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Multiple choice
The quantum Hamming bound for a non-degenerate
[
[
n
,
k
,
d
]
]
[[n,k,d]]
[[
n
,
k
,
d
]]
code that corrects
t
t
t
errors requires
2
k
∑
j
=
0
t
C
(
n
,
j
)
3
j
≤
2
n
2^k \sum_{j=0}^{t} C(n,j) 3^j \le 2^n
2
k
∑
j
=
0
t
C
(
n
,
j
)
3
j
≤
2
n
, where the
3
j
3^j
3
j
counts weight-
j
j
j
Pauli errors (
X
,
Y
,
Z
X,Y,Z
X
,
Y
,
Z
per location). For
n
=
5
,
k
=
1
,
t
=
1
n = 5, k = 1, t = 1
n
=
5
,
k
=
1
,
t
=
1
, what is the left-hand side
2
k
∑
j
=
0
1
C
(
5
,
j
)
3
j
2^k \sum_{j=0}^{1} C(5,j) 3^j
2
k
∑
j
=
0
1
C
(
5
,
j
)
3
j
?
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16
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