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Update lipkin.do.txt
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doc/src/week7/lipkin.do.txt

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TITLE: Lipkin Model Notebook (DocOnce Conversion)
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AUTHOR:
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DATE:
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TITLE: Lipkin Model Notebook
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AUTHOR: Morten Hjorth-Jensen
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DATE: Spring 2026
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# VQE for Lipkin Model: Complete Working Implementation
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- **Computational basis measurements** with proper basis rotations
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- **4-layer hardware-efficient ansatz** (24 parameters)
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## Key Corrections Applied:
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1. ✅ **Proper CNOT gates** (correct tensor products)
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2. ✅ **4-layer ansatz** (sufficient expressivity)
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3. ✅ **Correct Y measurement** (H·S†, not S†·H)
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## Expected Results:
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- Exact ground state: **E₀ = -3.0**
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- VQE (exact evaluation): **-3.0000** (error < 10⁻¹⁰)
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- VQE (with shots): **~-2.95 to -3.00** (depending on shots and optimization)
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## 1. Imports and Setup
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## 13. Summary
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### ✅ All Critical Bugs Fixed:
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1. **CNOT Gates:** Proper 3-qubit gates using `kron(CNOT_2qubit, I)`
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2. **Ansatz Depth:** 4 layers (24 parameters) for sufficient expressivity
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3. **Y Measurement:** H·S† rotation (NOT S†·H, NOT H·S)
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### 📊 Results:
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- **Exact energy:** -3.0000000000
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- **VQE (exact eval):** Essentially exact (error < 10⁻⁹)
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- **VQE (with shots):** Within shot noise of ground state
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### 🔬 Physical System:
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- **j = 2** (N = 4 particles)
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- **5D quasi-spin space** encoded in 3 qubits
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- **Ground state:** Superposition of |000⟩, |010⟩, |100⟩
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- **Correlation energy:** -1.0 (reference state at -2.0)
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### ✓ Verification:
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- Hamiltonian is Hermitian ✓
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- Pauli coefficients all real ✓
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- Measurements preserve variational principle ✓
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- VQE converges to ground state ✓

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