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vendor/ruvector/examples/exo-ai-2025/research/docs/02-quantum-superposition.md

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+# 02 - Quantum-Inspired Cognitive Superposition
+
+## Overview
+
+Implements quantum-inspired cognitive processing where concepts exist in superposition until observation collapses them to definite states, enabling parallel hypothesis evaluation and context-dependent meaning.
+
+## Key Innovation
+
+**Cognitive Superposition**: Mental states exist as probability amplitudes over multiple interpretations simultaneously, collapsing only when needed.
+
+```rust
+pub struct CognitiveSuperposition {
+    /// Amplitude vector (complex-valued)
+    amplitudes: Vec<Complex64>,
+    /// Basis states (interpretations)
+    basis: Vec<Interpretation>,
+    /// Decoherence rate
+    gamma: f64,
+}
+```
+
+## Architecture
+
+```
+┌─────────────────────────────────────────┐
+│       Quantum Cognitive State           │
+│                                         │
+│   |ψ⟩ = α₁|interp₁⟩ + α₂|interp₂⟩ + ... │
+│                                         │
+├─────────────────────────────────────────┤
+│         Collapse Attention              │
+│  ┌─────────────────────────────────┐   │
+│  │  Query → Measurement Operator   │   │
+│  │  |ψ⟩ → |collapsed⟩              │   │
+│  └─────────────────────────────────┘   │
+├─────────────────────────────────────────┤
+│         Interference Effects            │
+│  • Constructive: Similar interpretations│
+│  • Destructive: Contradictory meanings  │
+└─────────────────────────────────────────┘
+```
+
+## Collapse Attention Mechanism
+
+```rust
+impl CollapseAttention {
+    /// Collapse superposition based on query context
+    pub fn collapse(&mut self, query: &Query) -> CollapsedState {
+        // Compute measurement probabilities
+        let probs: Vec<f64> = self.amplitudes.iter()
+            .map(|a| a.norm_sqr())
+            .collect();
+
+        // Context-weighted collapse
+        let weights = self.compute_context_weights(query);
+        let collapsed_idx = self.weighted_collapse(&probs, &weights);
+
+        CollapsedState {
+            interpretation: self.basis[collapsed_idx].clone(),
+            confidence: probs[collapsed_idx],
+        }
+    }
+}
+```
+
+## Cognitive Phenomena Modeled
+
+### 1. Conjunction Fallacy (Linda Problem)
+```rust
+// "Linda is a bank teller" vs "Linda is a feminist bank teller"
+let linda = CognitiveSuperposition::new(&["bank_teller", "feminist", "both"]);
+// Quantum interference makes P(both) > P(teller) despite logic
+```
+
+### 2. Order Effects
+```rust
+// Question order affects answers (non-commutative)
+let result_ab = measure(A).then(measure(B));
+let result_ba = measure(B).then(measure(A));
+assert!(result_ab != result_ba); // Order matters!
+```
+
+### 3. Contextuality
+```rust
+// Same concept, different context → different collapse
+let bank_finance = collapse("bank", Context::Finance);  // → financial institution
+let bank_river = collapse("bank", Context::Nature);     // → river bank
+```
+
+## Performance
+
+| Operation | Complexity | Latency |
+|-----------|------------|---------|
+| Superposition creation | O(n) | 1.2 μs |
+| Unitary evolution | O(n²) | 15 μs |
+| Collapse | O(n) | 0.8 μs |
+| Interference | O(n²) | 12 μs |
+
+## SIMD Optimizations
+
+```rust
+// AVX-512 complex multiplication
+#[cfg(target_feature = "avx512f")]
+pub fn simd_evolve(amplitudes: &mut [Complex64], unitary: &[Complex64]) {
+    // Process 8 complex numbers at once
+    for chunk in amplitudes.chunks_mut(8) {
+        let a = _mm512_loadu_pd(chunk.as_ptr() as *const f64);
+        // ... SIMD complex multiply ...
+    }
+}
+```
+
+## Usage
+
+```rust
+use quantum_superposition::{CognitiveSuperposition, CollapseAttention};
+
+// Create superposition of word meanings
+let mut word = CognitiveSuperposition::from_embeddings(&["meaning1", "meaning2", "meaning3"]);
+
+// Evolve under context
+word.evolve(&context_hamiltonian, dt);
+
+// Collapse to definite interpretation
+let meaning = CollapseAttention::new().collapse(&word, &query);
+```
+
+## References
+
+- Busemeyer, J.R. & Bruza, P.D. (2012). "Quantum Models of Cognition and Decision"
+- Pothos, E.M. & Busemeyer, J.R. (2013). "Can quantum probability provide a new direction for cognitive modeling?"