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Multiple choice
A qubit in state
∣
0
⟩
|0\rangle
∣0
⟩
is perturbed by
H
′
=
0.3
σ
z
+
0.5
σ
x
H' = 0.3\,\sigma_z + 0.5\,\sigma_x
H
′
=
0.3
σ
z
+
0.5
σ
x
. Using
σ
z
∣
0
⟩
=
+
∣
0
⟩
\sigma_z|0\rangle = +|0\rangle
σ
z
∣0
⟩
=
+
∣0
⟩
and
σ
x
∣
0
⟩
=
∣
1
⟩
\sigma_x|0\rangle = |1\rangle
σ
x
∣0
⟩
=
∣1
⟩
, the first-order shift is
E
(
1
)
=
⟨
0
∣
H
′
∣
0
⟩
E^{(1)} = \langle 0|H'|0\rangle
E
(
1
)
=
⟨
0∣
H
′
∣0
⟩
. What is
E
(
1
)
E^{(1)}
E
(
1
)
?
0.5
0.3
0.8
0.0
Check answer