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the qubit to dissipate energy and thus needs to be avoided. As can be seen in
Figure 4.2b, for values of α smaller than 2.0 the squid can be biased with a current
I ∗ bias
at which the qubit does not couple to the squid’s bias line to first order. To
ensure the existence of such an insensitive point despite slight variations in the
critical currents during fabrication, a value of α = 1.7 makes good sense.
Another electrical characteristic of the squid that needs to be chosen is the
inductance L of the squid loop as shown in Figure 4.2c, which is used to generate
the mutual inductance with the qubit. The important concern here is the ratio of
this inductance to the inductance of the squid’s Josephson junctions at zero bias.
This ratio is given by:
β = 2π L I 0 /Φ 0 (4.4)
This ratio is chosen to balance two counter-acting effects: On the one hand, a
larger loop inductance of the squid allows for a larger mutual inductance with the
qubit and thus increases the coupling during the readout. On the other hand, a
larger inductance will drop more of the phase difference δ across the squid loop,
reducing the exposure of the junctions to the bias. A value of β around 0.9 seems
to balance these concerns well.
The exact critical current of the squid is not quite as important, so, for fabrication
convenience, one of the junctions, e.g. the single one, can be chosen to match
the qubit’s critical current around 2 µA. The other two junctions then need to be
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