VQE for H2O Molecule (Active Space)

Overview

Water (H₂O) is a 10-electron system that would require ~14 qubits for full simulation. This circuit demonstrates the active space approach, which reduces the problem to 4 qubits while capturing most of the electron correlation energy.

Active Space Approximation

Full H₂O has:

• 10 electrons
• ~14 spin-orbitals (minimal basis)
• Too large for current quantum computers

Active space (4e, 4o):

• 4 active electrons (valence)
• 4 active orbitals
• 6 frozen core electrons
• Reduces to 4 qubits

The Ansatz

Hardware-efficient ansatz with enhanced entanglement:

CODECopy
Layer 1:        Layer 2:
┌─────┐         ┌─────┐
┤ RY  ├──●──●──┤ RY  ├──●──●──
├─────┤  │  │  ├─────┤  │  │
┤ RY  ├──X──●──┤ RY  ├──X──●──
├─────┤     │  ├─────┤     │
┤ RY  ├──●──X──┤ RY  ├──●──X──
├─────┤  │     ├─────┤  │
┤ RY  ├──X─────┤ RY  ├──X─────
└─────┘        └─────┘

Running the Circuit

PYTHONCopy
from circuit import run_circuit

result = run_circuit()
print(f"Energy: {result['energy']:.4f} Ha")
print(f"Active space: {result['active_space']}")

Expected Output

Why Active Space?

The full H₂O Hamiltonian is intractable on current hardware, but:

• Core electrons (O 1s) don't participate in bonding
• "Freezing" them reduces qubit count
• Active space captures ~95%+ of correlation energy

Applications

• Water chemistry: Foundation for aqueous simulations
• Hydrogen bonding: Understanding water's unique properties
• Benchmark: Standard test for active space methods

Scaling to Real Molecules

Learn More

• Active Space Methods in Quantum Chemistry
• Qiskit Nature: Active Space Transformers