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9.2.5 Phase Calibration
The trickiest calibration is that of the relative phase of the microwave signals
as seen by the qubits. Due to the high frequency of the drive (∼ 6 GHz), even
the slightest difference in the electrical length of the wiring can lead to significant
phase shifts.
These need to be calibrated by interfering phase-sensitive states
created in the qubits via the coupling capacitor. The easiest way to do this is to
simultaneously drive each qubit with a π-pulse into the state | 0 〉 + 2 eiα | 1 〉 and
observe the qubits’ interaction (Figure 9.6b). If all qubits are driven with the
same phase, the resulting bell state (| 01 〉 + | 10 〉) will be an eigenstate of the
coupling Hamiltonian and thus show only the expected T 1 decay. If the qubits
are driven with different phases, the resulting states (e.g. | 01 〉 + i| 10 〉) are not
eigenstates and thus will show oscillations similar to the ones seen in the Swaps
experiment.
The problem with this calibration is that driving the qubits at the exact opposite
phase will also lead to an eigenstate (| 01 〉 − | 10 〉) that does not show swaps.
This ambiguity reflects the freedom in choosing the exact representation of states
on the Bloch sphere in terms of whether a left-handed or right-handed coordinate
system is used or (equivalently) whether then | 0 〉-state is placed at the South or
North pole of the sphere. The choice of which swapping minimum corresponds to
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