Wolfram/ QuantumFramework

(1.3.0) current version: 1.4.2 »

Perform analytic and numeric quantum computations

Contributed by: Wolfram Research, Quantum Computation Framework team

The Wolfram Quantum Framework brings a broad, coherent design for quantum computation, together with a host of leading-edge capabilities and full integration into Mathematica and Wolfram Language. Starting from discrete quantum mechanics, the Framework provides a high-level symbolic representation of quantum bases, states and operators. The Framework can perform measurements and is equipped with various well-known states and operators, such as Bell states and Pauli operators. Using such simulation capabilities as a foundation, one can use the Framework to model and simulate quantum circuits and algorithms, interoperate with many external quantum platforms, and send queries to quantum processing units from a Wolfram notebook.

Within the Framework, all quantum-related functions and objects are natively integrated with Wolfram Language, providing immediate access to a wide array of tools for exploring quantum computational queries and serving as a potent resource for education in the field.

Installation Instructions

To install this paclet in your Wolfram Language environment, evaluate this code:
PacletInstall["Wolfram/QuantumFramework"]


To load the code after installation, evaluate this code:
Needs["Wolfram`QuantumFramework`"]

Details

This paclet works with Version 13.1 and higher of Wolfram Language.

Paclet Guide

Examples

The Wolfram quantum framework handles many different quantum objects, including states, operators, channels, measurements, circuits, and more. It offers specialized functions for various computations like quantum evolution, entanglement monotones, partial tracing, Wigner or Weyl transformations, stabilizer formalism, and additional capabilities. Each functionality incorporates common named operations, such as Schwinger basis, GHZ state, Fourier operator, Grover circuit, and others. Perform computations seamlessly with the Wolfram quantum framework using the standard Wolfram kernel, such as the usual evaluation of codes in Mathematica. Alternatively, leverage the framework to send jobs to quantum processing units via service connections.


In[1]:=
qc = InterpretationBox[FrameBox[TagBox[TooltipBox[PaneBox[GridBox[List[List[GraphicsBox[List[Thickness[0.0025`], List[FaceForm[List[RGBColor[0.9607843137254902`, 0.5058823529411764`, 0.19607843137254902`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3]]], List[List[List[205.`, 22.863691329956055`], List[205.`, 212.31669425964355`], List[246.01799774169922`, 235.99870109558105`], List[369.0710144042969`, 307.0436840057373`], List[369.0710144042969`, 117.59068870544434`], List[205.`, 22.863691329956055`]], List[List[30.928985595703125`, 307.0436840057373`], List[153.98200225830078`, 235.99870109558105`], List[195.`, 212.31669425964355`], List[195.`, 22.863691329956055`], List[30.928985595703125`, 117.59068870544434`], List[30.928985595703125`, 307.0436840057373`]], List[List[200.`, 410.42970085144043`], List[364.0710144042969`, 315.7036876678467`], List[241.01799774169922`, 244.65868949890137`], List[200.`, 220.97669792175293`], List[158.98200225830078`, 244.65868949890137`], List[35.928985595703125`, 315.7036876678467`], List[200.`, 410.42970085144043`]], List[List[376.5710144042969`, 320.03370475769043`], List[202.5`, 420.53370475769043`], List[200.95300006866455`, 421.42667961120605`], List[199.04699993133545`, 421.42667961120605`], List[197.5`, 420.53370475769043`], List[23.428985595703125`, 320.03370475769043`], List[21.882003784179688`, 319.1406993865967`], List[20.928985595703125`, 317.4896984100342`], List[20.928985595703125`, 315.7036876678467`], List[20.928985595703125`, 114.70369529724121`], 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"Wolfram`QuantumFramework`QuantumCircuitOperator"]], Rule[ShowStringCharacters, True]], "Tooltip"]]], Rule[Background, RGBColor[0.968`, 0.976`, 0.984`]], Rule[BaselinePosition, Baseline], Rule[DefaultBaseStyle, List[]], Rule[FrameMargins, List[List[0, 0], List[1, 1]]], Rule[FrameStyle, RGBColor[0.831`, 0.847`, 0.85`]], Rule[RoundingRadius, 4]], PacletSymbol["Wolfram/QuantumFramework", "Wolfram`QuantumFramework`QuantumCircuitOperator"], Rule[Selectable, False], Rule[SelectWithContents, True], Rule[BoxID, "PacletSymbolBox"]][{"X" -> {1, 2}, "H", "CNOT", "RZ"[\[Phi]], "RZ"[\[Theta]] -> 2, "H" -> {1, 2}, {1}, {2}}];
qc["Diagram"]
Out[2]=
In[3]:=
$Assumptions = {\[Phi], \[Theta]} \[Element] Reals;
\[ScriptCapitalD] = qc[]["MultivariateDistribution"]
Out[4]=

