The Unitary Coupled Cluster Singles and Doubles (UCCSD) ansatz is the gold standard for quantum chemistry simulations. It systematically includes electron correlation effects through single and double excitation operators.
| Property | Value |
|---|
| Category | Ansatz |
| Difficulty | Advanced |
| Framework | Cirq |
| Qubits | 4 |
| Depth | O(n⁴) |
| Gates | RY, RZ, CNOT |
Where:
T = T₁ + T₂
T₁ = Σ θ_ia a†_a a_i (single excitations)
T₂ = Σ θ_ijab a†_a a†_b a_j a_i (double excitations)
q_i: ──●──RY(θ)──●──
│ │
q_a: ──X─────────X──
q_0: ──●────────────●──
│ │
q_1: ──X──●─────●──X──
│ │
q_2: ─────X─RZ──X─────
│ │
q_3: ─────●─────●─────
from circuit import run_circuit
result = run_circuit(n_qubits=4, n_electrons=2)
print(f"Singles: {result['n_singles']}")
print(f"Doubles: {result['n_doubles']}")
print(f"Parameters: {result['n_params']}")
| System | Singles | Doubles | Total |
|---|
| H₂ (4q) | 4 | 1 | 5 |
| LiH (6q) | 8 | 4 | 12 |
| H₂O (10q) | 20 | 45 | 65 |
| Aspect | UCCSD | HEA |
|---|
| Physical motivation | Yes | No |
| Parameter efficiency | Higher | Lower |
| Circuit depth | Higher | Lower |
| Convergence | Better | Variable |
- Ground state chemistry: Molecular energies
- Bond dissociation: Reaction pathways
- Excited states: Via VQD extension