Abstract
The third lesson described in greater detail superconducting qubits based on the Josephson effect. To manipulate the qubit's state and detect it, the junction must be inserted into external circuits. Qubit frequency control and detection can be achieved by sending a direct current through the junction, or inductively, by creating a magnetic flux through the circuit including the junction. The result is a modification of the system's Hamiltonian, which presents a local minimum around which the effective particle representing the qubit is trapped. A phasequbit is thus created, the frequency of which is finely tuned by adjusting the intensity of the DC current or control flux. The qubit state is detected by bringing its excited state close to the top of a potential barrier associated with the effective Hamiltonian, enabling the fictitious particle representing the qubit to escape the well in which it is confined. The resulting sudden change in quantum phase (or magnetic flux) is detected by a SQUID coupled to the qubit circuit. We have also described how to achieve unitary transformations of the qubit's state by coupling it through a capacitor to radio-frequency pulses. The capacitive coupling of two junctions to create logic gates has also been analyzed, as has the coupling of a qubit to an LC-type circuit constituting a radio-frequency resonator. The result is a system analogous to the cavity quantum electrodynamics of the ENS experiments, with the superconducting qubit replacing the Rydberg atom and the LC circuit replacing the superconducting cavity. In phase qubits, the phase (or flux) is relatively well defined, and the charge is the "fuzzy" variable with large fluctuations. We concluded the lesson by briefly describing the principle of charge qubits, in which, on the contrary, charge is the precise variable and phase the fuzzy one. We also described the principle of the fluxqubit, in which the effective particle tunnels between two symmetrical wells.
