Computer Science
Mathematics
Physics
Quantum Computation

Quantum State Visualization

Plot the Bloch vector or diagrammatic representation of a quantum state

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Install and load the QuantumFramework paclet:

In[1]:=

PacletInstall["Wolfram/QuantumFramework"]Needs["Wolfram`QuantumFramework`"]

Out[1]=

PacletObject

Name: Wolfram/QuantumFramework

Version: 1.2.7



Plot the Bloch vector of a random pure state:

In[2]:=

QuantumState["RandomPure"]["BlochPlot"]

Out[2]=

Plot the Bloch vector of a random mixed state:

In[3]:=

QuantumState["RandomMixed"]["BlochPlot"]

Out[3]=

Another commonly used visualization technique is the diagrammatic representation, which incorporates input and output elements.

Plot the diagram of a random pure state in 2D:

In[4]:=

QuantumState["RandomPure"]["Diagram"]

Out[4]=

Plot the diagram of a random pure state 2x3:

In[5]:=

QuantumState["RandomPure",{2,3}]["Diagram"]

Out[5]=

One can also visualize the corresponding formula in Dirac notation.

Get the traditional form of a random state:

In[6]:=

QuantumState["RandomPure",{3}]//TraditionalForm

Out[6]//TraditionalForm=

(0.464897+0.664035)|0〉+(0.339126+0.282107)|1〉-(0.306702-0.232964)|2〉

Quantum states, in the conventional way, have no input and only output (look at above diagrams). It can be generalized to cases with input and also output.

A bra state, with input and no output:

In[7]:=

AssociationMap[QuantumState["0"]["Dagger"][#]&,{"Input","Output"}]

Out[7]=

InputQuditBasis

Qudits: 1

Dimension: 2

,OutputQuditBasis

Qudits: 0

Dimension: 1



A ket-bra state, with input and no output:

In[8]:=

AssociationMap[QuantumState["1"][QuantumState["0"]["Dagger"]][#]&,{"Input","Output"}]

Out[8]=

InputQuditBasis

Qudits: 1

Dimension: 2

,OutputQuditBasis

Qudits: 1

Dimension: 2



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Contributed by: Wolfram Research, Quantum Computation Framework Team

Wolfram Language Example Repository

Quantum State Visualization

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