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-Cell[74580, 2062, 78, 0, 70, "FooterCell",ExpressionUUID->"262c2cb2-dde1-40a1-b221-4e7278aaf340"] +Cell[67018, 1869, 3423, 83, 70, "GuideTutorialsSection",ExpressionUUID->"e601ba2b-5a60-4157-8efb-f7b2567393c0"], +Cell[70444, 1954, 2232, 55, 70, "GuideMoreAboutSection",ExpressionUUID->"1d3f15e7-4466-4b29-a55a-a98997208dbd"], +Cell[72679, 2011, 1830, 49, 70, "GuideRelatedLinksSection",ExpressionUUID->"edc5a388-08f5-4ad0-a37c-90e105cd52c7"], +Cell[74512, 2062, 78, 0, 70, "FooterCell",ExpressionUUID->"f659be03-2a7e-459a-979a-cd3f7c3dd651"] } ] *) diff --git a/Q3/Documentation/English/Index/_0.cfs b/Q3/Documentation/English/Index/_0.cfs index f81c1ebf2..fcb7d8f2d 100644 Binary files a/Q3/Documentation/English/Index/_0.cfs and b/Q3/Documentation/English/Index/_0.cfs differ diff --git a/Q3/Documentation/English/Index/segments_3 b/Q3/Documentation/English/Index/segments_3 index 63cbe0b8b..743694926 100644 Binary files a/Q3/Documentation/English/Index/segments_3 and b/Q3/Documentation/English/Index/segments_3 differ diff --git a/Q3/Documentation/English/ReferencePages/Symbols/CliffordCircuit.nb b/Q3/Documentation/English/ReferencePages/Symbols/CliffordCircuit.nb index 7e3adbbbc..d0994d20d 100644 --- a/Q3/Documentation/English/ReferencePages/Symbols/CliffordCircuit.nb +++ b/Q3/Documentation/English/ReferencePages/Symbols/CliffordCircuit.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 154, 7] -NotebookDataLength[ 45515, 1182] -NotebookOptionsPosition[ 40861, 1089] -NotebookOutlinePosition[ 43065, 1144] -CellTagsIndexPosition[ 42979, 1139] +NotebookDataLength[ 82805, 2097] +NotebookOptionsPosition[ 75544, 1950] +NotebookOutlinePosition[ 77748, 2005] +CellTagsIndexPosition[ 77662, 2000] WindowTitle->CliffordCircuit WindowFrame->Normal*) @@ -27,11 +27,11 @@ Cell[BoxData[GridBox[{ TemplateBox[{12}, "Spacer1"], Cell["Q3 SYMBOL", "PacletNameCell", TextAlignment->Center,ExpressionUUID-> - "21cc2d08-fed6-4d18-93b9-d3eb498645d2"], + "fd66bfb1-f4fa-4380-b1b3-71e3cc01b5c8"], TemplateBox[{8}, "Spacer1"]}]], TextAlignment->Center,ExpressionUUID-> - "a43d97be-b602-46ae-8e7f-fd4b85da5377"], + "c6261236-1d58-4903-a80c-fa820a4c2c65"], Background->RGBColor[0.490196, 0.576471, 0.690196], ItemSize->Full], ""} }, @@ -54,8 +54,8 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "f738ba9c-d541-409c-b1ef-57cb68a5a444"] - }],ExpressionUUID->"193556a7-90de-4026-a502-67b2d578e5b6"], + "585d8f91-3c1e-4a4a-9525-6935ec361c2e"] + }],ExpressionUUID->"4b6173b2-61f2-47b8-a3d3-9edb8b156cd2"], StripOnInput->False],{ StyleBox[ "\"CliffordState\"", "SeeAlsoRelated", StripOnInput -> False] :> @@ -75,7 +75,7 @@ Cell[BoxData[GridBox[{ MenuStyle->"SeeAlso"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "bad4cec4-882a-46a1-bed5-91ac112c7bb2"], + "c61999ef-62cc-40fd-99d2-a58fca6649ef"], "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ \[ThickSpace]", Cell[BoxData[ @@ -94,8 +94,8 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "e08efce6-bfbb-4f20-b58e-a2cd745f54ba"] - }],ExpressionUUID->"fb934b80-4797-4a50-b9fd-18f599d1af3b"], + "73e8ed2d-ab92-4454-b465-2a0d5a391881"] + }],ExpressionUUID->"aa1f4d1f-9dd3-4040-afca-10e9f08288d5"], StripOnInput->False],{ "\"Clifford Quantum Circuits\"" :> Documentation`HelpLookup["paclet:Q3/guide/CliffordQuantumCircuits"], @@ -107,7 +107,7 @@ Cell[BoxData[GridBox[{ MenuStyle->"MoreAbout"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "31c18eeb-ab59-4f6a-9948-e4ba2e624882"], + "a8789789-3351-4501-b07e-74fd7a85a52a"], "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ \[ThickSpace]", Cell[BoxData[ @@ -126,8 +126,8 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, 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"91af2670-f602-4306-9cb4-1800ecc9ec35"], + "41dc1af8-8baf-4918-906b-348802f15949"], TemplateBox[{8}, "Spacer1"]}]], TextAlignment->Center,ExpressionUUID-> - "069c0f32-b415-440f-a1d8-e67412bc5907"], + "b3c28329-4f1e-4e60-939c-084b35ac774a"], Background->RGBColor[0.490196, 0.576471, 0.690196], ItemSize->Full], ""} }, @@ -54,8 +54,8 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "5ea0dac7-4232-45b2-8c50-4aa323e0c4b1"] - }],ExpressionUUID->"305723dd-90a6-496a-a5f9-728d0a2ab61d"], + "00a82bae-37bd-4cdf-9334-96de2072dc89"] + }],ExpressionUUID->"e6419aa8-1106-49bb-8ba3-fdcf38701074"], StripOnInput->False],{ StyleBox["\"CliffordQ\"", "SeeAlsoRelated", StripOnInput -> False] :> Documentation`HelpLookup["paclet:Q3/ref/CliffordQ"], @@ -78,7 +78,7 @@ Cell[BoxData[GridBox[{ MenuStyle->"SeeAlso"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "3ecdb2f8-36e2-4a34-9715-605398c8ed65"], + "a623386d-93e4-449f-b36f-15008ba2276c"], "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ \[ThickSpace]", Cell[BoxData[ @@ -97,8 +97,8 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "d79e831e-b7c0-4f3a-96e8-0a440dc46702"] - }],ExpressionUUID->"6b67710c-f220-45af-8033-3e0d5ae7d827"], + "ca91ca5a-5806-42e3-ac8b-997d21be7109"] + }],ExpressionUUID->"5d96843c-61f6-4c5d-b2e4-44f9305a3572"], StripOnInput->False],{ "\"Clifford Quantum Circuits\"" :> Documentation`HelpLookup["paclet:Q3/guide/CliffordQuantumCircuits"], @@ -110,7 +110,7 @@ Cell[BoxData[GridBox[{ MenuStyle->"MoreAbout"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "17508005-081d-40f2-b9e3-b28cf2b84969"], + "b2697e16-b976-4012-a0ab-3da5f94e81ae"], "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ \[ThickSpace]", Cell[BoxData[ @@ -129,8 +129,8 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "d7110d85-e64f-47db-93b0-77b7c79d6a4f"] - }],ExpressionUUID->"2e71318d-1fc1-4289-b016-5c221927434d"], + "aa254877-67c2-46f6-820a-8bc723ca1323"] + }],ExpressionUUID->"35c88310-24bd-40c0-9b91-1a6b283a5058"], StripOnInput->False],{ "\"Clifford Decomposition\"" :> Documentation`HelpLookup["paclet:Q3/tutorial/CliffordDecomposition"], @@ -158,7 +158,7 @@ Cell[BoxData[GridBox[{ MenuStyle->"Tutorials"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - 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}],ExpressionUUID->"9a28c3f1-ade0-441a-9d84-1d7bda56a4b6"]}, + }],ExpressionUUID->"e440d63f-bac9-4107-aed6-3c91b4ae4d67"]}, {"", Cell[TextData[{ Cell[BoxData[ RowBox[{ @@ -326,7 +326,7 @@ combine to yield Clifford operator ", FontFamily->"Source Sans Pro",ExpressionUUID-> "d142e523-f2a8-4137-8f1a-384a1cdd1cd1"], "." - }],ExpressionUUID->"af201562-e64d-4600-a792-a2ae7acfb63e"]} + }],ExpressionUUID->"8e675771-c53e-47ef-a9a5-7f027ad01200"]} }]], "Usage", CellID->212278340,ExpressionUUID->"8118ec52-a228-4fd0-98d8-71ed26daae9d"] }, Open ]], @@ -360,12 +360,12 @@ Cell[TextData[Cell[BoxData[ 0.68 Inherited], Rational[1, 2] Pi, {-1.65, -1}]]], ImageSizeCache->{ 13.600000000000003`, {-0.1685058593749993, 13.768505859375}}]], - ExpressionUUID->"cbe1eb79-4dcf-49de-8c7a-559520d89688"], + ExpressionUUID->"539dca65-e97b-49e1-b806-461fb9192102"], Cell[BoxData[ TemplateBox[{1}, - "Spacer1"]],ExpressionUUID->"8f39dffc-b6fe-46dc-94f7-5fdf27e89882"], + "Spacer1"]],ExpressionUUID->"1f5af117-b2db-447a-9478-c61f3f7b6a29"], "Details and Options" - 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71511, 1894] +NotebookOptionsPosition[ 62344, 1708] +NotebookOutlinePosition[ 64688, 1766] +CellTagsIndexPosition[ 64602, 1761] WindowTitle->CliffordState WindowFrame->Normal*) @@ -27,11 +27,11 @@ Cell[BoxData[GridBox[{ TemplateBox[{12}, "Spacer1"], Cell["Q3 SYMBOL", "PacletNameCell", TextAlignment->Center,ExpressionUUID-> - "a5dff2dd-25c1-4248-aab8-873f26a55848"], + "187cb3a5-4b9e-4364-816b-626ac2a2273a"], TemplateBox[{8}, "Spacer1"]}]], TextAlignment->Center,ExpressionUUID-> - "d59174d9-d4ba-4948-958c-ff0cb666e187"], + "34a3924e-43ce-45e0-a768-454da4b5b7b6"], Background->RGBColor[0.490196, 0.576471, 0.690196], ItemSize->Full], ""} }, @@ -54,8 +54,8 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "b924a009-36bf-42c3-a9fd-ac311e4636bf"] - }],ExpressionUUID->"de8cc986-71d5-4b69-9c0e-9ca7911aa8c8"], + "79d9fc0e-fc2a-4934-8f4e-7d33dbe970dc"] + }],ExpressionUUID->"a92079a2-5a8f-49af-aca3-0e3caa65651a"], 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"TechNotesSection",ExpressionUUID->"17c163be-76b7-468f-876a-\ +1e2a7bff0e8b"], Cell[BoxData[GridBox[{ { @@ -7635,7 +7635,7 @@ Cell[BoxData[GridBox[{ "paclet:Q3/guide/CliffordQuantumCircuits"}, "RefLinkPlain", BaseStyle->{"MoreAbout"}]], "MoreAbout",ExpressionUUID-> - "cc800b79-f021-4416-9e68-d4240db18ee6"]}]}, + "037f4db6-dc98-4948-83e0-f5befa73180d"]}]}, { RowBox[{"\[FilledVerySmallSquare]", Cell[BoxData[ TemplateBox[{ @@ -7644,10 +7644,10 @@ Cell[BoxData[GridBox[{ "paclet:Q3/guide/QuantumInformationSystems"}, "RefLinkPlain", BaseStyle->{"MoreAbout"}]], "MoreAbout",ExpressionUUID-> - "92861838-f9a1-40e9-bb66-fa006c2c281c"]}]} + "523dac99-0e6b-49b9-b339-c00a30412e3f"]}]} }]} - }]], "MoreAboutSection",ExpressionUUID->"b7c129ce-cd1b-45e6-afb1-\ -99abfb31e534"], + }]], "MoreAboutSection",ExpressionUUID->"2f009213-caca-43f7-a88a-\ +a32a5f310a8d"], Cell[BoxData[GridBox[{ { @@ -7676,8 +7676,8 @@ Cell[BoxData[GridBox[{ "https://dl.acm.org/doi/10.5555/2011350.2011356"}, "WebLink", BaseStyle->{"RelatedLinks"}]],ExpressionUUID-> - "ef88194b-f7b0-433e-aeb2-43d882527172"]}]],ExpressionUUID-> - "bc1642f3-440d-4eed-801e-79d961cc7f76"], + "0444db94-e917-40a9-ba38-72e6ea37a571"]}]],ExpressionUUID-> + "fad2e6e8-d867-4d37-a16d-2dc24b908541"], ", Quantum Information & Computation 10, 258 (2010), \"Classical \ simulation of quantum computation, the Gottesman-Knill theorem, and slightly \ beyond.\"" @@ -7700,8 +7700,8 @@ beyond.\"" "https://doi.org/10.1103/PRXQuantum.2.010307"}, "WebLink", BaseStyle->{"RelatedLinks"}]],ExpressionUUID-> - "a0b59c8c-d8bc-4afb-b3c9-75d3dffdab67"]}]],ExpressionUUID-> - "9841d648-bb2c-452d-8770-2ea09e0c4f39"], + "f3d47eaf-c528-4c79-9fa6-bd70d7b30229"]}]],ExpressionUUID-> + "ec94442e-f4a8-466f-80de-b797cfa58ba4"], ", PRX Quantum 2, 010307 (2021), \"Experimental Estimation of Quantum \ State Properties from Classical Shadows.\"" }], "RelatedLinks",ExpressionUUID-> @@ -7723,8 +7723,8 @@ State Properties from Classical Shadows.\"" Physics 55, 122202 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Aaronson and D. Gottesman, Physical Review A 70, 052328 \ -(2004)"}]]]], "https://doi.org/10.1103/physreva.70.052328"}, + "S. Aaronson and D. 