognitive biases — candidate for consolidation.
• quantum-opinion-dynamics-networks (2607.01452) ↔ quantum-probability-statistics — both use density matrix formalism for non-classical correlations.

Quantum Opinion Dynamics on Networks (arXiv:2607.01452)

• Cognitive states as density matrices in networked multi-agent systems
• Each agent's cognitive state = density matrix encoding expressed opinion + cognitive ambivalence
• Survey questions = non-commuting self-adjoint operators → principled explanation for order effects
• Under product state approximation, reduces to classical Friedkin-Johnsen opinion model
• Quantum coherence decays exponentially at network-independent rate; pairwise correlations converge to network-independent steady state
• Activation: "quantum opinion dynamics", "quantum social networks", "density matrix opinion", "cognitive ambivalence network"

Tensor Network Emotional Memory (arXiv:2606.28470)

• Skill: quantum-emotional-memory-tensor-networks
• Tensor networks model order-dependent emotional memory in children (77.98% accuracy)
• Emotional valence influences memory for adjacent items in a sequence
• Quantum-inspired method (not strictly quantum cognition) for order-dependent phenomena
• Novel task protocol for exploring emotional temporal memory in children

Quantum Structure in AI Language (arXiv:2511.21731)

• Skill: quantum-structure-in-ai-language
• LLMs violate Bell inequalities in conceptual combination tests (ChatGPT, Gemini)
• Word distributions follow Bose-Einstein statistics, not Maxwell-Boltzmann
• Evolutionary convergence: quantum-like meaning organization emerges in both human and artificial cognition
• Key insight: meaning-bearing vector spaces exhibit quantum organization regardless of physical substrate
• Extends quantum cognition from human to artificial intelligence
• See references/quantum-structure-in-ai-language.md for detailed analysis

Self-Modulating QFWP with Bounded Memory (arXiv:2607.02363)

• Quantum Fast-Weight Programmers store temporal info in circuit parameters, not recurrent hidden states
• Unbounded self-modulating QFWP diverges on long sequences; bounded variant uses sign-preserving tanh gate on recurrent memory branch
• Old-state modulation is key mechanism for improvement over standard QFWP
• Activation: "quantum fast weight", "QFWP", "bounded memory gate", "quantum sequence modeling"
• Related skill: quantum-fast-weight-memory-gates

XOR Games and Nonlocal Game Complexity (arXiv:2607.06876)

• Skill: tilted-xor-games
• Tilted XOR games (winning condition depends on XOR + one output bit) are RE-complete for quantum value approximation
• Standard XOR games are polynomial-time approximable; the single-bit extension creates dramatic complexity gap
• Classical complexity unchanged (both NP-complete) — the separation is purely quantum
• Relevance to cognition: Nonlocal games provide the mathematical foundation for contextuality tests (Bell-CHSH) used in quantum cognition. Tilted XOR results inform the limits of quantum vs classical cognitive model expressiveness.
• Related skill: quantum-opinion-dynamics-networks (density matrix formalism for networked cognition)