# T2 Relaxation¶

Simulating the T2 relaxation of a single qubit with `qutip.qip.device.Processor`. The single qubit is driven by a rotation around z axis. We measure the population of the plus state as a function of time to see the Ramsey signal. ```import numpy as np
import matplotlib.pyplot as plt
from qutip.qip.device import Processor
from qutip.operators import sigmaz, destroy
from qutip.qip.operations import snot
from qutip.states import basis

a = destroy(2)
Hadamard = snot()
plus_state = (basis(2,1) + basis(2,0)).unit()
tlist = np.arange(0.00, 20.2, 0.2)

T2 = 5
processor = Processor(1, t2=T2)
processor.add_control(sigmaz())
processor.pulses.coeff = np.ones(len(tlist))
processor.pulses.tlist = tlist
result = processor.run_state(
plus_state, e_ops=[a.dag()*a, Hadamard*a.dag()*a*Hadamard])

fig, ax = plt.subplots()
# detail about length of tlist needs to be fixed
ax.plot(tlist[:-1], result.expect[:-1], '.', label="simulation")
ax.plot(tlist[:-1], np.exp(-1./T2*tlist[:-1])*0.5 + 0.5, label="theory")
ax.set_xlabel("t")
ax.set_ylabel("Ramsey signal")
ax.legend()
ax.set_title("Relaxation T2=5")
ax.grid()
fig.tight_layout()
fig.show()
```

Total running time of the script: ( 0 minutes 0.184 seconds)

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