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4.2.1 Qubit
When designing the inductor of the qubit it is important to reduce the circuit’s
sensitivity to any potentially fluctuating external background magnetic fields.
This can be achieved to first order by arranging the inductor into a symmetric
figure-8 configuration. With this, any current induced in one of the loops by
a background field is exactly cancelled by the current induced in the other loop.
This makes the qubit sensitive only to gradients in magnetic fields and is therefore
also called a gradiometer design. The actual shape of the inductor is best designed
with modeling software. A very powerful free tool that serves this purpose well
is FastHenry. It allows for the specification of traces of given dimensions and will
then calculate the resulting inductance of all connected traces and all mutual inductances
between different sets of connected traces. Again, the design allows for
a lot of flexibility in the choices of exact parameters but there are a few concerns
to keep in mind. The width of traces used in the design should be large enough to
yield reproducible results during fabrication, but not too large to avoid trapping
magnetic flux vortices. A good size here seems 2 µm. The number of turns in the
inductor needs to be balanced between the overall size of the structure and the
added capacitance due to the needed crossovers. Two turns here seem to be a
good number.
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