Minimal, reproducible Variational Quantum Eigensolver (VQE) implementation using Qiskit Nature to compute the ground-state energy of the hydrogen molecule (H₂) in the minimal STO-3G basis.
Demonstrates:
- Full quantum chemistry pipeline: PySCF driver → second-quantized Hamiltonian → Jordan-Wigner mapping → UCCSD ansatz + HartreeFock initial state → VQE optimization
- Achieving chemical accuracy (~1 mHa or better) compared to exact classical diagonalization
| Ansatz / Configuration | Optimizer | Iterations | Energy (Hartree) | Error (mHa) |
|---|---|---|---|---|
| TwoLocal (rz/ry + cz, reps=4) | COBYLA | 500 | -1.624377 | 228 |
| UCCSD (reps=1) + HF initial | SLSQP | 1000 | -1.852... | ~0–1 |
| Exact (classical) | — | — | -1.8523881735695822 | 0 |
Chemical accuracy achieved with UCCSD ansatz — error reduced from 228 mHa to near-zero.
- Classic benchmark for quantum chemistry algorithms (H₂ in STO-3G)
- Shows transition from general-purpose ansatz → chemistry-aware UCCSD for dramatically better convergence
- Baseline for exploring quantum advantages in molecular simulation, optimization, and related domains (e.g., energy minimization in FinOps models, anomaly detection in quantum-enhanced ML)
- Quantum Chemistry: Qiskit Nature 0.7+, PySCFDriver, UCCSD, HartreeFock
- Algorithms: Qiskit Algorithms (VQE, COBYLA/SLSQP, NumPyMinimumEigensolver)
- Simulation: qiskit-aer (AerEstimator with V1 compatibility wrapper)
- Environment: Python 3.10+, Jupyter/Colab
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Open in Colab:
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Install dependencies (first cell):
!pip install qiskit-nature qiskit-aer pyscf qiskit-algorithms --quiet