Calculate the quantum correlation P00-P10-P01+P11

In[5]:=
Sum[(-1)^(i + j) PDF[\[ScriptCapitalD], {i, j}], {i, 0, 1}, {j, 0, 1}] // FullSimplify
Out[5]=

Create the quantum phase estimation circuit for a phase operator:

In[6]:=
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"PacletSymbolBox"]][{"Phase", 2 \[Pi]/5}], 4}];
qc["Diagram"]
Out[7]=
In[8]:=
measurement = N[qc][]
Out[8]=
In[9]:=
measurement["ProbabilityPlot", AspectRatio -> 1/4]
Out[9]=

Set time and other variables of the Hamiltonian (Rabi drive and detuning):

In[10]:=
\[CapitalOmega] = 15. Sin[t]^2;
\[CapitalDelta] = 10. Sin[t - 1];
Plot[{\[CapitalOmega], \[CapitalDelta]}, {t, 0, 3}, PlotLegends -> {"\[CapitalOmega]", "\[CapitalDelta]"}, AspectRatio -> 1/2]
Out[11]=

Create a 10-qubit Hamiltonian operator as

In[12]:=
hamiltonian = \[CapitalOmega]/
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    2 InterpretationBox[FrameBox[TagBox[TooltipBox[PaneBox[GridBox[List[List[GraphicsBox[List[Thickness[0.0025`], List[FaceForm[List[RGBColor[0.9607843137254902`, 0.5058823529411764`, 0.19607843137254902`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3]]], List[List[List[205.`, 22.863691329956055`], List[205.`, 212.31669425964355`], List[246.01799774169922`, 235.99870109558105`], List[369.0710144042969`, 307.0436840057373`], List[369.0710144042969`, 117.59068870544434`], List[205.`, 22.863691329956055`]], List[List[30.928985595703125`, 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List[63.928985595703125`, 315.4997024536133`], List[200.`, 394.0606994628906`]]]]]], List[Rule[BaselinePosition, Scaled[0.15`]], Rule[ImageSize, 10], Rule[ImageSize, 15]]], StyleBox[RowBox[List["QuantumOperator", " "]], Rule[ShowAutoStyles, False], Rule[ShowStringCharacters, False], Rule[FontSize, Times[0.9`, Inherited]], Rule[FontColor, GrayLevel[0.1`]]]]], Rule[GridBoxSpacings, List[Rule["Columns", List[List[0.25`]]]]]], Rule[Alignment, List[Left, Baseline]], Rule[BaselinePosition, Baseline], Rule[FrameMargins, List[List[3, 0], List[0, 0]]], Rule[BaseStyle, List[Rule[LineSpacing, List[0, 0]], Rule[LineBreakWithin, False]]]], RowBox[List["PacletSymbol", "[", RowBox[List["\"Wolfram/QuantumFramework\"", ",", "\"Wolfram`QuantumFramework`QuantumOperator\""]], "]"]], Rule[TooltipStyle, List[Rule[ShowAutoStyles, True], Rule[ShowStringCharacters, True]]]], Function[Annotation[Slot[1], Style[Defer[PacletSymbol["Wolfram/QuantumFramework", "Wolfram`QuantumFramework`QuantumOperator"]], Rule[ShowStringCharacters, True]], "Tooltip"]]], Rule[Background, RGBColor[0.968`, 0.976`, 0.984`]], Rule[BaselinePosition, Baseline], Rule[DefaultBaseStyle, List[]], Rule[FrameMargins, List[List[0, 0], List[1, 1]]], Rule[FrameStyle, RGBColor[0.831`, 0.847`, 0.85`]], Rule[RoundingRadius, 4]], PacletSymbol["Wolfram/QuantumFramework", "Wolfram`QuantumFramework`QuantumOperator"], Rule[Selectable, False], Rule[SelectWithContents, True], Rule[BoxID, "PacletSymbolBox"]]["I" + "Z"];

Evolve quantum state:

In[13]:=
\[Psi] = InterpretationBox[FrameBox[TagBox[TooltipBox[PaneBox[GridBox[List[List[GraphicsBox[List[Thickness[0.0025`], List[FaceForm[List[RGBColor[0.9607843137254902`, 0.5058823529411764`, 0.19607843137254902`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3]]], List[List[List[205.`, 22.863691329956055`], List[205.`, 212.31669425964355`], List[246.01799774169922`, 235.99870109558105`], List[369.0710144042969`, 307.0436840057373`], List[369.0710144042969`, 117.59068870544434`], List[205.`, 22.863691329956055`]], List[List[30.928985595703125`, 307.0436840057373`], List[153.98200225830078`, 235.99870109558105`], List[195.`, 212.31669425964355`], List[195.`, 22.863691329956055`], List[30.928985595703125`, 117.59068870544434`], List[30.928985595703125`, 307.0436840057373`]], List[List[200.`, 410.42970085144043`], List[364.0710144042969`, 315.7036876678467`], List[241.01799774169922`, 244.65868949890137`], List[200.`, 220.97669792175293`], List[158.98200225830078`, 244.65868949890137`], List[35.928985595703125`, 315.7036876678467`], List[200.`, 410.42970085144043`]], List[List[376.5710144042969`, 320.03370475769043`], List[202.5`, 420.53370475769043`], List[200.95300006866455`, 421.42667961120605`], List[199.04699993133545`, 421.42667961120605`], List[197.5`, 420.53370475769043`], List[23.428985595703125`, 320.03370475769043`], List[21.882003784179688`, 319.1406993865967`], List[20.928985595703125`, 317.4896984100342`], List[20.928985595703125`, 315.7036876678467`], List[20.928985595703125`, 114.70369529724121`], List[20.928985595703125`, 112.91769218444824`], List[21.882003784179688`, 111.26669120788574`], List[23.428985595703125`, 110.37369346618652`], List[197.5`, 9.87369155883789`], List[198.27300024032593`, 9.426692008972168`], List[199.13700008392334`, 9.203690528869629`], List[200.`, 9.203690528869629`], List[200.86299991607666`, 9.203690528869629`], List[201.72699999809265`, 9.426692008972168`], List[202.5`, 9.87369155883789`], List[376.5710144042969`, 110.37369346618652`], List[378.1179962158203`, 111.26669120788574`], List[379.0710144042969`, 112.91769218444824`], List[379.0710144042969`, 114.70369529724121`], List[379.0710144042969`, 315.7036876678467`], List[379.0710144042969`, 317.4896984100342`], List[378.1179962158203`, 319.1406993865967`], List[376.5710144042969`, 320.03370475769043`]]]]], List[FaceForm[List[RGBColor[0.5529411764705883`, 0.6745098039215687`, 0.8117647058823529`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]]], List[List[List[44.92900085449219`, 282.59088134765625`], List[181.00001525878906`, 204.0298843383789`], List[181.00001525878906`, 46.90887451171875`], List[44.92900085449219`, 125.46986389160156`], List[44.92900085449219`, 282.59088134765625`]]]]], List[FaceForm[List[RGBColor[0.6627450980392157`, 0.803921568627451`, 0.5686274509803921`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]]], List[List[List[355.0710144042969`, 282.59088134765625`], List[355.0710144042969`, 125.46986389160156`], List[219.`, 46.90887451171875`], List[219.`, 204.0298843383789`], List[355.0710144042969`, 282.59088134765625`]]]]], List[FaceForm[List[RGBColor[0.6901960784313725`, 0.5882352941176471`, 0.8117647058823529`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]]], List[List[List[200.`, 394.0606994628906`], List[336.0710144042969`, 315.4997024536133`], List[200.`, 236.93968200683594`], List[63.928985595703125`, 315.4997024536133`], List[200.`, 394.0606994628906`]]]]]], List[Rule[BaselinePosition, Scaled[0.15`]], Rule[ImageSize, 10], Rule[ImageSize, 15]]], StyleBox[RowBox[List["QuantumEvolve", " "]], Rule[ShowAutoStyles, False], Rule[ShowStringCharacters, False], Rule[FontSize, Times[0.9`, Inherited]], Rule[FontColor, GrayLevel[0.1`]]]]], Rule[GridBoxSpacings, List[Rule["Columns", List[List[0.25`]]]]]], Rule[Alignment, List[Left, Baseline]], Rule[BaselinePosition, Baseline], Rule[FrameMargins, List[List[3, 0], List[0, 0]]], Rule[BaseStyle, List[Rule[LineSpacing, List[0, 0]], Rule[LineBreakWithin, False]]]], RowBox[List["PacletSymbol", "[", RowBox[List["\"Wolfram/QuantumFramework\"", ",", "\"Wolfram`QuantumFramework`QuantumEvolve\""]], "]"]], Rule[TooltipStyle, List[Rule[ShowAutoStyles, True], Rule[ShowStringCharacters, True]]]], Function[Annotation[Slot[1], Style[Defer[PacletSymbol["Wolfram/QuantumFramework", "Wolfram`QuantumFramework`QuantumEvolve"]], Rule[ShowStringCharacters, True]], "Tooltip"]]], Rule[Background, RGBColor[0.968`, 0.976`, 0.984`]], Rule[BaselinePosition, Baseline], Rule[DefaultBaseStyle, List[]], Rule[FrameMargins, List[List[0, 0], List[1, 1]]], Rule[FrameStyle, RGBColor[0.831`, 0.847`, 0.85`]], Rule[RoundingRadius, 4]], PacletSymbol["Wolfram/QuantumFramework", "Wolfram`QuantumFramework`QuantumEvolve"], Rule[Selectable, False], Rule[SelectWithContents, True], Rule[BoxID, "PacletSymbolBox"]][
   hamiltonian, {t, 0, 3.}];