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}]], "RelatedLinksSection",ExpressionUUID->"4fd44c4d-7969-4434-8a0b-\ -1965db59a3af"], + }]], "RelatedLinksSection",ExpressionUUID->"3a5c895c-5918-49ea-ae6b-\ +f5109681076d"], -Cell[" ", "FooterCell",ExpressionUUID->"31dc455d-3678-481b-848d-c3a7a59968f5"] +Cell[" ", "FooterCell",ExpressionUUID->"8d6fd053-1af3-4b70-8cbb-f45e82145994"] }, Saveable->False, ScreenStyleEnvironment->"Working", @@ -7821,7 +7822,7 @@ TaggingRules->{ "CitationPopupData" -> $Failed, "ShowCitation" -> False, "HasOptions" -> True, "RootCaptions" -> "", "HeaderCoreAreaLink" -> {}, "Metadata" -> { - "built" -> "{2024, 9, 23, 10, 12, 5.658347}", + "built" -> "{2024, 9, 25, 9, 38, 48.007057}", "history" -> {"14.1", "", "", ""}, "context" -> "Q3`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Q3 Symbol", "language" -> "en", "paclet" -> "Q3", "status" -> @@ -7844,7 +7845,7 @@ StyleDefinitions->Notebook[{ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, FrontEndVersion -> "14.1 for Mac OS X ARM (64-bit) (July 16, 2024)", StyleDefinitions -> "Default.nb"], -ExpressionUUID->"7e6f230b-108c-43d9-a127-bd863b6ba0e4" +ExpressionUUID->"b7205036-726d-4798-8fdd-69a79d527177" ] (* End of Notebook Content *) @@ -7852,35 +7853,35 @@ ExpressionUUID->"7e6f230b-108c-43d9-a127-bd863b6ba0e4" (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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TextAlignment->Center,ExpressionUUID-> - "d3843cfd-0084-49a8-a4c6-2ef560b4eb9a"], + "dd2c7df4-7898-4e14-8ca5-90edc18859eb"], TemplateBox[{8}, "Spacer1"]}]], TextAlignment->Center,ExpressionUUID-> - "0ee5940f-6334-4854-a170-5837c1965c78"], + "760b696c-d7bb-4a3e-b8db-e960f4149944"], Background->RGBColor[0.490196, 0.576471, 0.690196], ItemSize->Full], ""} }, @@ -54,8 +54,8 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "cb691234-9c8b-4399-94eb-01af165dd543"] - }],ExpressionUUID->"5039ad4b-c8c4-4a48-acf7-1c8ceb1370cb"], + "4139fff0-cdff-4302-bdfb-1165d424a001"] + }],ExpressionUUID->"09c0e591-7019-497e-888d-1daffefbdd15"], StripOnInput->False],{ StyleBox[ "\"GottesmanVector\"", "SeeAlsoRelated", StripOnInput -> False] :> @@ -76,7 +76,7 @@ Cell[BoxData[GridBox[{ MenuStyle->"SeeAlso"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "b3e598af-2f68-4885-a54c-679288bb35a4"], + "e126cfe0-54e8-40f3-a078-7694db6a2da3"], "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ \[ThickSpace]", Cell[BoxData[ @@ -95,10 +95,12 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "3b615190-aeaf-4f7c-809d-f9a21ef1b94d"] - }],ExpressionUUID->"e50d56da-9253-4902-97df-27be0a55b667"], + "490f37cd-3a6c-480b-9cb8-f29e18c127d1"] + }],ExpressionUUID->"22fbcc82-e609-462c-affe-b791d9531d04"], StripOnInput->False],{ - "\"Quantum Information Systems\"" :> + "\"Clifford Quantum Circuits\"" :> + Documentation`HelpLookup["paclet:Q3/guide/CliffordQuantumCircuits"], + "\"Quantum Information Systems\"" :> Documentation`HelpLookup[ "paclet:Q3/guide/QuantumInformationSystems"]}, Appearance->None, @@ -106,7 +108,7 @@ Cell[BoxData[GridBox[{ MenuStyle->"MoreAbout"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "95d65e00-3187-4545-9b17-81b283b98179"], + 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-> - DocumentationBuild`Make`Private`visible$32527]]; + DocumentationBuild`Make`Private`visible$37669]]; SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; NotebookClose[DocumentationSearch`Private`nb$]; Null], @@ -205,14 +207,14 @@ FromGottesmanVector.html"], StandardForm]], "Input", TextClipboardType -> MenuStyle->"URLMenu"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "dc04f7b0-294e-448b-91d1-adeca552a36e"] + "93e75e00-17c6-42b6-ae57-25bb983c33bb"] }], "AnchorBar", CacheGraphics->False,ExpressionUUID-> - "e62aaa41-0c65-4b64-b611-cf0898c6c967"]} + "e0d7d6be-9d95-499b-84e7-529ab485a03a"]} }]], "AnchorBarGrid", - CellID->1,ExpressionUUID->"88aae807-3322-40bf-9395-c2258a824451"], + CellID->1,ExpressionUUID->"c02d80cb-0b72-4bac-ac0b-43e29858d87c"], -Cell["Q3`", "ContextNameCell",ExpressionUUID->"47cd96b6-9374-44cf-8c40-440fdc065e31"], +Cell["Q3`", 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index 9de934d42..5146ca29d 100644 --- a/Q3/Documentation/English/ReferencePages/Symbols/FullGottesmanMatrix.nb +++ b/Q3/Documentation/English/ReferencePages/Symbols/FullGottesmanMatrix.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 154, 7] -NotebookDataLength[ 142899, 3696] -NotebookOptionsPosition[ 135750, 3552] -NotebookOutlinePosition[ 138040, 3608] -CellTagsIndexPosition[ 137953, 3603] +NotebookDataLength[ 141988, 3672] +NotebookOptionsPosition[ 134842, 3528] +NotebookOutlinePosition[ 137131, 3584] +CellTagsIndexPosition[ 137044, 3579] WindowTitle->FullGottesmanMatrix WindowFrame->Normal*) @@ -27,11 +27,11 @@ Cell[BoxData[GridBox[{ TemplateBox[{12}, "Spacer1"], Cell["Q3 SYMBOL", "PacletNameCell", TextAlignment->Center,ExpressionUUID-> - "77bf653e-8196-4558-963f-dfa28c6840ee"], + "b8a95f61-2874-4f86-a87e-d721f609a9ed"], TemplateBox[{8}, "Spacer1"]}]], TextAlignment->Center,ExpressionUUID-> - "2baa23b3-fe9c-4307-99b9-f9c97e47b02b"], + 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98903, 2511] WindowTitle->FullPauliGroup WindowFrame->Normal*) @@ -27,11 +27,11 @@ Cell[BoxData[GridBox[{ TemplateBox[{12}, "Spacer1"], Cell["Q3 SYMBOL", "PacletNameCell", TextAlignment->Center,ExpressionUUID-> - "b125c757-b9c0-4608-9379-13c15f99e2c7"], + "c037e163-34ae-4e29-8a8c-2363d37b7612"], TemplateBox[{8}, "Spacer1"]}]], TextAlignment->Center,ExpressionUUID-> - "969aa0de-964b-4979-83bb-857759bec34f"], + "49c0ed49-c4e8-4ef6-ba79-e917f2e68632"], Background->RGBColor[0.490196, 0.576471, 0.690196], ItemSize->Full], ""} }, @@ -54,38 +54,49 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "901de8db-1642-4dea-a925-515d18ee60a9"] - }],ExpressionUUID->"1d228166-655e-4fe5-9223-34b33aa89713"], + "2c4e482b-3459-40ec-8043-6cf58fee0f51"] + }],ExpressionUUID->"aa325a58-2fd0-47b6-ad33-a2e9099be515"], StripOnInput->False],{ - "\"GroupElements\"" :> + StyleBox[ + "\"GroupElements\"", "SeeAlsoRelated", StripOnInput -> 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933] -NotebookOutlinePosition[ 35845, 995] -CellTagsIndexPosition[ 35760, 990] +NotebookDataPosition[ 154, 7] +NotebookDataLength[ 39253, 1053] +NotebookOptionsPosition[ 33625, 942] +NotebookOutlinePosition[ 36415, 1005] +CellTagsIndexPosition[ 36330, 1000] WindowTitle->GottesmanBasis WindowFrame->Normal*) @@ -27,11 +27,11 @@ Cell[BoxData[GridBox[{ TemplateBox[{12}, "Spacer1"], Cell["Q3 SYMBOL", "PacletNameCell", TextAlignment->Center,ExpressionUUID-> - "4aeaf687-93aa-44f8-bb89-ea5990013177"], + "f7854195-4ecb-4dd7-8811-d93530b58b25"], TemplateBox[{8}, "Spacer1"]}]], TextAlignment->Center,ExpressionUUID-> - "a9bdf69f-0da1-4afd-bdc8-11dc5edbbd44"], + "890c4ddf-3670-4dc1-9a68-b7d517fe614e"], Background->RGBColor[0.490196, 0.576471, 0.690196], ItemSize->Full], ""} }, @@ -54,25 +54,30 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "6fc9a09f-9e11-44fb-ae58-68c09b5a409d"] - }],ExpressionUUID->"0e5abc44-6904-4017-8507-c45496a36789"], + "4831ff4b-1aaf-4179-9a43-9b44ff7e8fb0"] + }],ExpressionUUID->"0083af20-8d2f-4ea8-91b1-f56bd57294b4"], StripOnInput->False],{ - "\"GottesmanVector\"" :> + StyleBox[ + "\"GottesmanVector\"", "SeeAlsoRelated", StripOnInput -> False] :> Documentation`HelpLookup["paclet:Q3/ref/GottesmanVector"], - "\"GottesmanInner\"" :> - Documentation`HelpLookup["paclet:Q3/ref/GottesmanInner"], - "\"BinarySymplecticGroup\"" :> - Documentation`HelpLookup["paclet:Q3/ref/BinarySymplecticGroup"], - "\"CliffordGroup\"" :> + StyleBox[ + "\"GottesmanDot\"", "SeeAlsoRelated", StripOnInput -> False] :> + Documentation`HelpLookup["paclet:Q3/ref/GottesmanDot"], + StyleBox[ + "\"BinarySymplecticGroup\"", "SeeAlsoRelated", StripOnInput -> + False] :> Documentation`HelpLookup[ + "paclet:Q3/ref/BinarySymplecticGroup"], + StyleBox[ + "\"CliffordGroup\"", "SeeAlsoRelated", StripOnInput -> False] :> Documentation`HelpLookup["paclet:Q3/ref/CliffordGroup"], - 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"FooterCell",ExpressionUUID->"805e1536-272c-4320-85e4-c6b41752b067"] +Cell[136790, 2675, 1872, 50, 70, "SeeAlsoSection",ExpressionUUID->"21ea728c-27c2-40e5-b26d-fbd31df6a6fe"], +Cell[138665, 2727, 2096, 53, 70, "TutorialsSection",ExpressionUUID->"e72b6f6b-5c1c-44db-be0e-83a6d6e2ed0b"], +Cell[140764, 2782, 1117, 28, 70, "MoreAboutSection",ExpressionUUID->"908824c2-d607-4d9d-b754-512df558ca7d"], +Cell[141884, 2812, 1166, 34, 70, "RelatedLinksSection",ExpressionUUID->"72c1771d-5159-48da-b519-cd9ebab9a1e0"], +Cell[143053, 2848, 78, 0, 70, "FooterCell",ExpressionUUID->"162143e4-2cd4-410f-b590-184dfffdc1f9"] } ] *) diff --git a/Q3/Documentation/English/ReferencePages/Symbols/GottesmanFlip.nb b/Q3/Documentation/English/ReferencePages/Symbols/GottesmanFlip.nb index 92f8d36b1..31187a098 100644 --- a/Q3/Documentation/English/ReferencePages/Symbols/GottesmanFlip.nb +++ b/Q3/Documentation/English/ReferencePages/Symbols/GottesmanFlip.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 154, 7] -NotebookDataLength[ 37931, 1009] -NotebookOptionsPosition[ 32286, 893] -NotebookOutlinePosition[ 34436, 947] -CellTagsIndexPosition[ 34351, 942] +NotebookDataLength[ 37923, 1009] +NotebookOptionsPosition[ 32281, 893] +NotebookOutlinePosition[ 34431, 947] +CellTagsIndexPosition[ 34346, 942] WindowTitle->GottesmanFlip WindowFrame->Normal*) @@ -27,11 +27,11 @@ Cell[BoxData[GridBox[{ TemplateBox[{12}, "Spacer1"], Cell["Q3 SYMBOL", "PacletNameCell", TextAlignment->Center,ExpressionUUID-> - "61e9e722-c3ac-400f-95e5-4611114b84d8"], + "a9285473-e420-470b-8204-e002ddf5040f"], TemplateBox[{8}, "Spacer1"]}]], TextAlignment->Center,ExpressionUUID-> - "4cf168ac-4615-4960-a352-721f445f07bf"], + "a348b4d6-3b5b-439e-b8ed-8653c76298c6"], Background->RGBColor[0.490196, 0.576471, 0.690196], ItemSize->Full], ""} }, @@ -54,8 +54,8 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "932e1e06-f3c0-42aa-8948-65249f29afdb"] - }],ExpressionUUID->"098fbdc1-658a-4883-bb9c-5305e7818e07"], + "c8a117fd-f8c6-475b-a35b-83a08ce88b99"] + }],ExpressionUUID->"afa53f2b-b9ed-4384-978a-8abdca8e9b64"], StripOnInput->False],{ StyleBox[ "\"GottesmanVector\"", "SeeAlsoRelated", StripOnInput -> False] :> @@ -76,7 +76,7 @@ Cell[BoxData[GridBox[{ MenuStyle->"SeeAlso"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "061cfd27-e4f4-4d04-b989-1d262552c238"], + "30937b01-5236-4281-91ef-adb7b1f66f14"], "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ \[ThickSpace]", Cell[BoxData[ @@ -95,8 +95,8 