# Ansatz

**Ansatz** (German for "starting point") is the family of [[qiskit-parameterized-circuits|parameterized quantum circuits]] used in [[qiskit-variational-algorithms|variational algorithms]]. The ansatz is the trainable part: you design its structure (which gates, how many layers), and a classical [[qiskit-optimizers|optimizer]] trains its parameters to minimize a cost function.

The quality of a variational algorithm depends entirely on the ansatz: if the true solution is not representable by your ansatz, the algorithm cannot find it, no matter how good the optimizer is.

## Ansatz Design

Ansatz design is an engineering trade-off:

- **Expressivity**: can it represent solutions to your problem? Larger ansatze are more expressive but harder to train.
- **Trainability**: is the landscape smooth and conducive to gradient-based optimization? Deep ansatze often have barren plateaus (flat cost landscapes) where gradients vanish.
- **Gate count**: fewer gates = less noise on real hardware, but less expressive.

## Common Ansatz Families

**Shallow ansatze** (good for NISQ hardware):
- Alternating layers of single-qubit rotations and two-qubit entanglers
- Hardware-efficient ansatz: RY + RZ on each qubit, CNOT ladder between layers

```python
from qiskit import QuantumCircuit
from qiskit.circuit import Parameter

def hardware_efficient_ansatz(num_qubits, depth):
    qc = QuantumCircuit(num_qubits)
    params = []
    
    for layer in range(depth):
        for q in range(num_qubits):
            theta = Parameter(f'θ_{layer}_{q}')
            qc.ry(theta, q)
            params.append(theta)
        
        for q in range(num_qubits - 1):
            qc.cx(q, q + 1)
    
    return qc, params

qc, params = hardware_efficient_ansatz(4, 3)
print(qc.draw())
```

**Structured ansatze** (domain-specific):
- Chemistry: UCC (Unitary Coupled Cluster) ansatz for molecular problems
- Optimization: problem-inspired ansatz encoding the cost structure

Choosing a good ansatz requires understanding the problem. Start simple, measure trainability and expressivity, then refine.