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# 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[0].coeff = np.ones(len(tlist))
    processor.pulses[0].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][:-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 0.111 seconds)

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