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A first-order Lie-Trotter step for
H
=
X
+
Z
H = X + Z
H
=
X
+
Z
has additive error bounded by
(
t
2
/
2
)
⋅
∣
∣
[
X
,
Z
]
∣
∣
(t^2 / 2) \cdot ||[X, Z]||
(
t
2
/2
)
⋅
∣∣
[
X
,
Z
]
∣∣
, where
[
X
,
Z
]
=
−
2
i
Y
[X, Z] = -2iY
[
X
,
Z
]
=
−
2
iY
so
∣
∣
[
X
,
Z
]
∣
∣
=
2
||[X, Z]|| = 2
∣∣
[
X
,
Z
]
∣∣
=
2
. For a single step of duration
t
=
0.1
t = 0.1
t
=
0.1
, what is this error bound?
0.02
0.005
0.1
0.01
Check answer