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starts to tunnel to the neighboring branch the “Step Edge”. To determine the
closest possible bias point to the step edge, it is useful to repeatedly run the qubit
through its biasing cycle while varying its operating bias V Operate as indicated in
Figure 8.4a. A scatter plot of the resulting switching times t Switch as a function
of the operating bias V Operate might then look like Figure 8.4b.
At this point it is useful to move to a representation of the data that describes
the qubit state not in terms of a collection of switching times, but instead as the
probability P T unnel of finding the qubit in the neighboring branch versus in the
operating branch. This probability is obtained by defining a cutoff time t Cutoff
that separates the switching times into two groups, each corresponding to one
branch. In the example here, all switching times t Switch < 14.2 µs correspond to
the qubit state being in the operating branch during the squid ramp, while all
switching times t Switch > 14.2 µs correspond to qubit states that have tunneled
out of the operating branch into the neighboring branch, i.e. t Cutoff
= 14.2 µs.
The probability P T unnel is then defined as:
P T unnel = # of runs with t Switch > 14.2 µs
total # of runs
(8.1)
From this equation it is clear that, to obtain an accurate measurement of P T unnel ,
the experiment of interest needs to be repeated many times to collect enough
statistical samples for t Switch .
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