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "3ec43f9a-4ffc-493c-9e24-24820cdb31b9"] - }],ExpressionUUID->"c3d174be-071c-433e-98a5-064f72d222be"], + "b3142e58-7b9f-4921-a9c6-0f9677af3c5d"] + }],ExpressionUUID->"bd0242c6-1cb5-4886-8ef5-e88ce81865be"], StripOnInput->False],{ "\"Clifford Quantum Circuits\"" :> Documentation`HelpLookup["paclet:Q3/guide/CliffordQuantumCircuits"], @@ -108,7 +108,7 @@ Cell[BoxData[GridBox[{ MenuStyle->"MoreAbout"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "220d9276-fcd9-4fba-bd00-0233d821e617"], + "c9efddae-d913-497c-87ed-bfa05dab7b37"], "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ \[ThickSpace]", Cell[BoxData[ @@ -127,8 +127,8 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "38e64d88-000f-47fb-ad52-d149a23cbdae"] - }],ExpressionUUID->"8ee78a87-d6db-4a89-9517-ebf7bffdf775"], + "ca8f4425-cd07-4341-b53b-bb758d156e8d"] + }],ExpressionUUID->"0e0c13bf-2426-4332-ba10-2701039830f1"], StripOnInput->False],{ "\"The Pauli and Clifford Groups\"" :> Documentation`HelpLookup[ @@ -148,7 +148,7 @@ Cell[BoxData[GridBox[{ MenuStyle->"Tutorials"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "dd1a06fc-fffe-427a-a222-c18558c46532"], + "487f2b3c-897e-4a13-9654-99f76b43eefc"], "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ \[ThickSpace]", Cell[BoxData[ @@ -167,8 +167,8 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "5d2eb5c8-4914-42cb-afdb-33563577677b"] - }],ExpressionUUID->"4f28ad55-191d-43b1-a6fe-363fefb7c080"], + "032698a9-7cd2-4d95-8914-37f0636f4c73"] + }],ExpressionUUID->"02921f38-b913-409c-b6f7-07d4269063c2"], StripOnInput->False],{ "\"Q3/ref/GottesmanFlip\"" :> None, "\"Copy Wolfram Documentation Center URL\"" :> @@ -176,7 +176,7 @@ Cell[BoxData[GridBox[{ DocumentationSearch`Private`nb$ = NotebookPut[ Notebook[{Cell["Q3/ref/GottesmanFlip"]}, Visible -> - DocumentationBuild`Make`Private`visible$127115]]; + DocumentationBuild`Make`Private`visible$41477]]; SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; NotebookClose[DocumentationSearch`Private`nb$]; Null], Delimiter, @@ -191,7 +191,7 @@ Cell[BoxData[GridBox[{ "http://reference.wolfram.com/language/Q3/ref/\ GottesmanFlip.html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> - DocumentationBuild`Make`Private`visible$127115]]; + DocumentationBuild`Make`Private`visible$41477]]; SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; NotebookClose[DocumentationSearch`Private`nb$]; Null], @@ -207,14 +207,14 @@ GottesmanFlip.html"], StandardForm]], "Input", TextClipboardType -> MenuStyle->"URLMenu"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "ce5e7a38-5d78-4658-afd2-484de7da3104"] + "e28f7edd-8fc9-42ee-b54e-b10127d6ff89"] }], "AnchorBar", CacheGraphics->False,ExpressionUUID-> - 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-NotebookOptionsPosition[ 43377, 1203] -NotebookOutlinePosition[ 45656, 1260] -CellTagsIndexPosition[ 45570, 1255] +NotebookDataLength[ 50574, 1351] +NotebookOptionsPosition[ 43578, 1210] +NotebookOutlinePosition[ 45854, 1267] +CellTagsIndexPosition[ 45768, 1262] WindowTitle->GottesmanInverse WindowFrame->Normal*) @@ -27,11 +27,11 @@ Cell[BoxData[GridBox[{ TemplateBox[{12}, "Spacer1"], Cell["Q3 SYMBOL", "PacletNameCell", TextAlignment->Center,ExpressionUUID-> - "479f97ca-92eb-4ef0-ad1a-057e3e76f9bc"], + "0bf0c821-70f3-4b6a-a524-64732feb64aa"], TemplateBox[{8}, "Spacer1"]}]], TextAlignment->Center,ExpressionUUID-> - "adb4b2b3-115c-4f71-9633-36e72ca86fd4"], + "c15a87d1-db97-43ac-b9ea-bd6a3e1ebfc5"], Background->RGBColor[0.490196, 0.576471, 0.690196], ItemSize->Full], ""} }, @@ -54,8 +54,8 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "282591f6-2b04-4022-a745-31a91f17f842"] - }],ExpressionUUID->"79e2ce28-226b-475b-b686-b5695daac074"], + "12be1e31-eaa9-4bcc-b2e9-58816ab89c57"] + }],ExpressionUUID->"1c124785-dfc2-4dd5-b213-0219f0758269"], StripOnInput->False],{ StyleBox[ "\"GottesmanMatrixQ\"", "SeeAlsoRelated", StripOnInput -> False] :> @@ -67,14 +67,14 @@ Cell[BoxData[GridBox[{ "\"FromGottesmanMatrix\"", "SeeAlsoRelated", StripOnInput -> False] :> Documentation`HelpLookup["paclet:Q3/ref/FromGottesmanMatrix"], StyleBox[ - "\"GottesmanInner\"", "SeeAlsoRelated", StripOnInput -> False] :> - Documentation`HelpLookup["paclet:Q3/ref/GottesmanInner"]}, + "\"GottesmanDot\"", "SeeAlsoRelated", StripOnInput -> False] :> + Documentation`HelpLookup["paclet:Q3/ref/GottesmanDot"]}, Appearance->None, MenuAppearance->Automatic, MenuStyle->"SeeAlso"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "7494ca0a-39a5-4f3a-93ff-690f5ab69403"], + "3d146117-72f6-400d-80d9-7b0290c574ac"], "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ \[ThickSpace]", Cell[BoxData[ @@ -93,10 +93,12 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "cb5186fb-59e0-42f1-9505-f2be5b9f69b1"] - }],ExpressionUUID->"b4b9142c-336f-43e9-a663-bddfa329ea95"], + "411d9733-bc23-4a33-a61d-8b578283f59b"] + }],ExpressionUUID->"47d7eb74-37d0-42d7-a2e9-98b71ff699f1"], StripOnInput->False],{ - "\"Quantum Information Systems\"" :> + "\"Clifford Quantum Circuits\"" :> + Documentation`HelpLookup["paclet:Q3/guide/CliffordQuantumCircuits"], + "\"Quantum Information Systems\"" :> Documentation`HelpLookup[ "paclet:Q3/guide/QuantumInformationSystems"]}, Appearance->None, @@ -104,7 +106,7 @@ Cell[BoxData[GridBox[{ MenuStyle->"MoreAbout"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "46896303-3435-4b96-afb8-8fb0ca9fc416"], + "60e5de28-8785-474d-ab64-f24375517471"], "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ \[ThickSpace]", Cell[BoxData[ @@ -123,8 +125,8 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "092cd63a-02be-497d-a0d6-1b9d5b8a9900"] - }],ExpressionUUID->"15a29cb4-7d00-4b74-a723-1dcd01419a8c"], + "912839bb-3dec-4cab-9e77-70c9a9cd4529"] + }],ExpressionUUID->"9c105f91-d268-4a31-a4ee-d7b4010f70cc"], StripOnInput->False],{ "\"The Pauli and Clifford Groups\"" :> Documentation`HelpLookup[ @@ -144,7 +146,7 @@ Cell[BoxData[GridBox[{ MenuStyle->"Tutorials"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "a58d7c9b-b108-4682-864d-0c1766174b60"], + "7675ec11-473f-4eec-a804-2537aacf1719"], "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ \[ThickSpace]", Cell[BoxData[ @@ -163,8 +165,8 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "1bfe1087-1332-48d9-b3f9-facd327afed0"] - }],ExpressionUUID->"81e6cf8b-825e-46e1-ad39-740bdc74337e"], + "52db17ff-9485-496c-8287-b8bf7d312ed9"] + }],ExpressionUUID->"a922c7f9-eeaa-463b-a9bc-e8d8312ca3f5"], StripOnInput->False],{ "\"Q3/ref/GottesmanInverse\"" :> None, "\"Copy Wolfram Documentation Center URL\"" :> @@ -172,7 +174,7 @@ Cell[BoxData[GridBox[{ DocumentationSearch`Private`nb$ = NotebookPut[ Notebook[{Cell["Q3/ref/GottesmanInverse"]}, Visible -> - DocumentationBuild`Make`Private`visible$35579]]; + DocumentationBuild`Make`Private`visible$42748]]; SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; NotebookClose[DocumentationSearch`Private`nb$]; Null], Delimiter, @@ -187,7 +189,7 @@ Cell[BoxData[GridBox[{ "http://reference.wolfram.com/language/Q3/ref/\ GottesmanInverse.html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> - DocumentationBuild`Make`Private`visible$35579]]; + DocumentationBuild`Make`Private`visible$42748]]; SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; NotebookClose[DocumentationSearch`Private`nb$]; Null], @@ -203,14 +205,14 @@ GottesmanInverse.html"], StandardForm]], "Input", TextClipboardType -> MenuStyle->"URLMenu"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "468d16a8-87c1-4f65-8652-cb7e1acce711"] + "3ff6a801-2727-4288-bf38-964409fddc3a"] }], "AnchorBar", CacheGraphics->False,ExpressionUUID-> - "1d6626f0-3a15-40a9-8d25-8481acd756c5"]} + "66219e57-797a-4451-92ed-a958c9505efb"]} }]], "AnchorBarGrid", - CellID->1,ExpressionUUID->"05b0d11a-d1e4-44af-93de-4fbb3eb380c3"], + CellID->1,ExpressionUUID->"3707a7f8-4aa6-4b36-ba2d-6f7db85a23b2"], -Cell["Q3`", "ContextNameCell",ExpressionUUID->"ca7c52ce-00a1-4112-8c65-04dcdd9ed8a2"], +Cell["Q3`", "ContextNameCell",ExpressionUUID->"219070c2-f776-42ad-9ee5-b8532d5bf91f"], Cell[CellGroupData[{ 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"93eb4a6d-ec8e-4924-a1f9-d3dbdf4be7d7"]}]}, { RowBox[{"\[FilledVerySmallSquare]", Cell[BoxData[ TemplateBox[{ @@ -2692,10 +2692,10 @@ Cell[BoxData[GridBox[{ "paclet:Q3/guide/QuantumInformationSystems"}, "RefLinkPlain", BaseStyle->{"MoreAbout"}]], "MoreAbout",ExpressionUUID-> - "a0ce1f64-a3c8-4da0-beeb-87a325e94339"]}]} + "a8aff0ba-e364-438c-8038-2e861dab6a3e"]}]} }]} - }]], "MoreAboutSection",ExpressionUUID->"ad253762-4bf4-4fc2-baa5-\ -c7045e1e64f0"], + }]], "MoreAboutSection",ExpressionUUID->"195c38d6-0775-45fc-a33b-\ +ee35288b843d"], Cell[BoxData[GridBox[{ { @@ -2724,8 +2724,8 @@ Cell[BoxData[GridBox[{ "https://dl.acm.org/doi/10.5555/2011350.2011356"}, "WebLink", BaseStyle->{"RelatedLinks"}]],ExpressionUUID-> - "65e392c4-d309-4ed1-9cbe-da5b084380ab"]}]],ExpressionUUID-> - "7c0b2313-1be3-42f3-8021-8fda6a0bea05"], + "c0c08dc9-0b80-4297-b508-be9753e1305e"]}]],ExpressionUUID-> + "03874393-8178-4f57-b807-7f155e632c27"], ", Quantum Information & Computation 10, 258 (2010), \"Classical \ simulation of quantum computation, the Gottesman-Knill theorem, and slightly \ beyond.\"" @@ -2748,8 +2748,8 @@ beyond.\"" "https://doi.org/10.1103/PRXQuantum.2.010307"}, "WebLink", BaseStyle->{"RelatedLinks"}]],ExpressionUUID-> - "3120179c-02a9-40f1-a085-0d9f8aa04bda"]}]],ExpressionUUID-> - "7258bc00-744a-42b2-be99-18ff094a3a62"], + "e8f7ab00-8ea0-4f59-aa1e-2879e4835e35"]}]],ExpressionUUID-> + "9502e62f-57df-4ab4-b668-1d3150f3b2c5"], ", PRX Quantum 2, 010307 (2021), \"Experimental Estimation of Quantum \ State Properties from Classical Shadows.\"" }], "RelatedLinks",ExpressionUUID-> @@ -2771,8 +2771,8 @@ State Properties from Classical Shadows.