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PDF (double-sided) - Physics Department, UCSB - University of ...

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• The energy difference between the ground and first excited state in the<br />

operating minimum as a function <strong>of</strong> flux bias: Dividing this number by <br />

will give the expected (angular) operating frequency <strong>of</strong> the qubit, i.e. the<br />

frequency with which it needs to be driven to perform operations.<br />

• The energy difference between the first and second excited levels in the<br />

operating minimum: The frequency corresponding to this transition will<br />

need to be significantly different from the operating frequency to allow for<br />

operations on the qubit without exciting it into unwanted higher levels.<br />

• The number <strong>of</strong> states in the right minimum: During measurement, the first<br />

excited state in the operating minimum (here: left minimum) will be selectively<br />

tunneled into the right minimum. There, it will end up in a level <strong>of</strong><br />

similar energy to the one it tunneled from, i.e. fairly high up in the minimum.<br />

The rate at which the state will decay in the right minimum, and thus<br />

the rate with which the measurement “latches” the outcome, is determined<br />

by the number <strong>of</strong> the level that the state tunnels into. Higher states decay<br />

faster with a rate <strong>of</strong> approximately T 1 /n, where n is the level number. Fast<br />

decay is important to reduce the chance <strong>of</strong> the state tunneling back to the<br />

left before latching.<br />

For the calculation to yield trustable results, a few things need to be kept in mind:<br />

46

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