# Couplings and Interactions

**Couplings** describe how multiple qubits interact. Common coupling mechanisms:

- **Capacitive coupling**: two qubits share a capacitor, Hamiltonian contains $\propto Q_1 Q_2$ terms
- **Inductive coupling**: qubits share an inductor, Hamiltonian contains $\propto \phi_1 \phi_2$ terms
- **Charge coupling**: gate voltage on one qubit affects another
- **Tunable coupling**: flux-dependent or controllable

```python
from scqubits import Transmon, HilbertSpace, InteractionTerm

qubit1 = Transmon(EJ=15.0, EC=0.3, ncut=30)
qubit2 = Transmon(EJ=15.0, EC=0.3, ncut=30)

hilbert = HilbertSpace([qubit1, qubit2])

# Capacitive coupling: g * n_1 * n_2
g = 0.01  # Coupling strength (GHz)
interaction = InteractionTerm(
    g=g,
    op1=qubit1.n_operator(),
    op2=qubit2.n_operator()
)
hilbert.add_interaction(interaction)

# Compute coupled spectrum
evals_coupled = hilbert.hamiltonian().eigenenergies()
```

## Coupling Engineering

Coupling strength $g$ sets the two-qubit gate speed: larger $g$ enables faster gates. But strong coupling increases error sensitivity and causes unwanted shifts in single-qubit frequencies ([[scqubits-dispersive-shift|dispersive shifts]]).

Typical two-qubit couplings: $g \sim 1$ MHz to $100$ MHz. Gate times: $\sim 10$ ns to $100$ ns.