\"" Physics 55, 122202 (2014)"}]]]], "https://doi.org/10.1063/1.4903507"}, "WebLink", BaseStyle->{"RelatedLinks"}]],ExpressionUUID-> - "99ddeae5-f014-4a89-9bfa-91896c102fe0"]}]],ExpressionUUID-> - "0c7d5a34-9340-4a30-92c4-0782a4fb4932"], + "ce00e4d2-8ebf-40d0-8f84-910985a0c2ba"]}]],ExpressionUUID-> + "09090b12-33f1-4981-aab9-e5749322f83e"], ", 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"df98fb99-ae2c-4b9c-9ef4-c6bb31b9fdb0"], + "f7e88061-db5c-4678-9699-876b6a75f013"], TemplateBox[{8}, "Spacer1"]}]], TextAlignment->Center,ExpressionUUID-> - "874ab248-da1c-4b45-9a9f-e6c3d54c2dd4"], + "df423d76-dc38-4cb1-b636-6e9c1573f3f5"], Background->RGBColor[0.490196, 0.576471, 0.690196], ItemSize->Full], ""} }, @@ -54,8 +54,8 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "6233a6a5-9895-4a87-bbcf-4f533a430abf"] - }],ExpressionUUID->"c373c1f5-3123-4f23-9ee0-64adba466170"], + "5d234ef4-7062-4ac9-9f45-eb8276e74a0b"] + }],ExpressionUUID->"379e163a-98ba-48a5-8cd5-eff7f57e08c6"], StripOnInput->False],{ StyleBox[ "\"GottesmanSplit\"", "SeeAlsoRelated", StripOnInput -> False] :> @@ -77,7 +77,7 @@ Cell[BoxData[GridBox[{ MenuStyle->"SeeAlso"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "587a77e7-b955-4250-853f-22220e0ba796"], + "e2c0b10b-a4ee-4b48-8079-08cf19e4c07c"], "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ \[ThickSpace]", Cell[BoxData[ @@ -96,10 +96,12 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "806e869d-e921-42f3-99fc-b06a48c04823"] - }],ExpressionUUID->"897bcc4b-63b0-40fb-bcea-24886263cb51"], + "1d78ddaa-65f7-4dd0-92a5-510d9284c079"] + }],ExpressionUUID->"2c6af187-8f35-46db-a06d-7c8394e9e060"], StripOnInput->False],{ - "\"Quantum Information Systems\"" :> + "\"Clifford Quantum Circuits\"" :> + Documentation`HelpLookup["paclet:Q3/guide/CliffordQuantumCircuits"], + "\"Quantum Information Systems\"" :> Documentation`HelpLookup[ "paclet:Q3/guide/QuantumInformationSystems"]}, Appearance->None, @@ -107,7 +109,7 @@ Cell[BoxData[GridBox[{ MenuStyle->"MoreAbout"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "882db637-6f28-4862-b7e8-2b49bee35775"], + "f0eccf0a-2c2e-4bb6-944d-0e63c74ecf71"], 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}],ExpressionUUID->"138a4493-3d4d-4b94-b063-b0ceb525dd4b"], + "944e260c-60cd-4602-9aca-0490457bdf83"] + }],ExpressionUUID->"d0811499-1fc5-4feb-af1c-1d9b2a73cd62"], StripOnInput->False],{ StyleBox[ "\"GottesmanMerge\"", "SeeAlsoRelated", StripOnInput -> False] :> @@ -77,7 +77,7 @@ Cell[BoxData[GridBox[{ MenuStyle->"SeeAlso"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "91be1a89-4ce3-4570-98fa-0122b1a2285a"], + "f2408678-43b6-432f-a25d-04b826cf782d"], "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ \[ThickSpace]", Cell[BoxData[ @@ -96,10 +96,12 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "a9b1639b-7442-4c3a-bbb8-a41e8d816d1c"] - }],ExpressionUUID->"8ac741e8-cdb0-4def-92f5-93b5b49a4862"], + "e58e4905-bcfa-4b49-80b3-c9b1809087a5"] + }],ExpressionUUID->"30002c4d-c94a-4032-9db9-812ea33ff1df"], StripOnInput->False],{ - "\"Quantum Information Systems\"" :> + 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b/Q3/Documentation/English/ReferencePages/Symbols/GottesmanStandard.nb @@ -3,17 +3,17 @@ (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) -(* CreatedBy='Mathematica 13.3' *) +(* CreatedBy='Wolfram 14.1' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest -NotebookDataPosition[ 158, 7] -NotebookDataLength[ 92367, 2513] -NotebookOptionsPosition[ 80736, 2278] -NotebookOutlinePosition[ 83747, 2346] -CellTagsIndexPosition[ 83625, 2340] +NotebookDataPosition[ 154, 7] +NotebookDataLength[ 95137, 2594] +NotebookOptionsPosition[ 83696, 2364] +NotebookOutlinePosition[ 86549, 2428] +CellTagsIndexPosition[ 86463, 2423] WindowTitle->GottesmanStandard WindowFrame->Normal*) @@ -27,11 +27,11 @@ Cell[BoxData[GridBox[{ TemplateBox[{12}, "Spacer1"], Cell["Q3 SYMBOL", "PacletNameCell", TextAlignment->Center,ExpressionUUID-> - "6e112840-c6aa-4dcc-b691-186503a6e1f7"], + "926726dc-2472-4833-a86e-8fbf29ae46c9"], TemplateBox[{8}, "Spacer1"]}]], TextAlignment->Center,ExpressionUUID-> - "b13727c0-81ec-49c8-b2c5-518b3a874820"], + "0bd3a6d5-f261-45d3-8e19-6188e5392373"], Background->RGBColor[0.490196, 0.576471, 0.690196], ItemSize->Full], ""} }, @@ -54,23 +54,27 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "3a2bd663-0e0e-4c95-97f8-dbe5ecd13b3b"] - }],ExpressionUUID->"23bfb2b6-3e08-4f11-a3b3-403198693335"], + "b885fff5-8b76-41e0-b6bf-fbf445c8fffe"] + }],ExpressionUUID->"06cd318f-b20c-4d88-b0ab-7a7e482ecda5"], StripOnInput->False],{ - "\"GottesmanSolve\"" :> + StyleBox[ + "\"GottesmanSolve\"", "SeeAlsoRelated", StripOnInput -> False] :> Documentation`HelpLookup["paclet:Q3/ref/GottesmanSolve"], - "\"GottesmanVector\"" :> + StyleBox[ + "\"GottesmanVector\"", "SeeAlsoRelated", StripOnInput -> False] :> Documentation`HelpLookup["paclet:Q3/ref/GottesmanVector"], - "\"GottesmanSplit\"" :> + StyleBox[ + "\"GottesmanSplit\"", "SeeAlsoRelated", StripOnInput -> False] :> Documentation`HelpLookup["paclet:Q3/ref/GottesmanSplit"], - "\"GottesmanMerge\"" :> + StyleBox[ + "\"GottesmanMerge\"", "SeeAlsoRelated", StripOnInput -> False] :> Documentation`HelpLookup["paclet:Q3/ref/GottesmanMerge"]}, Appearance->None, MenuAppearance->Automatic, MenuStyle->"SeeAlso"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "f9e065a0-29ad-4e58-8ef9-a806879f32c0"], + "7543514c-83ee-4198-b148-b0cef13225c1"], "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ \[ThickSpace]", Cell[BoxData[ @@ -89,10 +93,12 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "44faf098-0d72-4d3a-82c3-289643a6c6a1"] - }],ExpressionUUID->"d810f448-d4c9-4ffd-b02e-75d13fd549d1"], + "0c904518-4dfe-4fe3-a351-3ca0a6569693"] + }],ExpressionUUID->"40474b1f-540a-42a0-b2b4-b735a45b40ca"], StripOnInput->False],{ - "\"Quantum Information Systems\"" :> + "\"Clifford Quantum Circuits\"" :> + Documentation`HelpLookup["paclet:Q3/guide/CliffordQuantumCircuits"], + "\"Quantum Information Systems\"" :> Documentation`HelpLookup[ "paclet:Q3/guide/QuantumInformationSystems"]}, Appearance->None, @@ -100,7 +106,7 @@ Cell[BoxData[GridBox[{ MenuStyle->"MoreAbout"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "5fce4cbf-8bcc-4e55-8e33-8c7e8d43e9f4"], + "f4f93ce1-80ea-4af3-8752-a1d476a0c980"], "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ \[ThickSpace]", Cell[BoxData[ @@ -119,8 +125,8 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "517bba24-326e-4813-8986-677611ed28af"] - }],ExpressionUUID->"193406e4-83de-41a4-8e4f-5699e479fa4e"], + "b2e2a8b3-414f-4ae8-960c-7000f24848dd"] + }],ExpressionUUID->"e045fd72-59f8-47ee-b184-3383b915b921"], StripOnInput->False],{ "\"The Pauli and Clifford Groups\"" :> Documentation`HelpLookup[ @@ -137,7 +143,7 @@ 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TextAlignment->Center,ExpressionUUID-> - "292f9749-7d1b-4987-b809-df3f729d8204"], + "785fda33-3883-4758-a008-c10b59489518"], TemplateBox[{8}, "Spacer1"]}]], TextAlignment->Center,ExpressionUUID-> - "284a26a6-ed84-4c5c-865a-7d4364cc66b3"], + "063d5e58-f4ae-470b-90d0-28fa895a7e1d"], Background->RGBColor[0.490196, 0.576471, 0.690196], ItemSize->Full], ""} }, @@ -54,8 +54,8 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "9160706c-003b-47b0-9547-02693518b0e8"] - }],ExpressionUUID->"796f0c2a-c6bd-4f20-a3ce-be6821610c95"], + "9c18a435-dc89-4403-b8e6-739ff4366212"] + }],ExpressionUUID->"b6a30a76-bfef-4553-b4be-223808659ded"], StripOnInput->False],{ StyleBox[ "\"FullGottesmanVector\"", "SeeAlsoRelated", StripOnInput -> False] :> @@ -88,7 +88,7 @@ Cell[BoxData[GridBox[{ MenuStyle->"SeeAlso"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "8fe0241a-28f6-4fa8-a552-4a40e03b30b4"], + 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"TI"]]], "InlineFormula", + FontFamily->"Source Sans Pro",ExpressionUUID-> + "b8990cae-90e6-49aa-b87f-bb33e131f115"], + ", ", + Cell[BoxData[ + SubscriptBox[ + StyleBox["p", "TI"], + StyleBox["d", "TI"]]], "InlineFormula", + FontFamily->"Source Sans Pro",ExpressionUUID-> + "35ae8587-974c-464a-93b3-d3996113cdb3"], + ", and ", + Cell[BoxData[ + RowBox[{"1", "-", + SubscriptBox[ + StyleBox["p", "TI"], + StyleBox["m", "TI"]], "-", + SubscriptBox[ + StyleBox["p", "TI"], + StyleBox["d", "TI"]]}]], "InlineFormula", + FontFamily->"Source Sans Pro",ExpressionUUID-> + "50c0501b-a990-47b9-9c62-b6015c91740d"], + ", respectively, " + }],ExpressionUUID->"8b52f67c-a3e9-4447-9acb-15ba984c6e76"]} }]], "Usage", CellID->1472306447,ExpressionUUID->"97353bd0-b100-4ca8-aaa9-df45717b3a98"] }, Open ]], @@ -330,19 +465,19 @@ Cell[TextData[{ 0.68 Inherited], Rational[1, 2] Pi, {-1.65, -1}]]], ImageSizeCache->{ 13.600000000000001`, {4.251494140625001, 9.348505859375003}}]], - 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+Cell[BoxData[ + RowBox[{ + RowBox[{"SeedRandom", "[", "360", "]"}], ";"}]], "Input", + CellProlog:>Needs["Q3`"], + CellLabel->"In[2]:=", + CellID->1141857349,ExpressionUUID->"e7edfa2c-012a-4c9f-b18c-b1c491db2f33"], + +Cell["\<\ +Generate a quantum circuit with alternating layers of Clifford gates and \ +Pauli measurements.\ +\>", "ExampleText", + CellID->1296569647,ExpressionUUID->"2873696a-e3b3-486b-b158-1c32efa2a7ab"], + Cell[CellGroupData[{ Cell[BoxData[ - RowBox[{"cc", "=", + RowBox[{"cc1", "=", RowBox[{"RandomCliffordCircuit", "[", RowBox[{ RowBox[{"{", - RowBox[{"$n", ",", "7"}], "}"}], ",", "0.2"}], "]"}]}]], "Input", + RowBox[{"$n", ",", "3"}], "}"}], ",", "0.25"}], "]"}]}]], "Input", CellProlog:>Needs["Q3`"], - CellLabel->"In[2]:=", + CellLabel->"In[3]:=", CellID->559960169,ExpressionUUID->"eae9d050-d1bb-42a2-8365-8ecbf8323049"], Cell[BoxData[ @@ -426,7 +574,7 @@ Cell[BoxData[ RowBox[{ TagBox["\"Depth: \"", "SummaryItemAnnotation"], "\[InvisibleSpace]", - TagBox["22", "SummaryItem"]}]}}, + TagBox["10", "SummaryItem"]}]}}, GridBoxAlignment -> { "Columns" -> {{Left}}, "Rows" -> {{Automatic}}}, AutoDelete -> False, GridBoxItemSize -> { @@ -448,7 +596,7 @@ Cell[BoxData[ RowBox[{ TagBox["\"Depth: \"", "SummaryItemAnnotation"], "\[InvisibleSpace]", - TagBox["22", "SummaryItem"]}]}}, + TagBox["10", "SummaryItem"]}]}}, GridBoxAlignment -> { "Columns" -> {{Left}}, "Rows" -> {{Automatic}}}, AutoDelete -> False, GridBoxItemSize -> { @@ -475,194 +623,947 @@ Cell[BoxData[ Q3`CliffordUnitary[ SparseArray[ Automatic, {4, 5}, 0, { - 1, {{0, 3, 6, 8, 13}, {{1}, {4}, {5}, {2}, {4}, {5}, {4}, {5}, {1}, { - 2}, {3}, {4}, {5}}}, {1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1}}], { - 1, 2}], + 1, {{0, 3, 6, 10, 15}, {{1}, {4}, {5}, {3}, {4}, {5}, {2}, {3}, {4}, { + 5}, {1}, {2}, {3}, {4}, {5}}}, {1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, + 1, 1, 1, -1}}], {1, 2}], Q3`CliffordUnitary[ SparseArray[ Automatic, {4, 5}, 0, { - 1, {{0, 3, 7, 11, 13}, {{1}, {3}, {5}, {1}, {2}, {3}, {5}, 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Gottesman (2004)"}]]]], + "https://doi.org/10.1103/physreva.70.052328"}, "WebLink", BaseStyle->{"RelatedLinks"}]],ExpressionUUID-> - "6b2ab684-5f6c-4658-9e2a-ba1a0cfa795d"]}]],ExpressionUUID-> - "fcf87d80-2ab5-4b4f-a838-36f4cdc93649"], - ": Theory of fault-tolerant quantum computation" + "cbea2b6c-3ffe-4c70-8e79-a3016fe74bcf"]}]],ExpressionUUID-> + "035290a5-6af6-4808-8309-6ca9339f213f"], + ", Physical Review A 70, 052328 (2004), \ +\[OpenCurlyDoubleQuote]Improved simulation of stabilizer circuits.