Plot the probability of observing the register state:

In[14]:=
Plot[Evaluate@Normal@\[Psi][t]["Probabilities"], {t, 0, 3.}, PlotLabel -> "Population vs time", PlotLegends -> {"0", "1"}]
Out[14]=

Disclosures

Compatibility

Wolfram Language Version 13.1

Version History

  • 1.4.2 – 28 June 2024
  • 1.4.1 – 22 May 2024
  • 1.4.0 – 15 May 2024
  • 1.3.7 – 06 May 2024
  • 1.3.6 – 24 April 2024
  • 1.3.5 – 08 April 2024
  • 1.3.4 – 13 March 2024
  • 1.3.3 – 14 February 2024
  • 1.3.2 – 03 February 2024
  • 1.3.1 – 17 January 2024
  • 1.3.0 – 14 January 2024
  • 1.2.15 – 13 January 2024
  • 1.2.14 – 25 December 2023
  • 1.2.13 – 21 December 2023
  • 1.2.12 – 21 November 2023
  • 1.2.11 – 01 November 2023
  • 1.2.10 – 19 October 2023
  • 1.2.9 – 02 October 2023
  • 1.2.8 – 16 September 2023
  • 1.2.7 – 12 September 2023
  • 1.2.6 – 18 August 2023
  • 1.2.5 – 17 August 2023
  • 1.2.4 – 03 August 2023
  • 1.2.3 – 01 August 2023
  • 1.2.2 – 21 July 2023
  • 1.2.1 – 06 July 2023
  • 1.2.0 – 28 June 2023
  • 1.1.4 – 28 June 2023
  • 1.1.3 – 14 June 2023
  • 1.1.2 – 01 June 2023
  • 1.1.1 – 23 May 2023
  • 1.1.0 – 05 May 2023
  • 1.0.35 – 03 May 2023
  • 1.0.34 – 26 April 2023
  • 1.0.33 – 19 April 2023
  • 1.0.31 – 06 April 2023
  • 1.0.30 – 03 April 2023
  • 1.0.29 – 08 March 2023
  • 1.0.28 – 27 January 2023
  • 1.0.27 – 01 January 2023
  • 1.0.26 – 03 December 2022
  • 1.0.25 – 05 November 2022
  • 1.0.24 – 18 October 2022
  • 1.0.23 – 11 October 2022
  • 1.0.22 – 04 October 2022
  • 1.0.21 – 30 September 2022
  • 1.0.19 – 15 August 2022
  • 1.0.18 – 08 August 2022
  • 1.0.17 – 16 July 2022
  • 1.0.15 – 25 May 2022
  • 1.0.14 – 10 May 2022
  • 1.0.13 – 24 April 2022
  • 1.0.12 – 05 April 2022
  • 1.0.11 – 05 April 2022
  • 1.0.10 – 05 April 2022
  • 1.0.9 – 05 April 2022
  • 1.0.8 – 04 April 2022
  • 1.0.6 – 04 April 2022
  • 1.0.2 – 18 January 2022
  • 0.0.1 – 08 March 2023

License Information

MIT License

Paclet Source

Source Metadata

See Also