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Clifford gate
quantum gate constructible from Hadamard, S and CNOT gates alone
Clifford group
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Statements
subclass of
quantum gate
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defining formula
C
n
=
N
U
(
2
n
)
(
{
i
n
σ
j
1
⊗
⋯
⊗
σ
j
n
∣
j
k
∈
{
0
,
1
,
2
,
3
}
,
n
∈
Z
}
)
{\displaystyle C_{n}=N_{\operatorname {U} (2^{n})}(\{\mathrm {i} ^{n}\sigma _{j_{1}}\otimes \dotsb \otimes \sigma _{j_{n}}\mid j_{k}\in \{0,1,2,3\},n\in \mathbb {Z} \})}
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in defining formula
U
(
−
)
{\displaystyle \operatorname {U} (-)}
symbol represents
unitary group
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N
{\displaystyle N}
symbol represents
normalizer
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{
i
n
σ
j
1
⊗
⋯
⊗
σ
j
n
∣
j
k
∈
{
0
,
1
,
2
,
3
}
,
n
∈
Z
}
{\displaystyle \{\mathrm {i} ^{n}\sigma _{j_{1}}\otimes \dotsb \otimes \sigma _{j_{n}}\mid j_{k}\in \{0,1,2,3\},n\in \mathbb {Z} \}}
symbol represents
Pauli group
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maintained by WikiProject
WikiProject Mathematics
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Identifiers
Google Knowledge Graph ID
/g/11j082b3k8
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Clifford gates
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