\ +\[CloseCurlyDoubleQuote]" }], "RelatedLinks",ExpressionUUID-> - "de498ba8-ecdd-41cf-bc0c-9566e3393b54"]}, + "473dab17-7afa-4366-8a39-36aa17fd9b3f"]}, {Cell[TextData[{ Cell[BoxData[ RowBox[{ @@ -907,16 +1833,16 @@ Cell[BoxData[GridBox[{ "https://doi.org/10.1007/978-3-030-91214-7"}, "WebLink", BaseStyle->{"RelatedLinks"}]],ExpressionUUID-> - "957d5135-143d-4a09-be43-c132adaffb4a"]}]],ExpressionUUID-> - "7189427f-32fb-4dc1-a0b2-10efc2c1bcc7"], + "f7c941bf-48cf-4b14-a78c-d27069d90af1"]}]],ExpressionUUID-> + "8549e751-620a-4c0f-8b2f-12e12b92d152"], ", A Quantum Computation Workbook (Springer)." }], "RelatedLinks",ExpressionUUID-> "27400f17-398d-44e9-805f-a943e4d6cfa9"]} }]} - }]], "RelatedLinksSection",ExpressionUUID->"2aaf0a1d-4214-4b47-ba05-\ -4c474cf0aae0"], + }]], "RelatedLinksSection",ExpressionUUID->"466479e1-3481-4115-a20e-\ +66cac54faa4b"], -Cell[" ", "FooterCell",ExpressionUUID->"88727158-5878-44cd-b6cc-181adbdf49fd"] +Cell[" ", "FooterCell",ExpressionUUID->"e19fcb8a-7525-445b-b377-09858c078f05"] }, Saveable->False, ScreenStyleEnvironment->"Working", @@ -932,15 +1858,23 @@ TaggingRules->{ "CitationPopupData" -> $Failed, "ShowCitation" -> False, "HasOptions" -> True, "RootCaptions" -> "", "HeaderCoreAreaLink" -> {}, "Metadata" -> { - "built" -> "{2024, 9, 22, 20, 35, 34.560713}", + "built" -> "{2024, 9, 25, 9, 39, 6.396065}", "history" -> {"14.1", "", "", ""}, "context" -> "Q3`", "keywords" -> {}, "specialkeywords" -> {}, "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> "Q3 Symbol", "language" -> "en", "paclet" -> "Q3", "status" -> "None", "summary" -> "RandomCliffordCircuit[{n, t}, p] generates a Clifford circuit of depth 3 \ t on n qubits with alternating layers of randomly selected two-qubit Clifford \ -unitary gates and single-qubit Pauli measurements, where each qubit is \ -measured in the computational basis with probability p.", "synonyms" -> {}, +unitary gates (circuit elements of CliffordUnitary) and single-qubit Pauli \ +measurements in the computational basis (circuit elements of \ +PauliMeasurement), where each qubit is measured in the computational basis \ +with probability p. RandomCliffordCircuit[{n, t}, {0, p}] is similar, but \ +PauliDecoherence is used instead of PauliMeasurement in the non-unitary \ +layers. RandomCliffordCircuit[{n, t}, {pm, pd}] gives a mixed Clifford \ +circuit, in the non-unitary layers of which each qubit undergoes the Pauli \ +measurement in the computational basis (see PauliMeasurement), a Pauli \ +decoherence process (see PauliDecoherence), or nothing randomly with \ +probabilities pm, pd, and 1 - pm - pd, respectively, ", "synonyms" -> {}, "tabletags" -> {}, "title" -> "RandomCliffordCircuit", "titlemodifier" -> "", "metadescription" -> "", "windowtitle" -> "RandomCliffordCircuit", "type" -> "Symbol", "uri" -> "Q3/ref/RandomCliffordCircuit"}}, @@ -956,7 +1890,7 @@ StyleDefinitions->Notebook[{ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, FrontEndVersion -> "14.1 for Mac OS X ARM (64-bit) (July 16, 2024)", StyleDefinitions -> "Default.nb"], -ExpressionUUID->"2fe8cd77-438e-4ce4-a72f-7b567d620542" +ExpressionUUID->"bd2926e7-9597-4995-b24e-bb94bc4fa38c" ] (* End of Notebook Content *) @@ -964,50 +1898,94 @@ ExpressionUUID->"2fe8cd77-438e-4ce4-a72f-7b567d620542" (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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See also ", + Cell[BoxData[ + TemplateBox[{ + Cell[ + TextData["Li, Chen, and Fisher (2018)"]], + "https://doi.org/10.1103%2Fphysrevb.98.205136"}, + "WebLink", + BaseStyle->{"Notes"}]],ExpressionUUID-> + "e8a65956-8dc8-4daf-ab3c-058a061cebb4"], + ", ", + Cell[BoxData[ + TemplateBox[{ + Cell[ + TextData["Skinner, Ruhman, and Nahum (2019)"]], + "https://doi.org/10.1103%2Fphysrevx.9.031009"}, + "WebLink", + BaseStyle->{"Notes"}]],ExpressionUUID-> + "afc2ac89-34fe-4fad-b328-35bb2f24a6ad"], + ", ", + Cell[BoxData[ + TemplateBox[{ + Cell[ + TextData["Chan et. al. (2019)"]], + "https://doi.org/10.1103/PhysRevB.99.224307"}, + "WebLink", + BaseStyle->{"Notes"}]],ExpressionUUID-> + "9ecfd649-3d91-4067-ac32-a6f99a735d73"], + ", ", + Cell[BoxData[ + TemplateBox[{ + Cell[ + TextData["Sang et al. (2021)"]], + "https://doi.org/10.1103/PRXQuantum.2.030313"}, + "WebLink", + BaseStyle->{"Notes"}]],ExpressionUUID-> + "ff6c5449-8994-46e2-afeb-fb6b3c5565c9"], + ", and ", + Cell[BoxData[ + TemplateBox[{ + Cell[ + TextData["Weinstein, Bao, and Altman (2022)"]], + "https://doi.org/10.1103/PhysRevLett.129.080501"}, + "WebLink", + BaseStyle->{"Notes"}]],ExpressionUUID-> + "59e673bd-838b-438a-91ed-f16f3e116e10"], + "." +}], "Notes", + CellID->1815464681,ExpressionUUID->"c4b85cc4-93f5-458d-b771-4db0b355fb48"], + +Cell[TextData[{ + "For ", + StyleBox["efficient simulation of Clifford circuits", + FontSlant->"Italic"], + ", see ", + Cell[BoxData[ + TemplateBox[{ + Cell[ + TextData["Cleve and Gottesman (1997)"]], + "https://doi.org/10.1103%2Fphysreva.56.76"}, + "WebLink", + BaseStyle->{"Notes"}]],ExpressionUUID-> + "91545552-43e9-45a8-96e7-3667f1aaf320"], + ", ", + Cell[BoxData[ + TemplateBox[{ + Cell[ + TextData["Gottesman (1998)"]], "https://doi.org/10.1103/PhysRevA.57.127"}, + "WebLink", + 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"/", "2"}], "]"}]}]], "Input", CellProlog:>Needs["Q3`"], - CellLabel->"In[6]:=", + CellLabel->"In[7]:=", CellID->1814140099,ExpressionUUID->"788b9911-cb56-439e-a935-ed2b4c2c4800"], Cell[BoxData[ RowBox[{"{", RowBox[{"1", ",", "2", ",", "3", ",", "4"}], "}"}]], "Output", - CellLabel->"Out[6]=", - CellID->738673392,ExpressionUUID->"aff8986d-d240-440d-8b65-a41b6647c001"] + CellLabel->"Out[7]=", + CellID->1375448943,ExpressionUUID->"533ea548-a92f-4873-8d9b-56fee0c7f853"] }, Open ]], Cell["Calculate the logarithmic negativity in each state.", "ExampleText", @@ -659,11 +1602,11 @@ Cell[BoxData[ ",", RowBox[{"{", "2", "}"}]}], "]"}]}], ";"}], "]"}]], "Input", CellProlog:>Needs["Q3`"], - CellLabel->"In[7]:=", + CellLabel->"In[8]:=", CellID->9201179,ExpressionUUID->"e6e7acb4-a91b-4d90-b9aa-30a8caad0c89"], -Cell[BoxData["3.844258`"], "EchoTiming", - CellID->644686415,ExpressionUUID->"253e1438-9e29-420b-af49-c6b5898d7dcd"] +Cell[BoxData["0.229533`"], "EchoTiming", + 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b/Q3/Documentation/English/ReferencePages/Symbols/RandomCliffordState.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 154, 7] -NotebookDataLength[ 33449, 846] -NotebookOptionsPosition[ 29108, 756] -NotebookOutlinePosition[ 31275, 811] -CellTagsIndexPosition[ 31190, 806] +NotebookDataLength[ 33443, 846] +NotebookOptionsPosition[ 29105, 756] +NotebookOutlinePosition[ 31270, 811] +CellTagsIndexPosition[ 31185, 806] WindowTitle->RandomCliffordState WindowFrame->Normal*) @@ -27,11 +27,11 @@ Cell[BoxData[GridBox[{ TemplateBox[{12}, "Spacer1"], Cell["Q3 SYMBOL", "PacletNameCell", TextAlignment->Center,ExpressionUUID-> - "2f4c7822-304e-47aa-8f44-f085cbb2fcf7"], + "4bc8ef80-44d6-4bb0-9d28-bb01cb5ea279"], TemplateBox[{8}, "Spacer1"]}]], TextAlignment->Center,ExpressionUUID-> - "a71fceb0-5a39-4919-8e6e-e83a9cc461f8"], + "c005e0b7-0fe6-43a4-97da-eb7ef368984f"], Background->RGBColor[0.490196, 0.576471, 0.690196], ItemSize->Full], ""} }, @@ -54,8 +54,8 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "2ce56b84-9dee-4623-807d-56da73a7c39a"] - }],ExpressionUUID->"316ee7dd-ee8e-45fd-829d-90274c750222"], + "b45e2c96-b4cb-4c7c-8036-10e58932ee82"] + }],ExpressionUUID->"faea2066-400a-463d-9b84-500e9bbff228"], StripOnInput->False],{ StyleBox[ "\"CliffordState\"", "SeeAlsoRelated", StripOnInput -> False] :> @@ -74,7 +74,7 @@ Cell[BoxData[GridBox[{ MenuStyle->"SeeAlso"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "5c343284-c27d-45f9-92f6-60cffb2fcc97"], + "0ce95fa9-54dc-41e3-97ea-ce5ab08fbb50"], "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ \[ThickSpace]", Cell[BoxData[ @@ -93,8 +93,8 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "8fa3022f-5dc4-4bea-960f-f3209e92a5b6"] - }],ExpressionUUID->"9399ef02-fc82-4b1c-8bbf-87a6a7d63496"], + "399752b5-ac51-41ca-bb4e-196e964f49b1"] + }],ExpressionUUID->"eb138357-5b78-4aaf-be86-c0333df5f238"], StripOnInput->False],{ "\"Clifford Quantum Circuits\"" :> Documentation`HelpLookup["paclet:Q3/guide/CliffordQuantumCircuits"], @@ -106,7 +106,7 @@ Cell[BoxData[GridBox[{ MenuStyle->"MoreAbout"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "3729176e-8ec7-448d-adc3-1d8e2c0fd9df"], + "bbf5a2a7-f4af-49eb-9741-0ee654e3559e"], "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ \[ThickSpace]", Cell[BoxData[ @@ -125,8 +125,8 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "a50d340d-d774-4f52-bc3b-9e422e2dcff5"] - }],ExpressionUUID->"54ecff2c-a621-4f30-aed2-6a1edfa82283"], + "828ca27d-f037-462f-b7e7-ecb025f2da94"] + }],ExpressionUUID->"9b7e2924-db49-4bff-8279-15680776c1b7"], StripOnInput->False],{ "\"The Pauli and Clifford Groups\"" :> Documentation`HelpLookup[ @@ -146,7 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}]], "MoreAboutSection",ExpressionUUID->"2dd20e9c-ea53-4ac5-b56e-\ -17723c15866a"], + }]], "MoreAboutSection",ExpressionUUID->"a05c559a-e033-4f41-b6c0-\ +535af4f44498"], Cell[BoxData[GridBox[{ { @@ -696,8 +696,8 @@ Cell[BoxData[GridBox[{ "https://dl.acm.org/doi/10.5555/2011350.2011356"}, "WebLink", BaseStyle->{"RelatedLinks"}]],ExpressionUUID-> - "491d293f-09d6-46df-996f-d8cc73a31bae"]}]],ExpressionUUID-> - "02fb1297-c5b2-46eb-80ab-1ed369f73893"], + "c742b9bd-4430-4dc2-b3a6-cf964a36f270"]}]],ExpressionUUID-> + "51d905b3-84be-4d84-86ba-f8e25a8925eb"], ", Quantum Information & Computation 10, 258 (2010), \"Classical \ simulation of quantum computation, the Gottesman-Knill theorem, and slightly \ beyond.\"" @@ -720,8 +720,8 @@ beyond.\"" "https://doi.org/10.1103/PRXQuantum.2.010307"}, "WebLink", BaseStyle->{"RelatedLinks"}]],ExpressionUUID-> - "f2679b24-a0e9-4392-a365-546a6c75071f"]}]],ExpressionUUID-> - "ab35f881-f139-4f1e-9117-d46950920a19"], + 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BaseStyle->{"RelatedLinks"}]],ExpressionUUID-> - "b9a6e660-1fec-4c49-8bcc-c1a5f15bf254"]}]],ExpressionUUID-> - "e6139206-5699-480c-a136-bb74488a88af"], + "9496d253-3402-4358-b817-38bc16cdb6ff"]}]],ExpressionUUID-> + "922df06b-822a-4092-b152-d419c2374ba7"], ", Quantum Information & Computation 10, 258 (2010), \"Classical \ simulation of quantum computation, the Gottesman-Knill theorem, and slightly \ beyond.