Abstract
In the fourth lesson, we outlined the basics of dispersive quantum bit reading. The problem of reading the number of quantas contained in a circuit storing a quantum bit is a difficult one. On the one hand, we want the circuit to be sufficiently isolated when it's in dormant mode to retain the quantum information as well as possible. But on the other hand, we also want the circuit to be well coupled to the measuring device when reading, so that the result is as faithful as possible. The solution is to couple the quantum bit to a resonator whose resonant frequency is detuned from the transition frequency of the quantum bit. The resonator protects the quantum bit from external electromagnetic disturbances by acting as a filter. But the interaction between the quantum bit and the resonator induces a shift in the latter's frequency when the bit changes state. This effect can be represented by considering that the atom acts for the resonator like a piece of insulating material whose dielectric constant depends on the quantum state. By measuring the phase shift of a wavelet sent into the resonator, we can determine the state of the quantum bit. In the course of this lecture, we have established the relationship between wavelet amplitude and readout fidelity, as a function of system parameters. We have also highlighted the close link, for the transmon regime of the Cooper Pair box, between readout speed and the intensity of the Purcell effect. The latter is a parasitic effect associated with the coupling between the atom and the resonator. The greater the coupling, the faster the readout, but the more the atom inherits cavity dissipation, which impairs its coherence. This " curse " of the Purcell effect is warded off in the Fluxonium circuit described in detail in the sixth lesson.
