A single-qubit gate on a superconducting qubit has a systematic over-rotation error…

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Quantum Information and Technology, Ch What a qubit must do: requirements, tomography and benchmarking

Problem

A single-qubit gate on a superconducting qubit has a systematic over-rotation error of

\epsilon = 0.02\,\mathrm{rad}

on every application: instead of the intended rotation it performs a rotation larger by

\epsilon

about the same axis. ((a)) Calculate the average gate infidelity

1-\bar F

for a single application of the gate, using

1 - \bar F = \tfrac{2}{3}\sin^2(\epsilon/2)

. ((b)) Calculate the average gate infidelity of the composite operation formed by applying the gate

N=30

times in a row, treating the accumulated angle error

N\epsilon

as a single over-rotation. Compare with

N

times the answer to part (a).

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