Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Wolfram`QuantumFramework`
CliffordChannel  |
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▪
A encodes a Clifford channel Φ: T() T() by a Choi tableau, following Yashin25 (arXiv:2504.14101) Section 2.3.
ℋ
A
ℋ
B
▪
The internal representation is an Association where is a bit matrix on the input system (or if ), is a bit matrix on the output system, and is a length- sign bit vector.
"UA"uA,"UB"uB,"c"c,"InputQubits"nA,"OutputQubits"nB
uA
k×2nA
{}
nA=0
uB
k×2nB
c
k
▪
Each tableau row encodes a Pauli superoperator , and the channel acts as the average .
[c]
u
A
u
B
Π(c)[ρ]=··Tr[ρP()]·P()
u
A
u
B
c
(-1)
A
2
u
A
u
B
Φ[ρ]=·Π(row)[ρ]
-(A+B)
2
∑
row
▪
Special cases of the tableau:
▪
- A pure stabilizer state has , rows; is the state's stabilizer tableau.
- A Clifford unitary with has rows enumerating Pauli generators and their conjugates; encodes phase signs.
nA=0
k=nB
uB
- A Clifford unitary
U
AB
nA=nB=n
2n
c
▪
Composition applies first, then , and is implemented by Boolean null-space intersection on the -side bits, with Aaronson-Gottesman phase tracking and the contraction-sign correction for Y-bearing combined Paulis (Yashin25 §3.2/§3.3).
cc1[cc2]
cc2
cc1
B
|〉
+
Φ
B
′
B
u
B
▪
State evolution has three recognized dispatch cases: (i) identity channel returns unchanged; (ii) state-preparation channel () returns the state encoded by ; (iii) dim-matched channel builds , composes, and converts back to a .
cc[ps]
ps
nA=0
cc
PauliStabilizer
▪
QuantumChannel
"X"
"-XX"
"BitFlip"
"PhaseFlip"
CliffordChannel::stochastic
▪
The introspection key returns the full list of accepted accessor strings: , , , , , , , and .
cc["Properties"]
"UA"
"UB"
"c"
"InputQubits"
"OutputQubits"
"Rank"
"Tableau"
"Source"
Examples
(45)
Basic Examples
(5)
Construct the identity channel on a single qubit:
In[1]:=
 | CliffordChannel |
Out[1]=
CliffordChannel
 | |
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Identity on more qubits:
In[1]:=
| CliffordChannel |
Out[1]=
CliffordChannel
| |
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Build a state-preparation channel from a stabilizer state:
In[1]:=
| CliffordChannel |
 | PauliStabilizer |
Out[1]=
CliffordChannel
| |
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Construct directly from a Choi-tableau Association (raw form):
In[1]:=
| CliffordChannel |
Out[1]=
CliffordChannel
| |
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Interrogate via the property accessor:
In[1]:=
| CliffordChannel |
Out[1]=
{UA,UB,c,InputQubits,OutputQubits,Rank,Tableau,Source}
Scope
(18)
Generalizations & Extensions
(1)
Options
(11)
Applications
(2)
Properties & Relations
(4)
Possible Issues
(3)
Neat Examples
(1)
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