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

To couple qubits 2 and 3 out of five, one would use:
A(t + ∆t) = e −iπ∆t (C 23 I ⊗ C ⊗ I ⊗ I) A(t) (3.57)
To combine this operation with a simultaneous X-rotation on qubit 1, one would
use:
A(t + ∆t) = e −iπ∆t (X 1 σ x ⊗ I ⊗ I ⊗ I ⊗ I+C 23 I ⊗ C ⊗ I ⊗ I) A(t) (3.58)
If, instead, the coupling is followed by the X-rotation on qubit 1, the evolution is:
A(t + ∆t C + ∆t X ) = e −iπ∆t X (X 1 σ x ⊗ I ⊗ I ⊗ I ⊗ I) e −iπ∆t C (C 23 I ⊗ C ⊗ I ⊗ I) A(t) (3.59)
3.4 Simulating Imperfections
So far, apart from simulating an off-resonant drive via an additional Z-rotation,
all operations of the qubits have been assumed ideal. Unfortunately, in reality,
this is not the case, and to obtain useful predictions of experimental data, several
imperfections need to be taken into account.
3.4.1 Measurement Fidelities
Ideally, the probability of finding the qubit in one of the given states would be
calculated from:
P | 0 〉 (t) = |a 0 (t)| 2 and P | 1 〉 (t) = |a 1 (t)| 2 = 1 − P | 0 〉 (t) (3.60)
61