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QuantumFramework

Tutorials

  • Getting Started
  • Quantum Object Composition

Guides

  • Wolfram Quantum Computation Framework

Tech Notes

  • Bell's Theorem: CHSH inequality
  • Circuit Diagram
  • Exploring Fundamentals of Quantum Theory
  • QPU Service Connection
  • Quantum object abstraction
  • Quantum Optimization
  • Second Quantization Functions
  • Tensor Network
  • Quantum Computation

Symbols

  • CliffordChannel
  • EinsteinSummation
  • GraphState
  • LocalComplement
  • PauliStabilizer
  • QiskitTarget
  • QuantumBasis
  • QuantumChannel
  • QuantumCircuitMultiwayGraph [EXPERIMENTAL]
  • QuantumCircuitOperator
  • QuantumDistance
  • QuantumEntangledQ
  • QuantumEntanglementMonotone
  • QuantumEvolve
  • QuantumMeasurement
  • QuantumMeasurementOperator
  • QuantumMeasurementSimulation
  • QuantumMPS [EXPERIMENTAL]
  • QuantumOperator
  • QuantumPartialTrace
  • QuantumPhaseSpaceTransform
  • QuantumQASM
  • QuantumShortcut [EXPERIMENTAL]
  • QuantumSimilarity
  • QuantumStateEstimate [EXPERIMENTAL]
  • QuantumState
  • QuantumTensorProduct
  • QuantumWignerMICTransform [EXPERIMENTAL]
  • QuantumWignerTransform [EXPERIMENTAL]
  • QuditBasis
  • QuditName
  • StabilizerFrame
  • StabilizerStateQ
Wolfram`QuantumFramework`
StabilizerFrame
​
StabilizerFrame
[ps]
wraps a
PauliStabilizer
ps
as a single-component stabilizer frame with coefficient
1
.
​
​
StabilizerFrame
[{{
c
1
,
ps
1
},{
c
2
,
ps
2
},…}]
builds a frame representing the superposition
∑
i
c
i
|
s
i
〉
of stabilizer states with the given (possibly symbolic) coefficients.
​
​
f["gate",args]
distributes the named gate (Clifford or non-Clifford) over each component of the frame
f
.
​
​
f["InnerProduct",other]
computes the inner product of the frame
f
with another stabilizer state or frame.
​
Details and Options
▪
A
StabilizerFrame
represents a complex linear combination
∑
i
c
i
|
s
i
〉
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).
▪
The internal representation is the Association
"Components"{{
c
1
,
ps
1
},…}
where each
ps_i
is a
PauliStabilizer
and the
c_i
can be exact, numeric, or symbolic complex coefficients.
▪
The summary box reports the number of components, the qubit count, and the first coefficient. Inspect any property with the dispatch syntax
f["property"]
; the list of recognised property names is given by
f["Properties"]
.
▪
Clifford gates (
"H"
,
"S"
,
"X"
,
"CNOT"
, …) 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.
▪
The non-Clifford
"P"[θ]
gate is decomposed as
P(θ)|s〉=
1+
iθ/2
e
2
|s〉+
1-
iθ/2
e
2
Z
q
|s〉
, so each P-gate doubles the component count. The
"T"
gate is the alias
"P"[π/2]
and
†
"T"
is the alias
"P"[-π/2]
.
▪
f["State"]
or
f["StateVector"]
materialises the full quantum state by summing the dense state vectors of the components. This is only practical for small qubit counts and frame lengths.
▪
f["InnerProduct",other]
returns the inner product of
f
with
other
(a frame,
PauliStabilizer
, or stabilizer-compatible state) by reducing to the underlying tableau-level inner products via García-Markov's recursion.
▪
Plus
,
Times
, and
Equal
are defined on
StabilizerFrame
via
UpValues
: addition concatenates component lists, scalar multiplication rescales every coefficient, and equality compares the (ordered) component lists for structural sameness.
​
Examples  
(24)
Basic Examples  
(1)
A StabilizerFrame built from a single PauliStabilizer:
In[1]:=
StabilizerFrame

PauliStabilizer
[2]
Out[2]=
StabilizerFrame
ℱ
Components: 1
Qubits: 2

​
An explicit two-component frame with equal coefficients:
In[1]:=
StabilizerFrame
1Sqrt[2],
PauliStabilizer
[{"Z"}],1Sqrt[2],
PauliStabilizer
[{"-Z"}]
Out[2]=
StabilizerFrame
ℱ
Components: 2
Qubits: 1

​
Applying a T gate to a single-component frame doubles the frame size:
In[1]:=
StabilizerFrame

PauliStabilizer
[1]["T",1]
Out[2]=
StabilizerFrame
ℱ
Components: 2
Qubits: 1

​
Distributing a Hadamard gate over each component preserves the frame length:
In[1]:=
StabilizerFrame

PauliStabilizer
[2]["H",1]
Out[2]=
StabilizerFrame
ℱ
Components: 1
Qubits: 2

​
Inspecting structure with the accessor syntax:
In[1]:=
Module{f},f=
StabilizerFrame
1Sqrt[2],
PauliStabilizer
[1],1Sqrt[2],
PauliStabilizer
[{"Z"}];{f["Length"],f["Qubits"],f["Coefficients"]}
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)

SeeAlso
PauliStabilizer
 
▪
StabilizerStateQ
 
▪
CliffordChannel
 
▪
GraphState
 
▪
LocalComplement
 
▪
QuantumState
 
▪
QuantumOperator
 
▪
QuantumCircuitOperator
 
▪
PauliMatrix
 
▪
Total
RelatedGuides
▪
Wolfram Quantum Computation Framework
""

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