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will focus only on the integrated circuit, while the other two components will be
discussed later.
The electrical characteristics of the bias coil are fully described by three parameters:
The coil’s inductance, its mutual inductance with the qubit loop and
its mutual inductance with the squid loop.
Since the squid readout should be influenced as little as possible by the qubit
bias, the last value is easy to pick: The mutual inductance between the bias coil
and the squid loop should be as close to zero as possible.
The inductance of the bias coil and the mutual inductance between the qubit
loop and the bias coil are chosen based on two concerns: On the one hand, the
inductances need to be large enough to allow a reasonable current (< 2 mA)
in the bias inductor to cause a sufficiently large tilt of the qubit potential to
implement the reset.
For this, it is sufficient if the bias coil can apply about
two flux quanta (Φ 0 ) to the qubit loop. On the other hand, the bias line will be
subject to electrical noise generated in the elements at higher temperature stages
of the dilution refrigerator.
Furthermore, the bias line is terminated with the
usual 50 Ω impedance, which allows it to dissipate energy. To reduce the amount
of noise coupled into the qubit and energy dissipated by the bias line, the mutual
inductance should be kept as small as possible. A ratio of the inductance of the
qubit to the mutual inductance to the flux bias line of
L qubit
M qubit/flux bias
∼ 100 yields
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