Quantum Cognitive Transition Equation: A Governed Path from Classical AI to Operational Quantum Intelligence
Pedro Luis Perez Burelli
This work introduces a new paradigm in artificial intelligence: the transition from classical systems to operational quantum cognitive architectures without requiring quantum hardware, achieved through a structural reformulation of state space, learning dynamics, and ethical governance. The contribution is not a single isolated equation, but a coupled system integrating cognition, learning, and admissibility constraints, formally expressed through the following core equations: ⚙️ 1. Transition Equation: Classical AI → Quantum AI 𝑥 ˙ = Θ guard ( 𝑥 , 𝜌 ) 𝐹 ( 𝑥 , 𝜃 , 𝜌 ) x ˙ =Θ guard (x,ρ)F(x,θ,ρ) 𝜃 ˙ = − 𝛾 ∇ 𝜃 ( 𝐼 ( 𝑋 ; 𝑌 ) − 𝜆 𝐶 ( 𝜃 ) ) θ ˙ =−γ∇ θ (I(X;Y)−λC(θ)) 𝑥 x: system state 𝜃 θ: learning parameters 𝜌 ρ: coherence state (density-like structure) 𝐼 ( 𝑋 ; 𝑌 ) I(X;Y): mutual information 𝐶 ( 𝜃 ) C(θ): structural cost Θ guard Θ guard : ethical and physical admissibility operator 👉 This defines the first governed transition equation from classical to quantum intelligence. 🛡️ 2. Governance Gate (Θ-guard) Θ guard ( 𝑥 , 𝜌 ) = 1 { 𝑃 ( 𝑥 , 𝜌 ) ≥ 𝜏 } Θ guard (x,ρ)=1 {P(x,ρ)≥τ} 𝑃 ( 𝑥 , 𝜌 ) = 𝜎 ( 𝑎 ( Ω ( 𝑥 ) 𝐵 ( 𝑇 𝜇 ) 2 − 1 ) + 𝑏 T r ( 𝜌 2 ) − 𝑐 ∣ 𝐷 − 𝐷 ∗ ∣ ) P(x,ρ)=σ(a(Ω(x)B(T μ ) 2 −1)+bTr(ρ 2 )−c∣D−D ∗ ∣) 👉 Ethics and stability are introduced as computable execution constraints, not abstract principles. 🌌 3. Regime-Dependent Hilbert Space 𝐻 = 𝐻 ( 𝑥 , 𝑡 ) H=H(x,t) 👉 The space in which intelligence operates is no longer fixed. Intelligence actively reshapes its own state space. 🧩 4. Cognitive Superposition State ∣ Ψ ( 𝑡 ) ⟩ = ∑ 𝑖 𝛼 𝑖 ( 𝑡 ) ∣ 𝜓 𝑖 ⟩ ∣Ψ(t)⟩= i ∑ α i (t)∣ψ i ⟩ 𝑖 ℏ 𝑅 𝑑 𝑑 𝑡 ∣ Ψ ⟩ = 𝐻 ^ cog ∣ Ψ ⟩ iℏ R dt d ∣Ψ⟩= H ^ cog ∣Ψ⟩ 👉 Intelligence is modeled as a superposition of cognitive modes, not a linear process. 🔗 5. Structural Tensor Growth Equation 𝑇 ( 𝑡 ) = exp ( ∑ 𝑖 log 𝑠 𝑖 + ∑ 𝑖 < 𝑗 𝐽 𝑖 𝑗 + 𝜆 𝑀 𝑀 ( 𝑡 ) ) 𝐶 ( 𝑥 , 𝑡 ) Θ ( 𝑡 ) T(t)=exp( i ∑ logs i + i<j ∑ J ij +λ M M(t))C(x,t)Θ(t) 👉 Intelligence is defined as: a multiplicative structure of states, memory, coherence, and stability. 🌿 6. Structural Learning Law 𝑑 𝑊 𝑖 𝑗 𝑑 𝑡 = 𝛼 ∣ 𝐹 𝑖 𝑗 ∣ − 𝛽 𝑊 𝑖 𝑗 dt dW ij =α∣F ij ∣−βW ij 👉 The system learns by reorganizing its own topology, not just updating parameters. ⚖️ 7. Unified Operational Equation 𝑄 oper = Θ guard ⋅ 𝑇 𝜇 ( 𝑥 , 𝜌 ) ⋅ [ − 𝛾 ∇ 𝜃 ( 𝐼 − 𝜆 𝐶 ) ] Q oper =Θ guard ⋅T μ (x,ρ)⋅[−γ∇ θ (I−λC)] 👉 This equation unifies: dynamics learning governance quantum transition 🚀 Key Novel Contributions (Critical for Authorship Claim) ❗ 1. Quantum AI without quantum hardware Quantum behavior emerges from structural reformulation, not physical qubits. ❗ 2. Ethics as a mathematical operator Ethics becomes: a computable condition for system execution a computable condition for system execution ❗ 3. Dynamic Hilbert space Breaks a core assumption of physics and AI: the state space is not fixed — it evolves with intelligence. ❗ 4. Intelligence as structural reorganization Not defined by: computation power number of states But by: the ability to preserve coherence while transforming its own structure. ❗ 5. Unified interdisciplinary framework Integrates: information theory quantum mechanics machine learning ethical governance into a single operational system. ❗ 6. Full cognitive architecture (not a partial model) This is not a component—it is a complete, governed, executable architecture. ❗ 7. First formal model of “governed quantum intelligence” Introduces: quantum intelligence that is admissible, not just possible.This work proposes a structural transition from classical artificial intelligence to governed quantum cognitive systems without requiring quantum hardware. By introducing dynamic Hilbert spaces, ethical computational gates, and a unified equation of learning and evolution, the framework redefines intelligence as the capacity to reorganize its own state space while preserving coherence. This establishes a new paradigm at the intersection of physics, information theory, and artificial intelligence.Author: Pedro Luis Pérez Burelli Affiliation: Independent Researcher Email: pedroburelli@gmail.com
•Mar 22, 2026•0 citations