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excitations. Since these are a potential source of decoherence for the qubit, the
squid’s voltage jump needs to be kept low. This is achieved by externally shunting
the squid with a resistor on the order of 30 Ω. This resistor does not need to be
placed on the phase qubit integrated circuit chip, but can instead be placed outside
the sample mounting box.
The three-junction design was chosen as it allows for the squid to be decoupled
from the qubit when it is not needed for the readout [Neeley et al., 2008b]. This
can be understood by examining the circuit shown in Figure 4.2a. The squid is
externally biased with a current I bias . In addition, the qubit causes a current I Q
to flow in the squid’s loop. These currents are related via the phases across the
Josephson junctions as given by the Josephson relations:
I bias = I 0 sin δ + αI 0 sin δ 2
(4.2)
I Q = I 0 sin δ − αI 0 sin δ 2
(4.3)
These equations assume that the two junctions αI 0 are identical and therefore
show the same phase difference across them because of symmetry. Figure 4.2b,
a plot of I bias versus I Q , shows how a change in the qubit’s loop flux translates
into a change in the squid bias current. If the squid is biased such that the slope
dI Q /dI bias is non-zero, the qubit can couple to the squid’s bias line and drive
current through the above mentioned shunting resistor. This opens a path for
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