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Figure 2.4: Josephson Qubits: Slight differences in the circuit can lead to very different
qubits. – a) Charge qubit: By removing the inductor and replacing it with
a bias capacitor, the charge qubit circuit creates an island (dashed red box) onto
which cooper pairs can tunnel. This leads to a periodic potential that supports
the qubit states. b) Flux qubit: A small inductance leads to a parabolic potential
with a small bump created by the Josephson junction. This creates two minima
that together support the two qubit states. c) Phase qubit: A larger inductance
allows the Josephson junction to influence the potential more significantly. By
biasing the circuit, the potential can be tilted to create a shallow minimum along
one of the sidewalls of the parabolic part of the potential. This minimum holds
several unevenly spaced energy levels, the lowest two of which form the qubit
states.
Φ 0
2π I dc δ. This potential consists of three parts: a parabola created by the inductor,
a cosine oscillation created by the Josephson junction and a tilt that can be applied
by flux-biasing the inductor.
2.2.4 Circuit Parameters
Depending on the choice of the circuit parameters – the inductance, capacitance,
and critical current – the circuit can be turned into one of three different
types of quantum bits as indicated in Figure 2.4.
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