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P ′′
| 01 〉(t) = (1 − X 21 )P ′
| 01 〉(t) (3.64)
P ′′
| 10 〉(t) = (1 − X 12 )P ′
| 10 〉(t) (3.65)
P ′′
| 11 〉(t) = P ′
| 11 〉(t) + X 21 P ′
| 01 〉(t) + X 12 P ′
| 10 〉(t) (3.66)
Here, X 21 (X 12 ) capture the classical probability that a tunneling of qubit 2 (1)
causes a tunneling of qubit 1 (2).
3.4.3 Microwave Crosstalk
Another source of errors in an actual qubit experiment is the commonly insufficient
electrical isolation between the microwave drives of the different qubits.
Due to the high frequency of the driving field and the close proximity of the qubits
it is fairly difficult to ensure that no photons leak from one drive line to another
qubit. Even though this effect is usually fairly small (−20 dB) and can be compensated
for by sending a correction pulse to all other qubits, it can be easily
simulated if needed by applying a simultaneous rotation to the other qubits with
a proportionally smaller amplitude and a potential phase-shift.
3.4.4 Decoherence – The Density Matrix Formalism
The final error source that needs to be included in the simulation is the one
specifically highlighted in the DiVincenzo criteria: Decoherence.
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