Abstract
The first lesson began with a few reminders of classical circuit theory, such as definitions concerning node variables and loop variables, Kirchhoff's laws and the constitutive relationships of circuit elements, using the simple example of an LC resonant circuit (inductance + capacitance). The quantum information element, the quantum bit, is made up of a pair of quantum levels - generally the fundamental level and the first excited level - of an elementary degree of freedom, in this case that of an electromagnetic mode of the circuit. Since the mid 90s, we've understood that quantum information is extremely powerful when it comes to minimally representing the relations contained in the data of a function. But how can quantum bits be implemented in practice? Can we simply use the quantum levels of an LC circuit, as we would those of a mechanical harmonic oscillator ? In fact, the latter has the unpleasant property of having all transitions between neighboring levels located at the same frequency. So we need to introduce a non-linear, non-dissipative element into the circuit to isolate a pair of levels. This element is a Josephson tunnel junction, which acts as an inductance whose value varies with current. This leads to the elementary quantum circuit with a minimum of elements, the Cooper pair box, which consists of a simple tunnel junction in series with a capacitor and a current source. This circuit is the equivalent of a simple hydrogen atom in atomic physics.
