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# Decoherence and Dissipation

**Decoherence** is the loss of quantum coherence due to environmental interactions. **Dissipation** is the loss of energy. Both are modeled via [[qutip-collapse-operators|collapse operators]] in the [[qutip-master-equation|master equation]].

## Types of Decoherence

**Energy relaxation (T1 decay)**: Spontaneous emission of energy to the environment.
- Operator: $L = \sqrt{\gamma_1} \sigma_-$
- Timescale: $T_1$ (energy relaxation time)
- Result: system decays to ground state

**Dephasing (T2* decay)**: Loss of phase coherence without energy loss.
- Operator: $L = \sqrt{\gamma_{\phi}} \sigma_z$
- Timescale: $T_2^* < T_1$ (pure dephasing time)
- Result: superposition $(\vert 0 \rangle + |1\rangle)/\sqrt{2}$ becomes mixture

**Coherence time**: $T_2 = 2 T_1$ (best case, limited by T1); usually $T_2 < 2T_1$ due to dephasing.

## Modeling Realistic Noise

Real qubits have both T1 and T2:

```python
from qutip import *
import numpy as np

# Superconducting qubit with measured decoherence
T1 = 10.0     # microseconds
T2 = 5.0      # microseconds

H = 0.5 * sigmaz()
c_ops = [
    np.sqrt(1/T1) * sigmam(),        # T1 decay
    np.sqrt(2/T2 - 1/T1) * sigmaz()  # T2 dephasing
]

times = np.linspace(0, 20, 100)
psi0 = (basis(2, 0) + basis(2, 1)).unit()
result = mesolve(H, psi0, times, c_ops, [sigmaz()])
```

Decoherence limits quantum computation. Understanding and measuring T1 and T2 are essential for quantum engineering.