\"" @@ -826,8 +826,8 @@ beyond.\"" "https://doi.org/10.1103/PRXQuantum.2.010307"}, "WebLink", BaseStyle->{"RelatedLinks"}]],ExpressionUUID-> - "279dfda5-60c1-4de8-9242-9f2922c5db99"]}]],ExpressionUUID-> - "29df1c49-1bae-4678-98ab-ae8c60a3c17c"], + "6aa1a273-a7d4-4508-b8e5-7d189ac00f91"]}]],ExpressionUUID-> + "3437076f-0275-4131-bc7b-1e0deb74edcf"], ", PRX Quantum 2, 010307 (2021), \"Experimental Estimation of Quantum \ State Properties from Classical Shadows.\"" }], "RelatedLinks",ExpressionUUID-> @@ -849,8 +849,8 @@ State Properties from Classical Shadows.\"" Physics 55, 122202 (2014)"}]]]], "https://doi.org/10.1063/1.4903507"}, "WebLink", BaseStyle->{"RelatedLinks"}]],ExpressionUUID-> - "70aedf39-3e23-466b-8664-b5ce560155ab"]}]],ExpressionUUID-> - "942d53ab-d19a-4843-8233-78808dd67869"], + "5a03e8f3-6af2-431e-beb7-29c49552c8fc"]}]],ExpressionUUID-> + "24472604-afda-4e78-9ba7-884abeb01c7f"], ", \"How to efficiently select an arbitrary Clifford group \ element.\"" }], "RelatedLinks",ExpressionUUID-> @@ -872,8 +872,8 @@ element.\"" (2003)"}]]]], "https://doi.org/10.1103%2Fphysreva.68.042318"}, "WebLink", BaseStyle->{"RelatedLinks"}]],ExpressionUUID-> - "58b9ee14-0a21-4c70-a24e-89d500fb3d1e"]}]],ExpressionUUID-> - "16cebb7f-9f22-401d-b537-30a40af056c4"], + "9bdbab24-0362-475f-ac98-a4870747998b"]}]],ExpressionUUID-> + "e47e78e5-d936-4a6c-84c1-2d63e6180a3a"], ", \"Clifford group, stabilizer states, and linear and quadratic \ operations over GF(2).\"" }], "RelatedLinks",ExpressionUUID-> @@ -895,8 +895,8 @@ operations over GF(2).\"" (2004)"}]]]], "https://doi.org/10.1103/physreva.70.052328"}, "WebLink", BaseStyle->{"RelatedLinks"}]],ExpressionUUID-> - "e798c0f6-eec1-4369-a1d6-8a079d98ae37"]}]],ExpressionUUID-> - "d205c2c4-01b9-4182-a756-7a105091f610"], + "6f5c373f-d875-41be-8bf8-183226d5366a"]}]],ExpressionUUID-> + "74a1e21d-12e0-4692-b5c1-bd23b78b73a1"], ", \[OpenCurlyDoubleQuote]Improved simulation of stabilizer circuits.\ \[CloseCurlyDoubleQuote]" }], "RelatedLinks",ExpressionUUID-> @@ -918,16 +918,16 @@ operations over GF(2).\"" "https://doi.org/10.1007/978-3-030-91214-7"}, "WebLink", BaseStyle->{"RelatedLinks"}]],ExpressionUUID-> - "58be9a05-cae1-4851-8ff1-7d472c8fd21e"]}]],ExpressionUUID-> - "ae2819fe-3f39-4ef2-800e-3b3759a21b22"], + "c47ec010-9a00-4294-9301-f2791d63dd07"]}]],ExpressionUUID-> + "971d05e4-6e7f-44c8-852a-27655a88dd8a"], ", A Quantum Computation Workbook (Springer)." }], "RelatedLinks",ExpressionUUID-> "b1886a25-3cfb-4999-a6a8-a711a4f29472"]} }]} - }]], 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a/Q3/Documentation/English/ReferencePages/Symbols/RandomFullGottesmanVector.nb +++ b/Q3/Documentation/English/ReferencePages/Symbols/RandomFullGottesmanVector.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 154, 7] -NotebookDataLength[ 32330, 844] -NotebookOptionsPosition[ 27432, 742] -NotebookOutlinePosition[ 29628, 797] -CellTagsIndexPosition[ 29543, 792] +NotebookDataLength[ 32326, 844] +NotebookOptionsPosition[ 27429, 742] +NotebookOutlinePosition[ 29625, 797] +CellTagsIndexPosition[ 29540, 792] WindowTitle->RandomFullGottesmanVector WindowFrame->Normal*) @@ -27,11 +27,11 @@ Cell[BoxData[GridBox[{ TemplateBox[{12}, "Spacer1"], Cell["Q3 SYMBOL", "PacletNameCell", TextAlignment->Center,ExpressionUUID-> - "ba17d6f5-5a5b-41f5-b3be-546a15b9d91d"], + "63e1bbca-53a7-4b98-bb2f-17b3aa232c21"], TemplateBox[{8}, "Spacer1"]}]], TextAlignment->Center,ExpressionUUID-> - "1122ff46-246d-4d2a-9742-e140d22d1037"], + 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DocumentationSearch`Private`nb$ = NotebookPut[ Notebook[{Cell["Q3/ref/RandomFullGottesmanVector"]}, Visible -> - DocumentationBuild`Make`Private`visible$131040]]; + DocumentationBuild`Make`Private`visible$55191]]; SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; NotebookClose[DocumentationSearch`Private`nb$]; Null], Delimiter, @@ -194,7 +194,7 @@ Cell[BoxData[GridBox[{ "http://reference.wolfram.com/language/Q3/ref/\ RandomFullGottesmanVector.html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> - DocumentationBuild`Make`Private`visible$131040]]; + DocumentationBuild`Make`Private`visible$55191]]; SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; NotebookClose[DocumentationSearch`Private`nb$]; Null], @@ -210,14 +210,14 @@ RandomFullGottesmanVector.html"], StandardForm]], "Input", TextClipboardType -> 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"https://doi.org/10.1103/PhysRevA.57.127"}, "WebLink", BaseStyle->{"TutorialRelatedLinks"}]],ExpressionUUID-> - "79905392-d160-45bb-aaab-776737aed02b"]}]],ExpressionUUID-> - "664958f9-1160-4ae8-8a33-95710f9a4b20"], + "145d131b-13e6-4466-b6a8-be37f324db65"]}]],ExpressionUUID-> + "fd9e0487-d6a5-4590-b902-6549c1871fc7"], ", \[OpenCurlyDoubleQuote]Theory of fault-tolerant quantum \ computation.\[CloseCurlyDoubleQuote]" }], "TutorialRelatedLinks",ExpressionUUID-> @@ -8113,8 +8113,8 @@ computation.\[CloseCurlyDoubleQuote]" "https://doi.org/10.1002/9783527805785.ch21"}, "WebLink", BaseStyle->{"TutorialRelatedLinks"}]],ExpressionUUID-> - "df7540bb-2402-49e8-88b8-172ef07791b5"]}]],ExpressionUUID-> - "6dc15065-1e4f-4af0-ae07-2497c22e7adf"], + "3a80aeed-f21a-4b29-8c11-0644d5176987"]}]],ExpressionUUID-> + "bfca8ee4-a2f0-4a77-a950-73f6944eb3ef"], ", \"One-Way Quantum Computation,\" in Quantum Information: From \ Foundation to Quantum Technology Applications, edited by D. Bru\[SZ] and G. \ Leuchs (Wiley, 2016)." @@ -8137,8 +8137,8 @@ Leuchs (Wiley, 2016)." (1989)"}]]]], "https://arxiv.org/abs/0712.0921"}, "WebLink", BaseStyle->{"TutorialRelatedLinks"}]],ExpressionUUID-> - "611cfd2c-f646-475f-9668-0037b7255084"]}]],ExpressionUUID-> - "bef38c15-9a98-491f-a370-1f5e1532fb45"], + "64e8fb9b-859d-45ee-8d6c-cb0ad9a05c79"]}]],ExpressionUUID-> + "ec32f121-ccda-4375-8093-0612bfbcb447"], ", \"Going beyond Bell\[CloseCurlyQuote]s theorem,\ \[CloseCurlyDoubleQuote] in Bell\[CloseCurlyQuote]s Theorem, Quantum Theory, \ and Conceptions of the Universe, edited by M. Kafatos (Kluwer Academic, \ @@ -8162,8 +8162,8 @@ Dordrecht, The Netherlands, 1989)." (2004)"}]]]], "https://doi.org/10.1103/physreva.70.052328"}, "WebLink", BaseStyle->{"TutorialRelatedLinks"}]],ExpressionUUID-> - "10652521-f393-4179-a565-158895ef8318"]}]],ExpressionUUID-> - "35243eca-5c49-441f-bcdf-23d25d192a72"], + "b87c9e26-49f1-4be9-878a-7cea17193c83"]}]],ExpressionUUID-> + "660481ad-8ec5-41bf-a5ff-0ec014780c9a"], ", \[OpenCurlyDoubleQuote]Improved simulation of stabilizer circuits.\ \[CloseCurlyDoubleQuote]" }], "TutorialRelatedLinks",ExpressionUUID-> @@ -8185,8 +8185,8 @@ Dordrecht, The Netherlands, 1989)." 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We refer interested readers to ", "https://doi.org/10.1103/physreva.56.76"}, "WebLink", BaseStyle->{"TechNoteText"}]],ExpressionUUID-> - "aa7546c4-d573-4787-a6c4-99210462eff9"], + "3af08568-2bc6-4ed4-b2d9-1bbca9d55245"], "." }], "TechNoteText", CellID->391630128,ExpressionUUID->"a9b104ec-a5df-4d6e-b291-81ab6b641c46"] @@ -14993,7 +14995,7 @@ computation.\" Indeed, we recall that in addition to Clifford gates, we need ", "https://doi.org/10.1007/978-3-030-91214-7"}, "WebLink", BaseStyle->{"TechNoteText"}]],ExpressionUUID-> - "aba9f278-b166-48c9-8f92-bb463bbcacfe"], + "511985e3-2359-4881-9bbe-08d978c01f0a"], ")." }], "TechNoteText", CellID->2030692074,ExpressionUUID->"0ec7eea7-e308-4033-a05d-ee5a7a36ac39"], @@ -15097,7 +15099,7 @@ Cell[TextData[{ "https://doi.org/10.1103/physreva.70.052328"}, "WebLink", BaseStyle->{"TechNoteText"}]],ExpressionUUID-> - "d4010daf-a232-4016-ae72-686b6a981683"], + "b3d8d6d1-b08c-45a7-a552-5eff5cb01245"], ". 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(1989)"}]]]], "https://arxiv.org/abs/0712.0921"}, "WebLink", BaseStyle->{"TutorialRelatedLinks"}]],ExpressionUUID-> - "d6e2c9ad-6af4-4ea0-a075-fbd46e61977b"]}]],ExpressionUUID-> - "abbff30e-0d3a-4431-bc5a-1d7e2ffb3d2e"], + "189340a0-6731-4ee1-8ed7-87908e74f582"]}]],ExpressionUUID-> + "82fb7d1f-7d99-487f-9ea7-a4d7831a6ca9"], ", \"Going beyond Bell\[CloseCurlyQuote]s theorem,\ \[CloseCurlyDoubleQuote] in Bell\[CloseCurlyQuote]s Theorem, Quantum Theory, \ and Conceptions of the Universe, edited by M. Kafatos (Kluwer Academic, \ @@ -18497,8 +18507,8 @@ Dordrecht, The Netherlands, 1989)." 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CliffordState[data_, ss:{___?QubitQ}, rest___] := CliffordState[data, FlavorCap @ ss, rest] /; Not[FlavorCapQ @ ss] +(* quick initialization *) CliffordState[Ket[v_?VectorQ], rest___] := Module[ { n = Length[v], vv, pp }, @@ -50,6 +51,10 @@ CliffordState[Ket[v_?VectorQ], rest___] := Module[ CliffordState[Transpose @ Append[Transpose @ vv, IntegerParity @ v], rest] ] +(* quick initialization *) +CliffordState[Ket[a_Association], rest___] := + CliffordState[ Ket @ Values @ KeySelect[a, QubitQ] ] + CliffordState /: StabilizerGenerators[CliffordState[gnr_, ___?OptionQ]] := @@ -130,7 +135,7 @@ PauliMeasurement[msr_?GottesmanVectorQ, kk:{___Integer}][cs_CliffordState] := Mo { ii = Riffle[2kk-1, 2kk], vv = First[cs], ch, new, gnr }, vv = vv[[;;, ii]]; - ch = Map[GottesmanInner[msr, #]&, vv]; + ch = Map[GottesmanDot[msr, #]&, vv]; If[ ArrayZeroQ[ch], $MeasurementOut[msr] = Indeterminate; Return[cs] @@ -157,7 +162,7 @@ PauliMeasurement[msr_?GottesmanVectorQ, kk:{___Integer}][cs_CliffordState] := Mo PauliMeasurement[msr_?GottesmanVectorQ][cs_CliffordState] := Module[ { gnr = First[cs], chk, new }, - chk = Map[GottesmanInner[msr, #]&, Most /@ gnr]; + chk = Map[GottesmanDot[msr, #]&, Most /@ gnr]; If[ ArrayZeroQ[chk], $MeasurementOut[msr] = Indeterminate; Return[cs] @@ -177,7 +182,41 @@ PauliMeasurement /: Multiply[pre___, msr_PauliMeasurement, cs_CliffordState] := Multiply[pre, msr @ cs] -(**** ****) +(**** ****) + + +(**** ****) + +PauliDecoherence::usage = "PauliDecoherence[vec] represents the Pauli measurement corresponding to Gottesman vector vec.