Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Wolfram`QuantumFramework`
StabilizerFrame  |
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A represents a complex linear combination |〉 of stabilizer states, the natural object for circuits that contain a small number of non-Clifford gates, magic-state distillation, and stabilizer-rank simulation. Reference: García-Martín & Markov (arXiv:1712.03554).
∑
i
c
i
s
i
▪
The internal representation is the Association where each is a and the can be exact, numeric, or symbolic complex coefficients.
"Components"{{,},…}
c
1
ps
1
ps_i
c_i
▪
The summary box reports the number of components, the qubit count, and the first coefficient. Inspect any property with the dispatch syntax ; the list of recognised property names is given by .
f["property"]
f["Properties"]
▪
Clifford gates (, , , , …) are distributed over the components without changing the frame length, so a Clifford circuit acting on a single-component frame remains a single-component frame and is equivalent in cost to the underlying tableau update.
"H"
"S"
"X"
"CNOT"
▪
The non-Clifford gate is decomposed as , so each P-gate doubles the component count. The gate is the alias and is the alias .
"P"[θ]
P(θ)|s〉=|s〉+|s〉
1+
iθ/2
e
2
1-
iθ/2
e
2
Z
q
"T"
"P"[π/2]
†
"T"
"P"[-π/2]
▪
f["State"]
f["StateVector"]
▪
f["InnerProduct",other]
f
other
PauliStabilizer
▪
Plus
Times
Equal
UpValues
Examples
(24)
Basic Examples
(1)
A StabilizerFrame built from a single PauliStabilizer:
In[1]:=
 | StabilizerFrame |
 | PauliStabilizer |
Out[2]=
StabilizerFrame
 | ℱ |
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An explicit two-component frame with equal coefficients:
In[1]:=
| StabilizerFrame |
 | PauliStabilizer |
| PauliStabilizer |
Out[2]=
StabilizerFrame
| ℱ |
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Applying a T gate to a single-component frame doubles the frame size:
In[1]:=
| StabilizerFrame |
 | PauliStabilizer |
Out[2]=
StabilizerFrame
| ℱ |
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Distributing a Hadamard gate over each component preserves the frame length:
In[1]:=
| StabilizerFrame |
| PauliStabilizer |
Out[2]=
StabilizerFrame
| ℱ |
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Inspecting structure with the accessor syntax:
In[1]:=
Module{f},f=
1Sqrt[2],
[1],1Sqrt[2],
[{"Z"}];{f["Length"],f["Qubits"],f["Coefficients"]}
 | StabilizerFrame |
| PauliStabilizer |
| PauliStabilizer |
Out[2]=
2,1,,
1
2
1
2
Scope
(4)
Generalizations & Extensions
(1)
Options
(8)
Applications
(2)
Properties & Relations
(4)
Possible Issues
(3)
Neat Examples
(1)
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""