# Charge Qubits

**Charge qubit** (also Cooper pair box) is a Josephson junction shunted by a capacitor, without additional filtering inductors. The Hamiltonian is:

$$H = 4E_C (\hat{n} - n_g)^2 - E_J \cos(\hat{\phi})$$

where $n_g = C V_g / (2e)$ is the offset charge controlled by a gate voltage $V_g$.

Charge qubits are exquisitely sensitive to gate voltage—the energy levels shift dramatically with $n_g$. This sensitivity makes them powerful for control but vulnerable to charge noise.

```python
from scqubits import ChargeQubit

charge_qubit = ChargeQubit(
    EJ=1.0,     # Small Josephson energy
    EC=1.0,     # Comparable charging energy
    ng=0.5,     # Offset charge
    ncut=20
)

# Frequency vs. offset charge
ng_values = np.linspace(0, 1, 100)
freqs = [ChargeQubit(EJ=1.0, EC=1.0, ng=ng, ncut=20).f_01() 
         for ng in ng_values]
```

## Charge Noise

Fluctuations in offset charge $\delta n_g$ directly affect transition frequencies, causing decoherence. Charge noise is typically 1% per gate (relative to $e$), limiting charge qubit coherence.

Charge qubits are historically important (early experiments) but less practical than transmons due to charge noise sensitivity. scqubits supports charge qubits for completeness and historical study.