\nPauliDecoherence[vec, {{k1, k2, \[Ellipsis]}, n}] represents the Pauli measurement on particular qubits numbered k1, k2, \[Ellipsis] among n qubits." + +PauliDecoherence[msr_?GottesmanVectorQ, k_Integer] := + PauliDecoherence[msr, {k}] + +PauliDecoherence[msr_?GottesmanVectorQ, kk:{___Integer}][cs_CliffordState] := Module[ + { ii = Riffle[2kk-1, 2kk], + vv = First[cs], ch, new, gnr }, + vv = vv[[;;, ii]]; + ch = Map[GottesmanDot[msr, #]&, vv]; + If[ArrayZeroQ[ch], Return[cs]]; + (* Simulate the deocherence process. *) + ch = Position[ch, 1]; + Module[ + { gnr = First[cs], + alt }, + alt = gnr[[First @ First @ ch]]; + gnr = ReplaceAt[gnr, v_?VectorQ :> GottesmanTimes[alt, v], Rest @ ch]; + gnr = Delete[gnr, First @ ch]; + If[gnr == {}, gnr = Zero @ {1, Length @ alt}]; (* the maximally-mixed state *) + ReplacePart[cs, 1 -> SparseArray[gnr]] + ] +] + + +PauliDecoherence /: +Multiply[pre___, msr_PauliDecoherence, cs_CliffordState] := + Multiply[pre, msr @ cs] + +(**** ****) (**** ****) @@ -244,7 +283,7 @@ RandomCliffordUnitary[n_Integer, spec___] := (**** ****) -CliffordLogarithmicNegativity::usage = "CliffordLogarithmicNegativity[cs, {k1, k2, \[Ellipsis]}] returns the logarithmic negativity cs between qubits {k1, k2, \[Ellipsis]} and the rest of Clifford state.\nCliffordLogarithmicNegativity[{k1, k2, \[Ellipsis]}] is an operator form of CliffordLogarithmicNegativity that can be applied to Clifford states." +CliffordLogarithmicNegativity::usage = "CliffordLogarithmicNegativity[cs, {k1, k2, \[Ellipsis]}] returns the logarithmic negativity between qubits {k1, k2, \[Ellipsis]} and the rest in Clifford state cs.\nCliffordLogarithmicNegativity[{k1, k2, \[Ellipsis]}] is an operator form of CliffordLogarithmicNegativity that can be applied to Clifford states." (* SEE ALSO: Sang et at. (2021) and Weinstein et al. (2022) *) CliffordLogarithmicNegativity[kk:{___Integer}][cs_CliffordState] := @@ -253,12 +292,10 @@ CliffordLogarithmicNegativity[kk:{___Integer}][cs_CliffordState] := CliffordLogarithmicNegativity[cs_CliffordState, kk:{___Integer}] := Module[ { gnr = First[cs], chk }, - gnr = Map[Partition[#, 2]&, gnr]; - gnr = Flatten /@ gnr[[;;, kk]]; - (* chk = IntegerParity @ Outer[GottesmanInner, gnr, gnr, 1]; *) - (* MatrixRank[chk] / 2 *) - (* NOTE: The above two lines do not seem to work; hence, the following two lines instead. *) - chk = Outer[GottesmanInner, gnr, gnr, 1]; + gnr = gnr[[ ;; , Riffle[2kk-1, 2kk] ]]; + chk = GottesmanDot[gnr, gnr]; + (* MatrixRank[IntegerParity @ chk] / 2 *) + (* NOTE: The above line does not seem to work; hence, the following line instead. *) MatrixRank[chk, Modulus -> 2] / 2 ] @@ -301,19 +338,50 @@ CliffordCircuit[gg:{_CliffordState, ___}][cs_CliffordState] := CliffordCircuit[Rest @ gg][cs] CliffordCircuit[gg_List][cs_CliffordState] := - Fold[Construct[#2, #1]&, cs, gg] + Fold[Construct[#2, #1]&, cs, Flatten @ gg] +CliffordCircuit /: +Elaborate @ CliffordCircuit[gg:{_CliffordState, ___}] := + Fold[Construct[#2, #1]&, Flatten @ gg] -numberOfQubits[CliffordState[mat_?MatrixQ, ___]] := (Last[Dimensions @ mat] - 1)/2 -numberOfQubits[CliffordUnitary[_?MatrixQ, {_, n_Integer}, ___]] = n +CliffordCircuit /: +Show[cc_CliffordCircuit, S_Symbol?QubitQ, more___?OptionQ] := + Graphics[cc, S, more] + +CliffordCircuit /: +Graphics[CliffordCircuit[gg_List], S_Symbol?QubitQ, more___?OptionQ] := Module[ + { n, cs, ss, qc }, + n = FirstCase[gg, g:_Symbol[__] :> numberOfQubits[g], Indeterminate, Infinity]; + If[n === Indeterminate, n = 1]; + ss = S[Range @ n, $]; + qc = gg /. { + CliffordCircuit[{}] -> "Spacer", + CliffordCircuit -> Identity, + CliffordState[__] :> Ket[ss], + CliffordUnitary[m_, kk_, opts___?OptionQ] :> Gate[S[kk, $], opts], + CliffordUnitary[m_, opts___?OptionQ] :> Gate[ss, opts, "Label" -> "U"], + PauliMeasurement[v_, kk_, opts___?OptionQ] :> Gate[S[kk, $], opts, "Shape" -> "Measurement"], + PauliDecoherence[v_, kk_, opts___?OptionQ] :> Gate[S[kk, $], opts, "Label" -> "\[ScriptCapitalD]"], + CNOT[i_, j_] :> Gate[{S[i,$]->1}, {S[j,$]}, "Shape" -> "CirclePlus"], + SWAP[i_, j_] :> Gate[{S[i,$]->1}, {S[j,$]}, "Shape" -> "Cross", "ControlShape" -> "Cross"], + Hadamard[kk_] :> Map[Gate[{#}, "Label" -> "H"]&, S[kk,$]], + Quadrant[kk_] :> Map[Gate[{#}, "Label" -> "S"]&, S[kk,$]] + }; + QuantumCircuit[Sequence @@ qc, "PostMeasurementDashes" -> False] +] -numberOfQubits[CliffordUnitary[mat_?MatrixQ, ___?OptionQ]] := Length[mat] / 2 -numberOfQubits[PauliMeasurement[_?VectorQ, {_, n_Integer}, ___]] = n +numberOfQubits[CliffordState[mat_?MatrixQ, ___]] := (Last[Dimensions @ mat] - 1)/2 + +numberOfQubits[CliffordUnitary[mat_?MatrixQ, ___?OptionQ]] := Length[mat] / 2 numberOfQubits[PauliMeasurement[vec_?VectorQ, ___?OptionQ]] := Length[vec] / 2 +numberOfQubits[PauliDecoherence[vec_?VectorQ, ___?OptionQ]] := Length[vec] / 2 + +numberOfQubits[_] = Indeterminate + (**** ****) @@ -321,11 +389,11 @@ numberOfQubits[PauliMeasurement[vec_?VectorQ, ___?OptionQ]] := Length[vec] / 2 RandomCliffordCircuit::usage = "RandomCliffordCircuit[{n, t}, p] generates a Clifford circuit of depth 3t on n qubits with alternating layers of randomly selected two-qubit Clifford unitary gates and single-qubit Pauli measurements, where each qubit is measured with probability p in the computational basis." -RandomCliffordCircuit[vol:{n_Integer, t_Integer}, p_?NumericQ] := +RandomCliffordCircuit[vol:{n_Integer, t_Integer}, pp:(_?NumericQ|{_?NumericQ, _?NumericQ})] := CliffordCircuit @ Nest[ Append[ Join[#, randomCliffordUnitaryLayer @ n], - randomPauliMeasurementLayer[n, p] + randomPauliMeasurementLayer[n, pp] ]&, { CliffordState @ Ket @ Table[0, n] }, t @@ -339,6 +407,22 @@ randomPauliMeasurementLayer[n_Integer, p_?NumericQ] := Module[ CliffordCircuit @ Map[PauliMeasurement[{0, 1}, #]&, kk] ] +randomPauliMeasurementLayer[n_Integer, {0|0., p_?NumericQ}] := Module[ + { kk = RandomPick[Range @ n, p], + mm = {{1, 0}, {0, 1}, {1, 1}} }, + CliffordCircuit @ Map[PauliDecoherence[RandomChoice @ mm, #]&, kk] +] + +randomPauliMeasurementLayer[n_Integer, pp:{_?NumericQ, _?NumericQ}] := Module[ + { kk = RandomPick[Range @ n, Total @ pp], + mm = PauliMeasurement[{0, 1}], + dc = PauliDecoherence /@ {{1, 0}, {0, 1}, {1, 1}}, + pm = First[pp] / Total[pp] }, + CliffordCircuit @ Table[ + Append[If[RandomReal[] < pm, mm, RandomChoice @ dc], k], + {k, kk} + ] +] randomCliffordUnitaryLayer::usage = "randomPauliMeasurementLayer[n] generates a layer of random two-qubit Clifford unitaries on every pair of nearest-neighbor qubits among n qubits." @@ -371,7 +455,11 @@ Options[RandomCliffordCircuitSimulate] = { "Prefix" -> "RCC" } -RandomCliffordCircuitSimulate[{n_Integer, t_Integer}, p_?NumericQ, OptionsPattern[]] := Module[ +RandomCliffordCircuitSimulate[ + {n_Integer, t_Integer}, + pp:(_?NumericQ|{_?NumericQ, _?NumericQ}), + OptionsPattern[] +] := Module[ { k = 0, progress = 0, save, data, qc, sn, sm }, @@ -380,7 +468,7 @@ RandomCliffordCircuitSimulate[{n_Integer, t_Integer}, p_?NumericQ, OptionsPatter (* simulation *) {sn, sm} = doAssureList[OptionValue["Samples"], 2]; data = Transpose @ Table[ - qc = RandomCliffordCircuit[{n, t}, p]; + qc = RandomCliffordCircuit[{n, t}, pp]; { Table[ progress = ++k / (sn*sm); FoldList[Construct[#2, #1]&, First @ qc], diff --git a/Q3/Kernel/Einstein.wl b/Q3/Kernel/Einstein.wl index eb54c9f42..1ae44e1d2 100644 --- a/Q3/Kernel/Einstein.wl +++ b/Q3/Kernel/Einstein.wl @@ -3,6 +3,7 @@ BeginPackage["Q3`"] (**** ****) +{ GottesmanInner }; (* renamed *) { WickRandomCircuit }; (* renamed *) { WeightedLog }; (* renamed *) { PauliDecompose, PauliDecomposeRL, PauliCompose, PauliCompseRL }; (* renamed *) @@ -177,6 +178,11 @@ Phase[qq:{__?QubitQ}, phi_, rest___] := ( (**** ****) +GottesmanInner[any___] := ( + Message[Q3General::renamed, "GottesmanInner", "GottesmanDot"]; + GottesmanDot[any] +) + WickRandomCircuit[any___] := ( Message[Q3General::renamed, "WickRandomCircuit", "RandomWickCircuitSimulate"]; RandomWickCircuitSimulate[any] diff --git a/Q3/Kernel/Gottesman.wl b/Q3/Kernel/Gottesman.wl index 1ef38082a..f85ee5fa4 100644 --- a/Q3/Kernel/Gottesman.wl +++ b/Q3/Kernel/Gottesman.wl @@ -4,7 +4,7 @@ BeginPackage["Q3`"] { GottesmanVector, FullGottesmanVector, GottesmanVectorQ, FromGottesmanVector, - GottesmanTest, GottesmanInner, GottesmanBasis, + GottesmanTest, GottesmanDot, GottesmanBasis, GottesmanSplit, GottesmanMerge, GottesmanFlip, GottesmanVectorEmbed }; { GottesmanTimes, GottesmanMap }; @@ -643,26 +643,46 @@ GottesmanTest[a_, b_] := If[ ] -(**** ****) +(**** ****) -GottesmanInner::usage = "GottesmanInner[v, w] gives the symplectic inner product in the Gottesman vector space." +GottesmanDot::usage = "GottesmanDot[v, w] gives the symplectic inner product in the Gottesman vector space." +GottesmanDot[v_?VectorQ, w_?VectorQ] := + Mod[Dot[v, GottesmanFlip @ w], 2] /; + MatrixQ[{v, w}, BinaryQ] && EvenQ[Length @ v] -GottesmanInner::icmp = "Incompatible vectors `1` and `2`." +GottesmanDot[v_?MatrixQ, w_?MatrixQ] := + Mod[Dot[v, GottesmanFlip @ Transpose @ w], 2] /; + MatrixQ[Join[v, w], BinaryQ] && EvenQ[Last @ Dimensions @ v] -GottesmanInner[v_?VectorQ, w_?VectorQ] := - Mod[Dot[v, GottesmanFlip @ w], 2] /; - ArrayQ[{v, w}, 2, BinaryQ] && EvenQ[Length @ v] +GottesmanDot[v_?VectorQ, w_?MatrixQ] := + Mod[Dot[v, GottesmanFlip @ Transpose @ w], 2] /; + MatrixQ[Join[{v}, w], BinaryQ] && EvenQ[Length @ v] -GottesmanInner[v_?VectorQ, w_?VectorQ] := - Mod[Dot[v, GottesmanFlip @ w], 2] /; - If[ ArrayQ[{Most @ v, Most @ w}, 2, BinaryQ] && OddQ[Length @ v], True, - Message[GottesmanInner::icmp, v, w]; False - ] +GottesmanDot[v_?MatrixQ, w_?VectorQ] := + Mod[Dot[v, GottesmanFlip @ Transpose @ w], 2] /; + MatrixQ[Join[v, {w}], BinaryQ] && EvenQ[Length @ w] + +(**** ****) + + +(**** ****) + +GottesmanFlip::usage = "GottesmanFlip[vec] swaps the x-bit and z-bit of each qubit in Gottesman vector vec." + +(* for a reduced Gottesman vector or a matrix consisting of COLUMNS of Gottesman vectors *) +GottesmanFlip[obj_] := + SparseArray @ Flatten[Reverse /@ Partition[obj, 2], 1] /; + ArrayQ[obj, 1|2, BinaryQ] && EvenQ[Length @ obj] -(**** ****) +(* for a full Gottesman vector or a matrix consisting of COLUMNS of full Gottesman vectors *) +GottesmanFlip[obj_] := + Append[GottesmanFlip[Most @ obj], Last @ obj] /; + ArrayQ[Most @ obj, 1|2, BinaryQ] && OddQ[Length @ obj] + +(**** ****) -GottesmanBasis::usage = "GottesmanBasis[{v1, v2, \[Ellipsis]}] returns a symplectic basis of the vector space spanned by {v1, v2, \[Ellipsis]}.\nGottesmanBasis[v] returns a symplectic basis {v, \[Ellipsis]} spanning the Gottesman vector space containing v.\nGottesmanBasis[n] returns the standard basis of the n-qubit (2n-dimensional) Gottesman vector space, which happens to be a symplectic basis with respect to GottesmanInner." +GottesmanBasis::usage = "GottesmanBasis[{v1, v2, \[Ellipsis]}] returns a symplectic basis of the vector space spanned by {v1, v2, \[Ellipsis]}.\nGottesmanBasis[v] returns a symplectic basis {v, \[Ellipsis]} spanning the Gottesman vector space containing v.\nGottesmanBasis[n] returns the standard basis of the n-qubit (2n-dimensional) Gottesman vector space, which happens to be a symplectic basis with respect to the Gottesman inner prodcut." (* See: Koenig and Smolin (2021) *) GottesmanBasis[{}] = {} (* fallback *) @@ -672,11 +692,11 @@ GottesmanBasis[bs_?MatrixQ] := Module[ w, new }, If[ContainsOnly[v, {0}], Return @ GottesmanBasis @ Rest @ bs]; - w = Select[bs, GottesmanInner[v, #]==1&]; + w = Select[bs, GottesmanDot[v, #]==1&]; If[Length[w] == 0, Return[bs], w = First[w]]; new = Map[ - Mod[# + w * GottesmanInner[v, #] + v * GottesmanInner[w, #], 2]&, + Mod[# + w * GottesmanDot[v, #] + v * GottesmanDot[w, #], 2]&, DeleteCases[Rest @ bs, w] ]; Join[{v, w}, GottesmanBasis @ DeleteCases[new, Table[0, Length @ v]]] @@ -737,21 +757,6 @@ GottesmanMerge[xx_?MatrixQ, zz_?MatrixQ] := ( GottesmanMerge[xx_?MatrixQ, zz_?MatrixQ] := MapThread[Riffle, {xx, zz}] -(**** ****) - -GottesmanFlip::usage = "GottesmanFlip[vec] swaps the x-bit and z-bit of each qubit in Gottesman vector vec." - -GottesmanFlip[vec_?VectorQ] := - Append[GottesmanFlip[Most @ vec], Last @ vec] /; - OddQ[Length @ vec] - -GottesmanFlip[vec_] := - SparseArray @ Flatten[Reverse /@ Partition[vec, 2]] /; - VectorQ[vec, BinaryQ] && EvenQ[Length @ vec] - -(**** ****) - - (**** ****) Stabilizer::usage = "Stabilzier[state] returns the stabilizer subgroup of the Pauli group that stabilizes state, which may be a column vecotr or expressed in terms of Ket[\[Ellipsis]] or Ket[<|\[Ellipsis]|>].\nStabilizer[state, {s1,s2,\[Ellipsis]}] assumes that state belongs to the Hilbert space associated with qubits {s1,s2,\[Ellipsis]}.\nStabilizer[graph] returns the stabilizer subgroup of the Pauli group that stabilizes the graph state associated with graph.\nStabilizer[graph, vtx] returns the operator associated with vertex vtx (the so-called correlation operator on vtx) that stabilizes the graph state associated with graph." @@ -840,7 +845,7 @@ UpdateStabilizerGenerators::usage = "UpdateStabilizerGenerators[{g1, g2, \[Ellip UpdateStabilizerGenerators[gnr_?MatrixQ, msr_?VectorQ] := Module[ { alt, chk, new }, alt = Most[msr]; - chk = Map[GottesmanInner[alt, #]&, Transpose @ Most @ Transpose @ gnr]; + chk = Map[GottesmanDot[alt, #]&, Transpose @ Most @ Transpose @ gnr]; chk = Position[chk, 1]; If[chk == {}, Return @ gnr]; alt = gnr[[First @ First @ chk]]; @@ -1029,7 +1034,7 @@ GottesmanShear::usage = "GottesmanShear[v, w] gives w + v\[LeftAngleBracket]v,w\ GottesmanShear::incon = "Inconsistent vectors `` and ``." GottesmanShear[v_?VectorQ, w_?VectorQ] := - Mod[w + v * GottesmanInner[v, w], 2] /; + Mod[w + v * GottesmanDot[v, w], 2] /; ArrayQ @ {v, w} GottesmanShear[v_?VectorQ, w_?VectorQ] := ( @@ -1047,7 +1052,7 @@ FindGottesmanShears[x_?VectorQ, y_?VectorQ] := Zero[{2, Length @ x}] /; x == y FindGottesmanShears[x_?VectorQ, y_?VectorQ] := { Mod[x + y, 2], Zero[Length @ x] -} /; GottesmanInner[x, y] == 1 +} /; GottesmanDot[x, y] == 1 FindGottesmanShears[x_?VectorQ, y_?VectorQ] := Module[ { assoc, k, z }, @@ -1090,17 +1095,14 @@ solveBinaryEq[x:{_, _}] := If[First[x] == 0, {1, 0}, {0, 1}] GottesmanMatrixQ::usage = "GottesmanMatrixQ[mat] returns True if matrix mat is a (reduced) Gottesman matrix, which is symplectic with respect to the Gottesman inner prodcut." -GottesmanMatrixQ[mat_?SquareMatrixQ] := Module[ - { n = Length[mat], - x }, - x = CircleTimes[One[n/2], ThePauli[1]]; - ArrayZeroQ[Mod[mat . x . Transpose[mat], 2] - x] -] /; MatrixQ[mat, BinaryQ] && EvenQ[Length @ mat] +GottesmanMatrixQ[mat_?GttsMatrixQ] := + ArrayZeroQ[GottesmanFlip[GottesmanDot[mat, mat]] - One[Dimensions @ mat]] GottesmanMatrixQ[_] = False -GttsMatrixQ::usage = "GttsMatrixQ[mat] returns True if matrix mat is seemingly a (reduced) GottesmanMatrix.\nUnlike GottesmanMatrixQ, GttsMatrixQ does NOT test whether mat is actually symplectic or not. This test does not take really long, but may be expensive for a use in syntax arguments tests for functions when one has to call them repeatedly many times." +GttsMatrixQ::usage = "GttsMatrixQ[mat] returns True if matrix mat is seemingly a (reduced) Gottesman matrix." +(* NOTE: Unlike GottesmanMatrixQ, GttsMatrixQ does NOT test whether mat is actually symplectic or not. This test does not take really long, but may be expensive for a use in syntax arguments pattern tests for functions when one has to call them repeatedly many times." *) GttsMatrixQ[mat_?SquareMatrixQ] := MatrixQ[mat, BinaryQ] && EvenQ[Length @ mat] @@ -1518,7 +1520,7 @@ GottesmanFactor[mat_?GttsMatrixQ, ss:{_?QubitQ, __?QubitQ}] := Module[ opf, oph, opa, opb, opv, cyc, new }, ff = Transpose[Partition[#, 2]& /@ Take[mat, 2]]; - kk = FirstPosition[GottesmanInner @@@ ff, 1]; + kk = FirstPosition[GottesmanDot @@@ ff, 1]; If[ MissingQ[kk], Message[GottesmanFactor::badmat, MatrixForm @ mat]; diff --git a/Q3/Kernel/Pauli.wl b/Q3/Kernel/Pauli.wl index d6c5ccb8b..d20119c33 100644 --- a/Q3/Kernel/Pauli.wl +++ b/Q3/Kernel/Pauli.wl @@ -1531,6 +1531,8 @@ Hexadecant::usage = "Hexadecant represents the phase gate with phase angle 2*\[P Pauli::usage = "Pauli[n] represents the Pauli operator (n=1,2,3). Pauli[0] represents the 2x2 identity operator. Pauli[4] and Pauli[5] represent the Pauli raising and lowering operator, respectively. Pauli[6] represents the Hadamard operator. Pauli[7], Pauli[8], Pauli[9] represent the quadrant, octant, hexadecant phase operator, respectively.\nPauli[10] returns (Pauli[0]+Pauli[1])/2, the Projection to Ket[0].\nPauli[11] returns (Pauli[0]-Paui[1])/2, the projection to Ket[1].\nPauli[n1, n2, ...] represents the tensor product of the Pauli operators Pauil[n1], Pauli[n2], ... ." +Pauli::dot = "Different lengths of Pauli indices `` and ``." + SetAttributes[Pauli, NHoldAll] SyntaxInformation[Pauli] = {"ArgumentsPattern" -> {_}}; @@ -3010,6 +3012,9 @@ PauliDot::usage = "PauliDot[a, b, \[Ellipsis]] represents the non-commutative mu SetAttributes[PauliDot, {Flat, OneIdentity}]; +Format[PauliDot[a_Pauli, b_Pauli]] := Row @ {"(",a,")","(",b,")"} +(* NOTE: Normally, this should not occur. However, for example, incompatible Pauli strings are left unevaluated. *) + PauliDot[expr_Plus, a_] := Map[PauliDot[#, a]&, expr] PauliDot[a_, expr_Plus] := Map[PauliDot[a, #]&, expr] @@ -3080,7 +3085,10 @@ PauliDot[ Pauli[m_], Pauli[n_] ] := *) PauliDot[ Pauli[aa_List], Pauli[bb_List] ] := CircleTimes @@ - PauliDot @@@ Transpose[Elaborate @ {Pauli /@ aa, Pauli /@ bb}] + PauliDot @@@ Transpose[Elaborate @ {Pauli /@ aa, Pauli /@ bb}] /; + If[ ArrayQ[{aa, bb}], True, + Message[Pauli::dot, aa, bb]; False + ] PauliDot[ Pauli[aa_List], Ket[bb_List] ] := CircleTimes @@ PauliDot @@@ Transpose[{Pauli /@ aa, Ket /@ bb}] diff --git a/Q3/Kernel/QuantumCircuit.wl b/Q3/Kernel/QuantumCircuit.wl index e5dd84f94..a657def1c 100644 --- a/Q3/Kernel/QuantumCircuit.wl +++ b/Q3/Kernel/QuantumCircuit.wl @@ -255,7 +255,8 @@ Options[QuantumCircuit] = { "UnitLength" -> 36, (* 72 is a good choice for presentation *) "Visible" -> None, "Invisible" -> None, - "PortSize" -> 0.65 + "PortSize" -> 0.65, + "PostMeasurementDashes" -> True } Format[ qc:QuantumCircuit[__, opts___?OptionQ] ] := @@ -292,7 +293,10 @@ HoldPattern @ yy = AssociationThread[ss, -yy]; nodes = qcNodes[cc, Most @ xx, yy]; - lines = qcLines[cc, xx, KeyDrop[yy, ww]]; + lines = If[ "PostMeasurementDashes" /. {opts} /. Options[QuantumCircuit], + qcLines[cc, xx, KeyDrop[yy, ww]], + qcSimpleLines[cc, xx, KeyDrop[yy, ww]] + ]; marks = qcMarks @ Cases[{gg}, _Mark, Infinity]; @@ -1175,33 +1179,41 @@ qcDrawGate[g_, x_, yy_Association] := g (**** ****) -qcLines::usage = "qcLines[gg, x, y] finds when Measurement occurs in the QuantumCircuit and renders the qubit line after Measurement in dashes." +qcLines::usage = "qcLines[gg, x, y] finds when Measurement occurs in the QuantumCircuit and renders the qubit lines after Measurement in dashes." qcLines[ gg_List, xx_List, yy_Association ] := Module[ { mm, zz, dashed, plain }, mm = Map[ - Cases[ {#}, Gate[{S_?QubitQ}, - "Shape" -> "Measurement", ___?OptionQ] -> S, Infinity ]&, + Cases[ {#}, Gate[{S_?QubitQ}, "Shape" -> "Measurement", ___?OptionQ] -> S, Infinity ]&, gg ]; mm = Flatten[ Thread /@ Thread[mm -> Most[xx]] ]; mm = KeySort @ KeyTake[Association @ mm, Keys @ yy]; zz = Lookup[yy, Keys @ mm]; - dashed = Line @ Transpose@{ + dashed = Line @ Transpose @ { Thread[ {Values @ mm, zz} ], - Thread[ {Last @ xx, zz} ] }; + Thread[ {Last @ xx, zz} ] + }; - plain = Association @ Thread[ Keys[yy] -> Last[xx] ]; - plain = Join[ plain, mm ]; - plain = Line @ Transpose@{ + plain = AssociationThread[ Keys[yy] -> Last[xx] ]; + plain = Join[plain, mm]; + plain = Line @ Transpose @ { Thread[{0, Values @ yy}], - Transpose@{Values @ plain, Values @ yy} }; - + Transpose @ {Values @ plain, Values @ yy} + }; {{Dashed, dashed}, plain} ] +qcSimpleLines::usage = "qcSimpleLines[gg, x, y] renders the qubit lines (ignoring measurements)." + +qcSimpleLines[ gg_List, xx_List, yy_Association ] := + List @ Line @ Transpose @ { + Thread @ {0, Values @ yy}, + Thread @ {Last @ xx, Values @ yy} + } + (**** ****) qcPorts::usage = "qcPorts[type, expr] handles input (type = -1) or output (type = 1) states expr." diff --git a/Q3/PacletInfo.wl b/Q3/PacletInfo.wl index 239159d72..29dc3e4ff 100644 --- a/Q3/PacletInfo.wl +++ b/Q3/PacletInfo.wl @@ -1,6 +1,6 @@ Paclet[ "Name" -> "Q3", - "Version" -> "3.6.0", + "Version" -> "3.6.1", "WolframVersion" -> "12.3+", "Updating" -> Automatic, "Loading" -> "Startup", diff --git a/RELEASES.md b/RELEASES.md index 6acde372d..c4b91f550 100644 --- a/RELEASES.md +++ b/RELEASES.md @@ -1,5 +1,12 @@ # Release Notes +## 3.6.1 + +- GottesmanInner is greatly enhanced and renamed GottesmanDot. +- GottesmanFlip is enhanced and supports matrices consisting of COLUMNS of Gottesman vectors. +- Improved: GottesmanMatrixQ, CliffordLogarithmicNegativity +- New: PauliDecoherence + ## 3.6.0 - Tools for efficient simulation of Clifford quantum circuits: CliffordState, CliffordUnitary, CliffordLogarithmicNegativity, CliffordCircuit, RandomCliffordCircuit, RandomCliffordCircuitSimulate, CliffordLogarithmicNegativity, RandomCliffordUnitary, RandomCliffordState, etc.