diff --git a/Q3/Documentation/English/Index/_0.cfs b/Q3/Documentation/English/Index/_0.cfs index 802f928d2..f8714826a 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 5d2380642..3c9958c18 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/NambuJump.nb b/Q3/Documentation/English/ReferencePages/Symbols/NambuJump.nb index 1b1a92637..b9260a4fc 100644 --- a/Q3/Documentation/English/ReferencePages/Symbols/NambuJump.nb +++ b/Q3/Documentation/English/ReferencePages/Symbols/NambuJump.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 154, 7] -NotebookDataLength[ 154250, 3546] -NotebookOptionsPosition[ 143516, 3327] -NotebookOutlinePosition[ 145783, 3384] -CellTagsIndexPosition[ 145696, 3379] +NotebookDataLength[ 158690, 3626] +NotebookOptionsPosition[ 147948, 3407] +NotebookOutlinePosition[ 150214, 3464] +CellTagsIndexPosition[ 150127, 3459] WindowTitle->NambuJump WindowFrame->Normal*) @@ -27,11 +27,11 @@ Cell[BoxData[GridBox[{ TemplateBox[{12}, "Spacer1"], Cell["Q3 SYMBOL", "PacletNameCell", TextAlignment->Center,ExpressionUUID-> - "b5053bbc-fac4-42dd-a2c9-cd08fb80f84c"], + "c522299d-da8b-403d-8fea-b6ab30918461"], TemplateBox[{8}, "Spacer1"]}]], TextAlignment->Center,ExpressionUUID-> - "a66a5c02-986a-4a30-a123-f25963b36470"], + "41975317-acd9-488b-b7b0-36fa98011e9f"], 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-> - "111c20cd-78d3-412e-b5f9-57fe6dec4ab2"] - }],ExpressionUUID->"524516b7-25ad-4852-80f6-8fa76ab870fb"], + "c9756d6f-90c3-4905-b229-b223d038803d"] + }],ExpressionUUID->"c074f21b-163a-438e-a9a9-53b6ac2c6e40"], StripOnInput->False],{ StyleBox["\"WickJump\"", "SeeAlsoRelated", StripOnInput -> False] :> Documentation`HelpLookup["paclet:Q3/ref/WickJump"], @@ -82,7 +82,7 @@ Cell[BoxData[GridBox[{ MenuStyle->"SeeAlso"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "6d0d0d75-90fb-41dd-b404-8bb2fe69fb48"], + "cf4fdf1f-aa67-4f02-aa0a-722288f7c3e6"], "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ \[ThickSpace]", Cell[BoxData[ @@ -101,8 +101,8 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "925e284b-f79f-43ba-8a01-cceb72a3e150"] - }],ExpressionUUID->"1c125656-60b5-48d8-878c-bb5a3b030ad5"], + "00866175-fc1d-4843-9baa-1aa4c5862ec3"] + }],ExpressionUUID->"c5d375e3-c4f4-45e5-87ee-c7a2b5825222"], StripOnInput->False],{ "\"Fermionic Quantum Computation\"" :> Documentation`HelpLookup[ @@ -118,7 +118,7 @@ Cell[BoxData[GridBox[{ MenuStyle->"MoreAbout"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "06cb3bda-b6c0-4e5b-80a8-13a6c2a2535c"], + "39e562a1-cab4-4f41-9063-19ce115f9de8"], "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ \[ThickSpace]", Cell[BoxData[ @@ -137,8 +137,8 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "2046961e-c4eb-4f7e-85bd-81b959ab6354"] - }],ExpressionUUID->"feef5dbb-f40f-4037-a245-8b6a47c79c1b"], + "f4e57bbc-7ea7-4263-9a05-ae16eb4e94b2"] + }],ExpressionUUID->"44c03e5c-47a3-4fc9-91f3-33701d4812b2"], StripOnInput->False],{ "\"Majorana Fermions\"" :> Documentation`HelpLookup["paclet:Q3/tutorial/MajoranaFermions"], @@ -155,7 +155,7 @@ Cell[BoxData[GridBox[{ MenuStyle->"Tutorials"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "2d349a2f-70f1-4ff2-b36d-7c99842b773a"], + "423ae793-b401-4329-a036-18816f3c9e26"], "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ \[ThickSpace]", Cell[BoxData[ @@ -174,8 +174,8 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "a16d13be-3d71-4995-85a4-acf7f692ed9c"] - }],ExpressionUUID->"a8e50ed3-5649-4f36-8ec1-b3d39287a9e3"], + "0be680e4-c9cc-4f6e-9449-d24e3ae23bca"] + }],ExpressionUUID->"371e0dc7-a3fa-4bc5-83ef-51e02f9d412e"], StripOnInput->False],{ "\"Q3/ref/NambuJump\"" :> None, "\"Copy Wolfram Documentation Center URL\"" :> @@ -183,7 +183,7 @@ Cell[BoxData[GridBox[{ DocumentationSearch`Private`nb$ = NotebookPut[ Notebook[{Cell["Q3/ref/NambuJump"]}, Visible -> - DocumentationBuild`Make`Private`visible$28280]]; + DocumentationBuild`Make`Private`visible$79878]]; SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; NotebookClose[DocumentationSearch`Private`nb$]; Null], Delimiter, @@ -197,7 +197,7 @@ Cell[BoxData[GridBox[{ Hyperlink[ "http://reference.wolfram.com/language/Q3/ref/NambuJump.\ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> - DocumentationBuild`Make`Private`visible$28280]]; + DocumentationBuild`Make`Private`visible$79878]]; SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; NotebookClose[DocumentationSearch`Private`nb$]; Null], @@ -213,14 +213,14 @@ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> MenuStyle->"URLMenu"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "ae90c8dd-1d9f-49c0-884c-835cf6a5cade"] + "c27d93ef-fe19-449a-a02c-e6b5b74778d9"] }], "AnchorBar", CacheGraphics->False,ExpressionUUID-> - "c3eab9e1-0cda-4c7c-9c31-54cbb132c9d3"]} + "08d5bd2e-f593-4c1c-ab24-c4226c60f907"]} }]], "AnchorBarGrid", - CellID->1,ExpressionUUID->"422b7ee2-d21c-445a-b209-29e764949bc6"], + CellID->1,ExpressionUUID->"183a2f40-cf26-4458-baa7-9cf45ea07265"], -Cell["Q3`", "ContextNameCell",ExpressionUUID->"4f4857be-0785-499e-b13a-dce9c6f80342"], +Cell["Q3`", "ContextNameCell",ExpressionUUID->"c1c325c9-5e56-4b10-b335-319533fd4bca"], Cell[CellGroupData[{ @@ -228,14 +228,14 @@ Cell[BoxData[GridBox[{ {Cell[TextData[{ Cell[ "NambuJump", "ObjectName",ExpressionUUID-> - "0fc5d53f-0ff8-4d8b-b5c6-bd7692b30ebf"], + "231ddeab-8906-4fac-b8ad-0465a59e2c98"], Cell[BoxData[ TemplateBox[{8}, - "Spacer1"]],ExpressionUUID->"177ef1dc-29cc-4f71-9984-e034e4aa3e90"], + "Spacer1"]],ExpressionUUID->"a76f1b04-9e34-4ecc-bc4a-c33b6fda60f7"], Cell[BoxData[ ""], "ObjectNameTranslation",ExpressionUUID-> - "28db3cff-ddf1-4530-aeb1-0c1df473c0a7"] - }],ExpressionUUID->"f72d99d7-1c56-44ab-a55a-40c006261c36"], Cell[BoxData[ + "cfdfa76b-f51d-4082-9964-0e5e70a206d2"] + }],ExpressionUUID->"8f6c6d2d-6b0d-48a4-93bc-7743fa59b6fe"], Cell[BoxData[ TooltipBox[ StyleBox[ TagBox[ @@ -260,9 +260,9 @@ Cell[BoxData[GridBox[{ "New in 14", TooltipDelay->0.3]], Magnification->1,ExpressionUUID-> - "6d38730c-78cc-48c2-b070-0de5e44f86c1"]} + "f1650c4c-b78d-48db-b924-17efef8859ce"]} }]], "ObjectNameGrid", - CacheGraphics->False,ExpressionUUID->"33e6481e-0291-4de4-a24e-288d21c50abb"], + CacheGraphics->False,ExpressionUUID->"5d0b457e-7a73-401d-b4b8-87caaedf28fd"], Cell[BoxData[GridBox[{ {"", Cell[TextData[{ @@ -289,7 +289,7 @@ Cell[BoxData[GridBox[{ StyleBox["Majorana fermion", FontSlant->"Italic"], " operators." - }],ExpressionUUID->"e767b55e-5035-4e1b-bb43-5f1794e02ce0"]} + }],ExpressionUUID->"6caae864-e311-480a-a5d9-e65a830636fa"]} }]], "Usage", CellID->2013771933,ExpressionUUID->"133f160f-9d8d-4440-b84c-9b54f09fbdc0"] }, Open ]], @@ -323,12 +323,12 @@ Cell[TextData[Cell[BoxData[ 0.68 Inherited], Rational[1, 2] Pi, {-1.65, -1}]]], ImageSizeCache->{ 13.600000000000003`, {-0.1685058593749993, 13.768505859375}}]], - ExpressionUUID->"02a12825-0573-4a28-aba3-6ffd38f604e6"], + ExpressionUUID->"93e7fad7-a9c6-45b8-bd9b-80ad16fadcd9"], Cell[BoxData[ TemplateBox[{1}, - "Spacer1"]],ExpressionUUID->"16929113-afa9-4f54-bb91-3879a25571fe"], + "Spacer1"]],ExpressionUUID->"fc3e69ff-faee-4c52-9f9c-cd6794d3f53c"], "Details and Options" - }], "NotesFrameText",ExpressionUUID->"dbbe6290-4482-46a9-9489-5273c93a1dc5"], + }], "NotesFrameText",ExpressionUUID->"f2892334-8113-404f-82b5-2526fbb5b883"], Appearance->{Automatic, None, "Normal", Automatic}, BaseStyle->None, ButtonFunction:>(FrontEndExecute[{ @@ -339,12 +339,12 @@ Cell[TextData[Cell[BoxData[ FrontEnd`SelectedNotebook[], After, CellContents]}]& ), Evaluator->None, Method-> - "Preemptive"]],ExpressionUUID->"82e82244-d0b6-4b2c-bec3-35c8eb18bfdc"]], \ + "Preemptive"]],ExpressionUUID->"796d74ae-0371-4b50-8921-8f4d76782436"]], \ "NotesSection", WholeCellGroupOpener->True, CellGroupingRules->{"SectionGrouping", 50}, CacheGraphics->False, - CellID->757307108,ExpressionUUID->"eb30b2ce-ac70-4a85-9883-2928043fc0d2"], + CellID->1031574673,ExpressionUUID->"dd87da2b-cd60-46be-8c26-e61dfb5f51e9"], Cell[TextData[{ "It merely provides a shortcut tool for convenience as most calculations in \ @@ -392,19 +392,19 @@ Cell[TextData[{ 0.68 Inherited], Rational[1, 2] Pi, {-1.65, -1}]]], ImageSizeCache->{ 13.600000000000001`, {4.251494140625001, 9.348505859375003}}]], - ExpressionUUID->"3fb92335-4e5a-4be4-87ab-c7c4ef6ead07"], + ExpressionUUID->"03a6bdea-8f0b-4cc9-8535-24275656ce8d"], Cell[BoxData[ TemplateBox[{1}, - "Spacer1"]],ExpressionUUID->"153e5810-0410-42a3-8063-1705893f1e62"], + "Spacer1"]],ExpressionUUID->"438920b6-0538-46aa-afdc-59019860cc22"], "Examples", "\[NonBreakingSpace]\[NonBreakingSpace]", Cell["(5)", "ExampleCount",ExpressionUUID-> - 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"c12a5555-e9fd-410b-811b-05bcea911514"], + "80c09186-315e-4fa6-9163-a3e0a63052cc"], TemplateBox[{8}, "Spacer1"]}]], TextAlignment->Center,ExpressionUUID-> - "77486e76-3a87-44af-ae50-cbcca309a8c7"], + "6d01583b-655e-483b-88b1-1159af685109"], 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-> - "a1a2bebd-7d2c-456b-a421-18fdf715984f"] - }],ExpressionUUID->"b72bb028-dd0f-47d1-9f6f-6682ce186278"], + "ff668f8e-1f66-43b3-aa03-a184ecd08d8a"] + }],ExpressionUUID->"30068b49-61a0-487f-b502-9f8155f95491"], StripOnInput->False],{ StyleBox["\"WickOperator\"", "SeeAlsoRelated", StripOnInput -> False] :> Documentation`HelpLookup["paclet:Q3/ref/WickOperator"], @@ -79,7 +79,7 @@ Cell[BoxData[GridBox[{ MenuStyle->"SeeAlso"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "bbbf4f6b-8283-4c4e-bde5-cd7ed2ad8bc4"], + "ce0ac9b8-f311-4504-8018-de87454f582c"], "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ \[ThickSpace]", Cell[BoxData[ @@ -98,8 +98,8 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "ca956827-f0fc-4a35-be62-9131a5054d45"] - }],ExpressionUUID->"31419c7c-ec7f-4769-b35c-95026c8a5793"], + "3f1413b3-3c3e-46d5-8713-276958b5fe87"] + }],ExpressionUUID->"16f7216f-1681-4783-8979-298cf8b59ac6"], StripOnInput->False],{ "\"Fermionic Quantum Computation\"" :> Documentation`HelpLookup[ @@ -115,7 +115,7 @@ Cell[BoxData[GridBox[{ MenuStyle->"MoreAbout"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "ecf2c663-96cf-44e5-a78e-9578b6b3b40d"], + "fd4b8762-92ba-497b-887c-7dfa9304981a"], "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ \[ThickSpace]", Cell[BoxData[ @@ -134,8 +134,8 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "a7e5ac08-ac49-4229-880f-ffaee8af138e"] - }],ExpressionUUID->"fc3c4d8a-a54e-4f28-9232-e7ca72477d0e"], + "54028171-357d-4628-aeaa-7196cf49bf36"] + }],ExpressionUUID->"65e9e94a-7a20-4ca4-930c-92b65acfd2e4"], StripOnInput->False],{ "\"Majorana Fermions\"" :> Documentation`HelpLookup["paclet:Q3/tutorial/MajoranaFermions"], @@ -152,7 +152,7 @@ Cell[BoxData[GridBox[{ MenuStyle->"Tutorials"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - 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DocumentationBuild`Make`Private`visible$31642]]; + DocumentationBuild`Make`Private`visible$80625]]; SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; NotebookClose[DocumentationSearch`Private`nb$]; Null], @@ -211,14 +211,14 @@ NambuOperator.html"], StandardForm]], "Input", TextClipboardType -> MenuStyle->"URLMenu"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "ac4b61b9-2509-4fa5-bbc8-c8089459158e"] + "3f42ff90-f4a9-4607-822d-ec26831d0de4"] }], "AnchorBar", CacheGraphics->False,ExpressionUUID-> - "4c35fe5d-9c58-4f32-96fd-7e3895a87a97"]} + "72dddf66-13bd-4c72-a18e-183d66d099fe"]} }]], "AnchorBarGrid", - CellID->1,ExpressionUUID->"f04a339c-00f2-4a64-87ff-809de94a1160"], + CellID->1,ExpressionUUID->"414a0dde-bca2-4f5a-9393-402f71125fd1"], -Cell["Q3`", "ContextNameCell",ExpressionUUID->"6278d667-937e-4898-aedb-c738468204ad"], +Cell["Q3`", "ContextNameCell",ExpressionUUID->"328cbb63-b9e0-4dc3-a1bd-fe3882bd9f0a"], Cell[CellGroupData[{ @@ -226,14 +226,14 @@ Cell[BoxData[GridBox[{ {Cell[TextData[{ Cell[ "NambuOperator", "ObjectName",ExpressionUUID-> - 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"93e4aac3-7a46-43fc-9c17-884f6f56fecf"] - }],ExpressionUUID->"c292db85-92cc-4a48-9677-8f9fb80389f3"], + "ecc534af-842a-4f70-9041-d811886008dc"] + }],ExpressionUUID->"290f5a13-8220-4b60-a2e5-927a312bdcb4"], StripOnInput->False],{ "\"Fermionic Quantum Computation\"" :> Documentation`HelpLookup[ @@ -111,7 +111,7 @@ Cell[BoxData[GridBox[{ MenuStyle->"MoreAbout"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "4587637a-fa62-4e79-9850-5cd72e185d9d"], + "748fa1f6-08be-44f3-979f-426455793f5e"], "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ \[ThickSpace]", Cell[BoxData[ @@ -130,8 +130,8 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "9ab6e719-f970-4356-b4e4-b8708613fa74"] - }],ExpressionUUID->"e6a4958b-ef44-46ef-99bf-71f426aadc57"], + "ab9c5169-8942-4b11-a168-d9440bd416f8"] + }],ExpressionUUID->"0fc27cff-0e65-4125-9f4e-f345005bc502"], StripOnInput->False],{ "\"Quantum Many-Body Systems with Q3\"" :> Documentation`HelpLookup[ @@ -146,7 +146,7 @@ Cell[BoxData[GridBox[{ MenuStyle->"Tutorials"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - 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CellID->1386038813,ExpressionUUID->"b0aca557-06c5-4fc2-8e59-e683c38fa8c2"] + CellID->568612520,ExpressionUUID->"21e0c7d8-3a52-4a27-8737-8cb6e479b23b"] }, Open ]], Cell["\<\ @@ -2111,7 +2150,7 @@ XSxuIcIiInxEHYugobsfFrq4PY0v7VLHIoy0CwBDd0rB SelectWithContents->True, Selectable->False]}], "}"}]], "Output", CellLabel->"Out[4]=", - CellID->143985629,ExpressionUUID->"41bc5aba-ad25-4f73-b969-c8ecbc4f7c8e"] + CellID->368394490,ExpressionUUID->"94363745-22a1-4a4f-8e3c-e503f58adbdc"] }, Open ]], Cell[CellGroupData[{ @@ -2157,7 +2196,7 @@ Cell[BoxData[ "RowWithSeparators"]], $CellContext`a[3]]}], "}"}]], "Output", CellLabel->"Out[1]=", - CellID->79868472,ExpressionUUID->"a99009b7-3b0d-42df-903b-595e2695cdf4"] + CellID->1948723950,ExpressionUUID->"f0f28816-5553-47c0-afa2-52f7bc86588a"] }, Open ]], Cell[CellGroupData[{ @@ -2297,7 +2336,7 @@ Cell[BoxData[ Q3`Dagger[ $CellContext`a[3]]]}]}]}], "}"}]], "Output", CellLabel->"Out[2]=", - CellID->394645625,ExpressionUUID->"d9d75dbf-81c2-42a5-aaed-225f4c1b215b"] + CellID->930327253,ExpressionUUID->"2f75e62b-f5b7-46d2-bec1-f06941ce6244"] }, Open ]], Cell[CellGroupData[{ @@ -2811,7 +2850,7 @@ XSxuIcIiInxEHYugobsfFrq4PY0v7VLHIoy0CwBDd0rB SelectWithContents->True, Selectable->False]}], "}"}]], "Output", CellLabel->"Out[3]=", - CellID->833328677,ExpressionUUID->"08b55b59-d4d5-4edc-861a-6e4c31ea61cf"] + CellID->181707364,ExpressionUUID->"f787a87f-ab67-4770-9694-44318f557bd1"] }, Open ]], Cell[CellGroupData[{ @@ -2825,7 +2864,7 @@ Cell[BoxData[ Cell[BoxData["True"], "Output", CellLabel->"Out[4]=", - CellID->834754775,ExpressionUUID->"14af6186-92d7-4189-851f-2baa828e24ef"] + CellID->233920714,ExpressionUUID->"2976c6b5-cae2-453d-9de8-63f38b1e33e4"] }, Open ]] }, Open ]] }, Dynamic[CurrentValue[ @@ -2860,14 +2899,14 @@ Cell[TextData[{ 0.68 Inherited], Rational[1, 2] Pi, {-1.65, -1}]]], ImageSizeCache->{ 13.600000000000003`, {0.43114257812500156`, 13.168857421875}}]], - ExpressionUUID->"d2353978-c2e9-492d-980e-ac98810fa84d"], + ExpressionUUID->"d6a04d8c-1f78-4160-830b-1a5e66b2d6ec"], Cell[BoxData[ TemplateBox[{1}, - "Spacer1"]],ExpressionUUID->"29421e12-9e3b-4974-a5b2-22d4e538e659"], + "Spacer1"]],ExpressionUUID->"18620820-acd1-446d-a5b5-7d1b5e65eaa1"], "Shortcuts", "\[NonBreakingSpace]\[NonBreakingSpace]", Cell["(1)", "ExampleCount",ExpressionUUID-> - "9a38805a-83c8-40fb-bcfe-31430dcb8c28"] + "61082226-2dc8-473e-933c-e660f0b6d8e5"] }], "ExampleSubsection", "ExampleSubsection", WholeCellGroupOpener->True, CacheGraphics->False, @@ -2920,7 +2959,7 @@ Cell[BoxData[ "RowWithSeparators"]], $CellContext`a[3]]}], "}"}]], "Output", CellLabel->"Out[2]=", - CellID->1003117376,ExpressionUUID->"da91aecd-ecdc-451a-9b2e-0cced5bbb706"] + CellID->638018357,ExpressionUUID->"ba00a3f0-a5fc-4f85-88f0-1aa17113e700"] }, Open ]], Cell["\<\ @@ -3056,7 +3095,7 @@ Cell[BoxData[ SelectWithContents->True, Selectable->False]], "Output", CellLabel->"Out[3]=", - CellID->854607993,ExpressionUUID->"d3b99e1c-c844-4505-840e-7d1ad86c0113"] + CellID->788676628,ExpressionUUID->"c0dc0f8c-170a-4697-a845-3515cbb19b2a"] }, Open ]], Cell[CellGroupData[{ @@ -3082,7 +3121,7 @@ Cell[BoxData[ "RowWithSeparators"]], $CellContext`a[2]]}], "}"}]], "Output", CellLabel->"Out[4]=", - CellID->517616868,ExpressionUUID->"2a96e42b-8058-4dd6-a11c-5ec4274f0fcd"] + CellID->1019017512,ExpressionUUID->"2cb794ab-04db-47e2-a371-504508f9a8c6"] }, Open ]], Cell["\<\ @@ -3221,7 +3260,7 @@ Cell[BoxData[ SelectWithContents->True, Selectable->False]], "Output", CellLabel->"Out[5]=", - CellID->1932519580,ExpressionUUID->"d249c1bd-93a8-4bba-b1b4-b0b434a60c0f"] + CellID->445239359,ExpressionUUID->"2d16b80a-936e-486e-868e-8308100e0055"] }, Open ]], Cell[CellGroupData[{ @@ -3251,7 +3290,7 @@ Cell[BoxData[ Q3`Dagger[ $CellContext`a[2]]]}], "}"}]], "Output", CellLabel->"Out[6]=", - CellID->1893061701,ExpressionUUID->"473e19d4-1f75-4b6a-b6f2-eda874ab124a"] + CellID->1304880565,ExpressionUUID->"1a0927f6-bf9a-4e2e-8d1d-28995a33a681"] }, Open ]], Cell["\<\ @@ -3389,7 +3428,7 @@ Cell[BoxData[ SelectWithContents->True, Selectable->False]], "Output", CellLabel->"Out[7]=", - CellID->572382193,ExpressionUUID->"2d310331-6237-4d72-9d8a-4d33f08315f2"] + CellID->1024652791,ExpressionUUID->"13452d87-0ad3-4b43-b6ee-235a6fde638b"] }, Open ]], Cell[CellGroupData[{ @@ -3417,7 +3456,7 @@ Cell[BoxData[ "RowWithSeparators"]], $CellContext`a[2]]}], "}"}]], "Output", CellLabel->"Out[8]=", - CellID->1521554577,ExpressionUUID->"e8591ad1-dac5-4b9c-80fe-fc4da77e84bc"] + CellID->668093044,ExpressionUUID->"4e575227-3eef-4c65-8bc6-cac653b10a68"] }, Open ]] }, Dynamic[CurrentValue[ EvaluationNotebook[], {TaggingRules, "Openers", "ExampleSubsection", "1"}, @@ -3451,14 +3490,14 @@ Cell[TextData[{ 0.68 Inherited], Rational[1, 2] Pi, {-1.65, -1}]]], ImageSizeCache->{ 13.600000000000003`, {0.43114257812500156`, 13.168857421875}}]], - 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MatrixForm[BoxForm`e$, {}]]], "SummaryItem"]}]}}, + MatrixForm[ + SparseArray[ + Automatic, {5, 5}, 0, { + 1, {{0, 2, 4, 6, 8, 13}, {{2}, {5}, {1}, {5}, {4}, {5}, { + 3}, {5}, {1}, {2}, {3}, {4}, {5}}}, {-1, "\[Ellipsis]", 1, + "\[Ellipsis]", -1, "\[Ellipsis]", 1, "\[Ellipsis]", + "\[Ellipsis]", "\[Ellipsis]", "\[Ellipsis]", + "\[Ellipsis]", "\[Ellipsis]"}}], {}]]], + "SummaryItem"]}]}}, GridBoxAlignment -> { "Columns" -> {{Left}}, "Rows" -> {{Automatic}}}, AutoDelete -> False, GridBoxItemSize -> { @@ -3624,13 +3671,15 @@ Cell[BoxData[ "SummaryPanel"], DynamicModuleValues:>{}], "]"}], Q3`WickState[{ - 1, {{0, -1, 0, 0, 0, 0}, {1, 0, 0, 0, 0, 0}, {0, 0, 0, -1, 0, 0}, {0, 0, 1, - 0, 0, 0}, {0, 0, 0, 0, 0, -1}, {0, 0, 0, 0, 1, 0}}}], + 1, SparseArray[ + Automatic, {6, 6}, 0, { + 1, {{0, 2, 4, 6, 8, 10, 12}, {{1}, {2}, {2}, {1}, {3}, {4}, {4}, {3}, { + 5}, {6}, {6}, {5}}}, {0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1}}]}], Editable->False, SelectWithContents->True, Selectable->False]], "Output", CellLabel->"Out[3]=", - 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pi) ** \\[Rho] ** (1 - pi), where the both summations \ -are from 1 to the number of rows in matrix mat, pi := b_i^\\[Dagger] ** bi \ -are projection operators, and bi := \\[CapitalSigma]j matij cj are the \ -dressed Dirac fermion modes consisting of bare Majorana fermion modes cj. \ -WickMap[mat, False] represents \\[Rho] \\[RightTeeArrow] \\[CapitalSigma]i pi \ -** \\[Rho] ** pi. WickMap[{k1, k2, ...}] or WickMap[{k1, k2, ...}, flag] \ -assumes the projections pi := a_ki^\\[Dagger] ** a SubscriptBox[k, i] \ -associated with the bare Dirac fermion modes a Subscript[k, i] for flag = \ -True, False. WickMap[k] and WickMap[k, flag] are equivalent to WickMap[{k}] \ -and WickMap[{k}, flag], respectively.", "synonyms" -> {}, "tabletags" -> {}, - "title" -> "WickMap", "titlemodifier" -> "", "metadescription" -> "", - "windowtitle" -> "WickMap", "type" -> "Symbol", "uri" -> "Q3/ref/WickMap", - "WorkflowDockedCell" -> ""}, "SearchTextTranslated" -> ""}, + "WickMap[{a, b, d, fac}] or WickMap[{a, b, d, fac}, flag] represents a \ +fermionic Gaussian supermap \\[Rho] \\[RightTeeArrow] \\[CapitalSigma]i li ** \ +\\[Rho] ** l_i^\\[Dagger] with each Gaussian elements li ** \\[Rho] ** \ +l_i^\\[Dagger] described by the action kernel of the block form {{ai, bi}, \ +{-Transpose[bi], di}} with prefactor faci. The additional argument flag \ +indicates the completion of each projective Gaussian element (True) or not \ +(False). WickMap[jmp] converts WickJump object jmp to the canonical form \ +above, where li is a linear combination of Majorana operators. WickMap[msr] \ +converts WickMeasurement object msr to the canonical form above, where l$i is \ +a projection operator pi := b_i^\\[Dagger] bi associated with dressed Dirac \ +fermion mode bi. WickMap[msr, True] converts WickMeasurement object msr to \ +the canonical form with completions (1 - pi) for each projection operator \ +pi.", "synonyms" -> {}, "tabletags" -> {}, "title" -> "WickMap", + "titlemodifier" -> "", "metadescription" -> "", "windowtitle" -> + "WickMap", "type" -> "Symbol", "uri" -> "Q3/ref/WickMap"}}, CellContext->"Global`", FrontEndVersion->"14.1 for Mac OS X ARM (64-bit) (July 16, 2024)", StyleDefinitions->Notebook[{ @@ -4286,7 +4245,7 @@ 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->"609b2a64-1b03-434b-a879-7ef8bca03bee" +ExpressionUUID->"c57a2037-e5cb-495f-b9dc-969a9523c6e6" ] (* End of Notebook Content *) @@ -4294,271 +4253,271 @@ ExpressionUUID->"609b2a64-1b03-434b-a879-7ef8bca03bee" (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - Cell[34276, 1006, 1441, 38, 34, 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TemplateBox[{12}, "Spacer1"], Cell["Q3 SYMBOL", "PacletNameCell", TextAlignment->Center,ExpressionUUID-> - "0bc8d1a8-990d-4057-ad37-15eb085380c7"], + "d2b2d1dd-06da-4bad-8e3d-cc152b17ad7f"], TemplateBox[{8}, "Spacer1"]}]], TextAlignment->Center,ExpressionUUID-> - "0b32d016-ce74-4390-ae2b-11d16997eb43"], + "f556d82d-1cf7-4b6c-8cc1-465b5f99b71f"], 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-> - "ee888c7c-0578-4a79-8a30-c6941af86c07"] - }],ExpressionUUID->"333af3d4-18a0-4ba1-985f-6c1f0946aabe"], + "ae1e26bb-bf9b-4b2b-a3ca-f16df517a284"] + }],ExpressionUUID->"c430cc0c-63af-484e-982a-e2d6cf809e56"], StripOnInput->False],{ StyleBox["\"WickMap\"", "SeeAlsoRelated", StripOnInput -> False] :> Documentation`HelpLookup["paclet:Q3/ref/WickMap"], @@ -75,7 +75,7 @@ Cell[BoxData[GridBox[{ MenuStyle->"SeeAlso"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "e7eb6850-8dba-483c-922e-25f2ef904a5b"], + "688d5a5b-1733-4b21-968b-304f11c1679e"], "\[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-> - "beb4a4a3-89e4-4f0f-86b2-51b30a880568"] - }],ExpressionUUID->"0c982d5b-ac7e-478f-9a5f-9eeaccb6290f"], + "af3d63bf-fa30-482a-9150-bb80254e239a"] + }],ExpressionUUID->"60e440de-5d17-4602-aa23-21c9a37c410d"], StripOnInput->False],{ "\"Fermionic Quantum Computation\"" :> Documentation`HelpLookup[ @@ -111,7 +111,7 @@ Cell[BoxData[GridBox[{ MenuStyle->"MoreAbout"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "39e3e1d6-1d93-46e4-a8e0-4fc96f6f525b"], + "86e1f369-c5f7-4e62-bbd0-7e023c3d14d7"], "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ 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}],ExpressionUUID->"46e651ab-4b73-4151-8cbf-4d46339e3d14"], + "0df4346e-821b-4ec0-beff-859f7f7ee31a"] + }],ExpressionUUID->"c3e25435-120b-4236-bac5-4c42a79707fd"], StripOnInput->False],{ "\"Q3/ref/WickMapOdds\"" :> None, "\"Copy Wolfram Documentation Center URL\"" :> @@ -174,7 +174,7 @@ Cell[BoxData[GridBox[{ DocumentationSearch`Private`nb$ = NotebookPut[ Notebook[{Cell["Q3/ref/WickMapOdds"]}, Visible -> - DocumentationBuild`Make`Private`visible$31078]]; + DocumentationBuild`Make`Private`visible$83673]]; SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; NotebookClose[DocumentationSearch`Private`nb$]; Null], Delimiter, @@ -188,7 +188,7 @@ Cell[BoxData[GridBox[{ Hyperlink[ "http://reference.wolfram.com/language/Q3/ref/WickMapOdds.\ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> - DocumentationBuild`Make`Private`visible$31078]]; + DocumentationBuild`Make`Private`visible$83673]]; 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Wolfram Documentation Center URL\"" :> @@ -175,7 +175,7 @@ Cell[BoxData[GridBox[{ DocumentationSearch`Private`nb$ = NotebookPut[ Notebook[{Cell["Q3/ref/WickMonitor"]}, Visible -> - DocumentationBuild`Make`Private`visible$31233]]; + DocumentationBuild`Make`Private`visible$28392]]; SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; NotebookClose[DocumentationSearch`Private`nb$]; Null], Delimiter, @@ -189,7 +189,7 @@ Cell[BoxData[GridBox[{ Hyperlink[ "http://reference.wolfram.com/language/Q3/ref/WickMonitor.\ html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> - DocumentationBuild`Make`Private`visible$31233]]; + DocumentationBuild`Make`Private`visible$28392]]; SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; NotebookClose[DocumentationSearch`Private`nb$]; Null], @@ -205,14 +205,14 @@ html"], StandardForm]], 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True}}, "AxesOrigin" -> {0, 0}, "ImageSize" -> {576, 576/GoldenRatio}, "Axes" -> {False, False}, "LabelStyle" -> {}, "AspectRatio" -> GoldenRatio^(-1), @@ -1906,7 +1911,7 @@ AK5fRVk= "Label" -> {"XYLabel"}, "Ball" -> {"InterpolatedBall"}|>, "LayoutOptions" -> <| "PanelPlotLayout" -> <||>, - "PlotRange" -> {{0, 2.}, {0, 0.7748642508578336}}, + "PlotRange" -> {{0, 2.}, {0, 0.7291687018886949}}, "Frame" -> {{True, True}, {True, True}}, "AxesOrigin" -> {0, 0}, "ImageSize" -> {576, 576/GoldenRatio}, "Axes" -> {False, False}, "LabelStyle" -> {}, "AspectRatio" -> GoldenRatio^(-1), @@ -1941,56 +1946,55 @@ AK5fRVk= AbsoluteThickness[2], Thickness[Large]], Line[CompressedData[" -1:eJxd1nk41fkeB3Cp5hpNxaTLTVdo0oaYmiHJ+2QqFWWpZFC08kwlWlTayzIi -dWuq6bbJkm0uJ5xByZotS/Z9OQdnyZJjORwczGE+/rnf5/F4vn7n+/1+Pu/X -93ceGodO2RyVlZGRKZD+TP7+/3FJKdaM4+WNtacd/Swiw/H3/DcYtFlab1Rm -IVnNp9M6+QUYF5x0ZUPS6XkYJNqq6+Uuf8B/n0yOKLS4rVMeaMynz8diM6tY -7sbBYnRZT/7lDf7w2Nfs1lJK6xMR3m1Se82yHPI1oe4b5ZMg6hKfbQiqpP1S 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FontSlant->\\\"Italic\\\"]\\)\"", HoldForm], TraditionalForm], None}}, Scaled[0.025]}}, Ticks->{Automatic, Automatic}]], "Output", CellLabel->"Out[5]=", - CellID->1731867209,ExpressionUUID->"6b0ad647-8a95-437f-ac26-5577140e75ec"] + CellID->347623923,ExpressionUUID->"064f2e46-7cd7-435d-a665-6a5dfb98b05e"] }, Open ]] }, Open ]] }, Dynamic[CurrentValue[ @@ -2223,14 +2227,14 @@ Cell[TextData[{ 0.68 Inherited], Rational[1, 2] Pi, {-1.65, -1}]]], ImageSizeCache->{ 13.600000000000003`, {0.43114257812500156`, 13.168857421875}}]], - ExpressionUUID->"9b0b18ce-8189-4182-b682-adf0b9245961"], + ExpressionUUID->"6ced5b71-8807-4e8f-9774-73d93839f24b"], Cell[BoxData[ TemplateBox[{1}, - "Spacer1"]],ExpressionUUID->"832fbd12-d4bc-4fbf-b2c9-846dc41e4501"], + "Spacer1"]],ExpressionUUID->"c3fd54a5-9c74-40ff-81b3-9207277e0261"], "Applications", "\[NonBreakingSpace]\[NonBreakingSpace]", Cell["(8)", "ExampleCount",ExpressionUUID-> - "b4b8ec2e-84df-407f-82db-aa2c62f28907"] + "925e97c4-f385-4c37-8a5e-fc848ce1cf9e"] }], "ExampleSection", "ExampleSection", WholeCellGroupOpener->True, CacheGraphics->False, @@ -2264,14 +2268,14 @@ Cell[TextData[{ 0.68 Inherited], Rational[1, 2] Pi, {-1.65, -1}]]], ImageSizeCache->{ 13.600000000000003`, {0.43114257812500156`, 13.168857421875}}]], - ExpressionUUID->"5ae878f8-c2db-4978-b6ef-f9df551b3855"], + ExpressionUUID->"374b73a3-4eb5-44d6-86b7-977ed95999a6"], Cell[BoxData[ TemplateBox[{1}, - "Spacer1"]],ExpressionUUID->"d63e3996-d73b-4ac6-9b27-4ca5b90755f3"], + "Spacer1"]],ExpressionUUID->"61c8c559-b840-49f7-bd4b-f55b1345c934"], "Kitaev Chain", "\[NonBreakingSpace]\[NonBreakingSpace]", Cell["(2)", "ExampleCount",ExpressionUUID-> - "7bbb727f-483c-4b9f-bc71-41211334e78f"] + "fce2cda5-8d1c-4113-aa03-aadb178b97e4"] }], "ExampleSubsection", "ExampleSubsection", WholeCellGroupOpener->True, CacheGraphics->False, @@ -2494,7 +2498,7 @@ Cell[BoxData[ SelectWithContents->True, Selectable->False]], "Output", CellLabel->"Out[3]=", - CellID->5553273,ExpressionUUID->"ed628343-ca27-4003-b970-711488173eed"], + CellID->997605178,ExpressionUUID->"8facc45c-b2fc-483e-982e-7e5e8fd95bd7"], Cell[BoxData[ RowBox[{"{", @@ -2555,7 +2559,7 @@ Cell[BoxData[ 1, {{0, 1, 3, 5, 6}, {{2}, {1}, {3}, {2}, {4}, {3}}}, {-1, 1, -1, 1, -1, 1}}], {}]]]}], "}"}]], "Output", CellLabel->"Out[3]=", - CellID->992062490,ExpressionUUID->"a19d4383-42cf-4fb3-a131-883b07019444"], + CellID->1345394517,ExpressionUUID->"997a55c6-831d-46f8-ba9e-549b7cb8c0b6"], Cell[BoxData[ InterpretationBox[ @@ -2678,7 +2682,7 @@ Cell[BoxData[ SelectWithContents->True, Selectable->False]], "Output", CellLabel->"Out[3]=", - CellID->531234122,ExpressionUUID->"f6b4eef3-f361-4585-9710-f8575e11702f"], + CellID->1190327956,ExpressionUUID->"2dc18bea-a89b-4dd1-bc93-5c5edda9eb2a"], Cell[BoxData[ TagBox[ @@ -2711,7 +2715,7 @@ Cell[BoxData[ "\[Ellipsis]", "\[Ellipsis]", "\[Ellipsis]", "\[Ellipsis]", "\[Ellipsis]"}}], {}]]]], "Output", CellLabel->"Out[3]//MatrixForm=", - CellID->1362367875,ExpressionUUID->"22ad0aa3-486a-4b3c-8f2f-6ba179db29a6"] + CellID->2031784687,ExpressionUUID->"e00f2e82-bfe6-46e8-826a-f2ddbdbcef0a"] }, Open ]], Cell["Pick a initial state with half filling.", "ExampleText", @@ -2842,7 +2846,7 @@ Cell[BoxData[ SelectWithContents->True, Selectable->False]], "Output", CellLabel->"Out[4]=", - CellID->846230811,ExpressionUUID->"7515271f-502b-4b63-9750-870827bb3713"] + CellID->1067763462,ExpressionUUID->"0cc9c831-87d7-48d7-95c4-69670421f2c6"] }, Open ]], Cell[TextData[{ @@ -2875,7 +2879,7 @@ Cell[BoxData[{ RowBox[{"ham", "/", "\[Gamma]"}], ",", RowBox[{"{", RowBox[{ - RowBox[{"$T", "=", "100"}], ",", + RowBox[{"$T", "=", "2"}], ",", RowBox[{"$dt", "=", "0.01"}]}], "}"}], ",", RowBox[{"\"\\"", "->", "150"}]}], "]"}]}], "\[IndentingNewLine]", "]"}], ";"}], "\[IndentingNewLine]", @@ -2884,14 +2888,14 @@ Cell[BoxData[{ CellLabel->"In[6]:=", CellID->260746012,ExpressionUUID->"9874145a-7bfc-4c29-875c-bf261201ebb6"], -Cell[BoxData["1.106369`"], 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The model is specified by the single-particle Hamiltonian \ -ham in the WickHermitian form, and the dressed fermion modes the occupation \ -numbers of which to be monitored are specified by measurement msr in the \ -WickMeasurement form. The simulation starts from the initial state in in the \ -WickState form at time 0 and goes nt time steps of size dt. WickMonitor[in, \ -ham, {nt, dt}] assumes the continuous monitor of the occupation numbers the \ -bare fermion modes; that is , it equivalent to WickMonitor[in, ham, \ -WickMeasurement[{1, 2, ..., n}], {nt, dt}].", "synonyms" -> {}, - "tabletags" -> {}, "title" -> "WickMonitor", "titlemodifier" -> "", - "metadescription" -> "", "windowtitle" -> "WickMonitor", "type" -> - "Symbol", "uri" -> "Q3/ref/WickMonitor"}}, + "WickMonitor[in, ham, msr, {\\[Tau], dt}] solves the problem of \ +continuous monitoring of a non-interacting many-fermion system by using the \ +Monte Carlo simulation method. The model is specified by the single-particle \ +Hamiltonian ham in the WickHermitian form, and the dressed fermion modes the \ +occupation numbers of which to be monitored are specified by measurement msr \ +in the WickMeasurement form. The simulation starts from the initial state in \ +in the WickState form at time 0 and runs to time tau in steps of size dt. \ +WickMonitor[in, ham, {\\[Tau], dt}] assumes the continuous monitor of the \ +occupation numbers the bare fermion modes; that is , it equivalent to \ +WickMonitor[in, ham, WickMeasurement[{1, 2, ..., n}], {\\[Tau], dt}].", + "synonyms" -> {}, "tabletags" -> {}, "title" -> "WickMonitor", + "titlemodifier" -> "", "metadescription" -> "", "windowtitle" -> + "WickMonitor", "type" -> "Symbol", "uri" -> "Q3/ref/WickMonitor", + "WorkflowDockedCell" -> ""}, "SearchTextTranslated" -> ""}, CellContext->"Global`", FrontEndVersion->"14.1 for Mac OS X ARM (64-bit) (July 16, 2024)", StyleDefinitions->Notebook[{ @@ -7918,7 +8902,7 @@ StyleDefinitions->Notebook[{ StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, FrontEndVersion -> "14.1 for Mac OS X ARM (64-bit) (July 16, 2024)", StyleDefinitions -> "Default.nb"], 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45, 70, "MoreAboutSection",ExpressionUUID->"c10adcb3-035b-46fb-ba8e-03af2202e666"], +Cell[396700, 8677, 6610, 176, 70, "RelatedLinksSection",ExpressionUUID->"e017578e-757e-42f8-b630-7abdebba446e"], +Cell[403313, 8855, 78, 0, 70, "FooterCell",ExpressionUUID->"a2898c25-3591-4b88-9642-c85b3d171610"] } ] *) diff --git a/Q3/Documentation/English/ReferencePages/Symbols/WickSimulate.nb b/Q3/Documentation/English/ReferencePages/Symbols/WickSimulate.nb index 8cce6f423..a2fcf59a7 100644 --- a/Q3/Documentation/English/ReferencePages/Symbols/WickSimulate.nb +++ b/Q3/Documentation/English/ReferencePages/Symbols/WickSimulate.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 154, 7] -NotebookDataLength[ 179211, 4307] -NotebookOptionsPosition[ 166188, 4045] -NotebookOutlinePosition[ 168939, 4109] -CellTagsIndexPosition[ 168852, 4104] +NotebookDataLength[ 179197, 4304] +NotebookOptionsPosition[ 166095, 4041] +NotebookOutlinePosition[ 168928, 4106] +CellTagsIndexPosition[ 168841, 4101] WindowTitle->WickSimulate WindowFrame->Normal*) @@ -27,11 +27,11 @@ Cell[BoxData[GridBox[{ TemplateBox[{12}, "Spacer1"], Cell["Q3 SYMBOL", "PacletNameCell", TextAlignment->Center,ExpressionUUID-> - "4f2cc224-9590-4c56-90e5-7c0255587a59"], + "7e19d9c6-60ca-4f00-9b90-12363680c3f0"], TemplateBox[{8}, "Spacer1"]}]], TextAlignment->Center,ExpressionUUID-> - "ee178b9b-13f1-4faf-a9c1-af38f4100822"], + "ecd7f35d-745a-4a3b-afcb-11a5eda4c03c"], 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-> - "5741fb86-da37-4d7e-aa39-a2abe04f69f1"] - }],ExpressionUUID->"16c2a1b9-ead4-4921-bb47-edb70fce1327"], + "80c82b50-e7df-4b53-974b-1fa1236f81d5"] + }],ExpressionUUID->"7d8a4390-ce9b-404e-af58-89169d4516c2"], StripOnInput->False],{ StyleBox["\"WickState\"", "SeeAlsoRelated", StripOnInput -> False] :> Documentation`HelpLookup["paclet:Q3/ref/WickState"], @@ -81,7 +81,7 @@ Cell[BoxData[GridBox[{ MenuStyle->"SeeAlso"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "97362a6d-e3c7-4a37-8033-6f7b51840982"], + "dcbf2716-8c8c-407f-889a-acd0ac42ffab"], "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ \[ThickSpace]", Cell[BoxData[ @@ -100,8 +100,8 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "48618208-865a-4be0-8449-ad37d895c96b"] - }],ExpressionUUID->"e94db9e8-fda3-46ab-bab3-2926c525a8d9"], + "29999cf7-0bdb-40e2-81d7-c169f010133a"] + }],ExpressionUUID->"3b7ac5d6-1105-4049-a267-49444013c169"], StripOnInput->False],{ "\"Fermionic Quantum Computation\"" :> Documentation`HelpLookup[ @@ -117,7 +117,7 @@ Cell[BoxData[GridBox[{ MenuStyle->"MoreAbout"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "4afa1a1f-7606-406b-8f3e-a31b8b29088a"], + "efcbeda4-8bf1-4bfa-b8c0-0f178e9d8d1e"], "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ \[ThickSpace]", Cell[BoxData[ @@ -136,8 +136,8 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, PlotRangePadding->Scaled[0.025]]],ExpressionUUID-> - "4ee6bcf2-e6dd-4663-88aa-b7761da23697"] - }],ExpressionUUID->"318a08ab-5e3c-471f-a4a1-a8945a0d895f"], + "befde0c0-8260-4d0c-978d-4943b0ae8477"] + }],ExpressionUUID->"32055b0b-ef61-44de-b58f-75a9d34f8017"], StripOnInput->False],{ "\"Quantum Many-Body Systems with Q3\"" :> Documentation`HelpLookup[ @@ -152,7 +152,7 @@ Cell[BoxData[GridBox[{ MenuStyle->"Tutorials"], MouseAppearanceTag["LinkHand"]]], LineSpacing->{1.4, 0},ExpressionUUID-> - "457f15da-7cc2-4608-8d34-ba92098aadc5"], + "51a503e8-080b-4b8b-8cdb-de55395c2292"], "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\ \[ThickSpace]", Cell[BoxData[ @@ -171,8 +171,8 @@ Cell[BoxData[GridBox[{ ImageSize->20, PlotRange->{{-3, 4}, {-1, 1}}, 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CellID->2012143701,ExpressionUUID->"3745c41c-48c5-464e-a519-c7aa7e6096a4"] + CellID->1451261179,ExpressionUUID->"8e68120b-c882-4861-a760-ffb437785e38"] }, Open ]], Cell["Choose a initial state with half filling.", "ExampleText", @@ -902,7 +902,7 @@ Cell[BoxData[ SelectWithContents->True, Selectable->False]], "Output", CellLabel->"Out[3]=", - CellID->1674193398,ExpressionUUID->"904cf8c0-1dd8-4f62-938b-1ff1b033dc8a"] + CellID->1771468423,ExpressionUUID->"68ffad80-2cb6-4248-8997-2ed2ec2c7ba1"] }, Open ]], Cell[CellGroupData[{ @@ -947,7 +947,7 @@ Cell[BoxData[ Ket[<|$CellContext`c[1] -> 1, $CellContext`c[2] -> 0, $CellContext`c[3] -> 1, $CellContext`c[4] -> 0|>]]], "Output", CellLabel->"Out[4]=", - CellID->1837697192,ExpressionUUID->"477c598e-ea77-4a3e-91c5-dc6032275fe1"] + CellID->1899668351,ExpressionUUID->"288707a6-d357-48c7-9535-3892c06e4407"] }, Open ]], Cell["Construct the single-particle Hamiltonian matrix.", "ExampleText", @@ -1001,7 +1001,7 @@ Cell[BoxData[ Function[BoxForm`e$, MatrixForm[BoxForm`e$, {}]]]], "Output", CellLabel->"Out[6]//MatrixForm=", - CellID->1066894790,ExpressionUUID->"19e0d223-ce69-42d5-b8c5-735628f37f5b"] + CellID->1425693229,ExpressionUUID->"9ce240de-a535-4d18-8df9-5723dd3688e3"] }, Open ]], Cell["Take quantum jump operators.", "ExampleText", @@ -1174,7 +1174,7 @@ Cell[BoxData[ SelectWithContents->True, Selectable->False]], "Output", CellLabel->"Out[7]=", - CellID->1959766727,ExpressionUUID->"9329e4b0-5293-4ffa-b171-3b8818023a8d"] + CellID->3566577,ExpressionUUID->"6435128a-9f6f-465a-8be9-0fc747c99683"] }, Open ]], Cell[CellGroupData[{ @@ -1383,7 +1383,7 @@ Cell[BoxData[ Function[BoxForm`e$, TableForm[BoxForm`e$]]]], "Output", CellLabel->"Out[8]//TableForm=", - CellID->1842686650,ExpressionUUID->"89aa60aa-b260-4bfa-8802-8bd40f1a5162"] + CellID->1479675397,ExpressionUUID->"c159eef5-a763-4628-a35e-832febd371cb"] }, Open ]], Cell["Now, perform the Monte Carlo simulation.", "ExampleText", @@ -1399,7 +1399,7 @@ Cell[BoxData[ RowBox[{"in", 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The model is specified by the \ +single-particle Hamiltonian ham in the WickHermitian form and the quantum \ +jump operators are specified by jmp in the WickJump or WickMeasurement form. \ +The simulation starts from the initial state in in the WickState form at time \ +0 and runs to time n\\[Tau] in steps of size dt.", "synonyms" -> {}, + "tabletags" -> {}, "title" -> "WickSimulate", "titlemodifier" -> "", + "metadescription" -> "", "windowtitle" -> "WickSimulate", "type" -> + "Symbol", "uri" -> "Q3/ref/WickSimulate", "WorkflowDockedCell" -> ""}, + "SearchTextTranslated" -> ""}, CellContext->"Global`", FrontEndVersion->"14.1 for Mac OS X ARM (64-bit) (July 16, 2024)", StyleDefinitions->Notebook[{ @@ -4088,7 +4085,7 @@ 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->"54817859-e68d-4ee9-9339-30799e0670a5" +ExpressionUUID->"0cae5aab-432d-498c-a5e1-9f6b5eb1234b" ] (* End of Notebook Content *) @@ -4096,219 +4093,219 @@ ExpressionUUID->"54817859-e68d-4ee9-9339-30799e0670a5" (*CellTagsOutline CellTagsIndex->{ "PrimaryExamplesSection"->{ - 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"CreationDate" -> DateObject[{2025, 1, 5, 10, 20, - 49.098886`8.443646614363212}, "Instant", "Gregorian", 9.], - "Version" -> 5, "Synonyms" -> None, "Method" -> "BM25", - "Language" -> "English", "ContentFieldOptions" -> - <|"Title" -> <|"Stored" -> True, "Weight" -> 2|>, + "CreationDate" -> DateObject[{2025, 1, 7, 23, 7, 57.25437`8.51038361387309}, + "Instant", "Gregorian", 9.], "Version" -> 5, "Synonyms" -> None, + "Method" -> "BM25", "Language" -> "English", + "ContentFieldOptions" -> <|"Title" -> <|"Stored" -> True, "Weight" -> 2|>, "ExactTitle" -> <|"Stored" -> True, "Tokenized" -> False, "LengthWeighted" -> False|>, "NormalizedTitle" -> <|"Tokenized" -> False, "LengthWeighted" -> False|>, diff --git a/Q3/Documentation/English/SearchIndex/5/segments_2 b/Q3/Documentation/English/SearchIndex/5/segments_2 index 927cc13e8..2ab73c42d 100644 Binary files a/Q3/Documentation/English/SearchIndex/5/segments_2 and b/Q3/Documentation/English/SearchIndex/5/segments_2 differ diff --git a/Q3/Documentation/English/SpellIndex/_37.cfs b/Q3/Documentation/English/SpellIndex/_37.cfs index 831472250..cd7b833af 100644 Binary files a/Q3/Documentation/English/SpellIndex/_37.cfs and b/Q3/Documentation/English/SpellIndex/_37.cfs differ diff --git a/Q3/Documentation/English/SpellIndex/segments_6h b/Q3/Documentation/English/SpellIndex/segments_6h index 06cb34579..e23d85ddf 100644 Binary files a/Q3/Documentation/English/SpellIndex/segments_6h and b/Q3/Documentation/English/SpellIndex/segments_6h differ diff --git a/Q3/Kernel/Wick.wl b/Q3/Kernel/Wick.wl index 55d0a6957..8830472da 100644 --- a/Q3/Kernel/Wick.wl +++ b/Q3/Kernel/Wick.wl @@ -9,8 +9,7 @@ BeginPackage["Q3`"] { WickUnitary, WickHermitian, WickCovariance, RandomWickUnitary, RandomWickHermitian, RandomWickCovariance }; -{ WickJump, WickJumpOdds, $WickJumpOut, - RandomWickJump }; +{ WickJump, WickJumpOdds,RandomWickJump }; { WickMeasurement, WickMeasurementOdds, RandomWickMeasurement }; { WickOperator, RandomWickOperator }; @@ -23,7 +22,7 @@ BeginPackage["Q3`"] WickMean, WickCanonicalize }; { WickCircuit, RandomWickCircuit, RandomWickCircuitSimulate }; -{ WickSimulate, WickDampingOperator }; +{ WickSimulate, WickDampingOperator, $WickMinorSteps }; { WickMonitor }; { WickLogarithmicNegativity, WickTimeReversalMoment }; @@ -776,7 +775,7 @@ WickFlop::usage = "WickFlop[vec] represents a single linear combination of Major WickFlop[vec_?VectorQ, ___][WickState[{fac_?NumericQ, cvr_?MatrixQ}, rest___]] := Module[ { aa, bb, nn, id, mm, prb, new }, - {aa, bb, nn} = WickJumpKernel[vec]; + {aa, bb, nn} = WickFlopKernel[vec]; id = One[Dimensions @ aa]; mm = id + aa.cvr; prb = nn * Sqrt[Det @ mm]; @@ -787,6 +786,21 @@ WickFlop[vec_?VectorQ, ___][WickState[{fac_?NumericQ, cvr_?MatrixQ}, rest___]] : WickState[{fac*prb, new}, rest] ] +WickFlopKernel::usage = "WickFlopKernel[vec] returns {A, B, nrm}, where A and B are 2n\[Times]2n real matrices and nrm is the norm square of vec. The 4n\[Times]4n matrix {{A, B}, {-Transpose[B], A}} gives the Gaussian kernel of the Grassmann representation of the Gaussian map \[Rho] \[RightTeeArrow] b \[Rho] Dagger[b], where b := Sum[vec[[k]] c[k], {k, 2n}] is a linear combination of bare Majorana modes c[k]." + +WickFlopKernel[vec_?VectorQ] := Module[ + { nn = NormSquare[vec], + re = Re[vec], + im = Im[vec], + id, aa, bb }, + aa = Dyad[re, im] - Dyad[im, re]; + bb = Dyad[re, re] + Dyad[im, im]; + id = One[Dimensions @ aa]; + aa = -aa*2/nn; + bb = id - (bb*2/nn); + {aa, bb, nn} +] + (**** ****) @@ -801,12 +815,8 @@ RandomWickOperator[n_Integer] := (**** ****) -$WickJumpOut::usage = "$WickJumpOut returs the index of quantum jump that has occurred at the last instance of WickJump." - WickJump::usage = "WickJump[mat] represents a set of quantum jump operators, which are linear combinations of Majorana fermion operators with coefficients given by the elements of complex matrix mat." -WickJump::null = "The quantum operation returns the null state." - WickJump /: MakeBoxes[jmp:WickJump[mat_?MatrixQ, rest___], fmt_] := Module[ {m, n}, @@ -902,29 +912,7 @@ WickJump[mat_?MatrixQ, ___][in_WickState] := (* null state *) WickState[{0, Zero[2*FermionCount[in]*{1, 1}]}, Rest @ in] /; WickNullQ[in] -WickJump[mat_?MatrixQ, ___][WickState[{fac_?NumericQ, cvr_?MatrixQ}, rest___]] := Module[ - { aa, bb, nn, mm, id, pp, new, k }, - {aa, bb, nn} = Transpose @ WickJumpKernel[mat]; - id = ConstantArray[One[Length @ cvr], Length @ mat]; - mm = id + aa.cvr; - Quiet[pp = nn*Sqrt[Det /@ mm], Det::luc]; - pp = Ramp[Re @ pp]; (* Ramp and Re to quickly handle numerical errors. *) - If[ ArrayZeroQ[pp], - Message[WickJump::null]; - $WickJumpOut = Indeterminate; - Return @ WickState[{0, Zero[Dimensions @ cvr]}, rest] - ]; - - k = RandomChoice[pp -> Range[Length @ mat]]; - $WickJumpOut = k; - - aa = aa[[k]]; - bb = bb[[k]]; - nn = nn[[k]]; - mm = mm[[k]]; - new = aa + bb . cvr . Inverse[mm] . Transpose[bb]; - WickState[{1, new}, rest] -] +WickJump[mat_?MatrixQ, ___][in_WickState] := WickMap[WickJump @ mat][in] (**** ****) @@ -934,46 +922,11 @@ WickJump[mat_?MatrixQ, ___][WickState[{fac_?NumericQ, cvr_?MatrixQ}, rest___]] : WickJumpOdds::usage = "WickJumpOdds[mat][\[Rho]] returns the probabilities for the quantum jump processes \[Rho] \[RightTeeArrow] b[i]**\[Rho]**Dagger[b[i]], where b[i]:=Sum[mat[[i,j]] c[j], {j, 2n}] are the dressed Dirac fermion modes consisting of 2n bare Majorana fermion modes c[j]." WickJumpOdds[jmp_WickJump, ___] := - WickJumpOdds[First @ jmp] - -WickJumpOdds[mat_?MatrixQ, ___][WickState[{_?NumericQ, cvr_?MatrixQ}, ___]] := - WickJumpOdds[mat][cvr] - -WickJumpOdds[mat_?MatrixQ, ___][cvr_?MatrixQ] := Module[ - { aa, bb, nn, mm, id, pp }, - {aa, bb, nn} = Transpose @ WickJumpKernel[mat]; - id = One[Length @ cvr]; - mm = Map[(id + #.cvr)&, aa]; - Quiet[pp = nn*Sqrt[Det /@ mm], Det::luc]; - Normalize[Ramp @ Re @ pp, Norm[#, 1]&] - (* NOTE: Ramp and Re to quickly handle numerical errors, and Normalize[...] instead of pp/Total[pp] to handle a rare case of zero vector. *) -] + WickMapOdds[First @ WickMap @ jmp] (**** ****) -(**** ****) - -WickJumpKernel::usage = "WickJumpKernel[vec] returns {A, B, nrm}, where A and B are 2n\[Times]2n real matrices and nrm is the norm square of vec. The 4n\[Times]4n matrix {{A, B}, {-Transpose[B], A}} gives the Gaussian kernel of the Grassmann representation of the Gaussian map \[Rho] \[RightTeeArrow] b \[Rho] Dagger[b], where b := Sum[vec[[k]] c[k], {k, 2n}] is a linear combination of bare Majorana modes c[k]." - -WickJumpKernel[vec_?VectorQ] := Module[ - { nn = NormSquare[vec], - re = Re[vec], - im = Im[vec], - id, aa, bb }, - aa = Dyad[re, im] - Dyad[im, re]; - bb = Dyad[re, re] + Dyad[im, im]; - id = One[Dimensions @ aa]; - aa = -aa*2/nn; - bb = id - (bb*2/nn); - {aa, bb, nn} -] - -WickJumpKernel[mat_?MatrixQ] := Map[WickJumpKernel, mat] - -(**** ****) - - RandomWickJump::usage = "RandomWickJump[k_Integer, n_Integer] returns WickJump consisting of k linear combinations of Majorana operators." RandomWickJump[k_Integer, n_Integer, opts___?OptionQ] := @@ -1009,6 +962,14 @@ MakeBoxes[msr:WickMeasurement[mat_?MatrixQ, ___], fmt_] := Module[ Readout[WickMeasurement[op_]] := Readout[op] +(* canonicalization *) +WickMeasurement[k_Integer, n_Integer, rest___] := + WickMeasurement[{k}, n, rest] + +(* canonicalization *) +WickMeasurement[kk:{__Integer}, n_Integer, rest___] := + WickMeasurement @ NambuMeasurement @ One[{n, 2n}] + WickMeasurement /: Matrix[WickMeasurement[mat_?MatrixQ, ___], rest___] := Module[ { ops = Matrix[WickJump @ mat, rest] }, @@ -1023,6 +984,15 @@ Normalize[WickMeasurement[mat_?MatrixQ, rest___], ___] := Module[ WickMeasurement[new, rest] ] +WickMeasurement /: +Dagger @ WickMeasurement[mat_?MatrixQ, rest___] := + WickMeasurement[Conjugate @ mat, rest] + +WickMeasurement /: +Times[z_, WickMeasurement[mm_, rest___]] := + WickMeasurement[z * mm, rest] + + WickMeasurement /: NonCommutativeQ[_WickMeasurement] = True @@ -1049,7 +1019,7 @@ ArrayShort[WickMeasurement[mm_?MatrixQ, rest___], opts___?OptionQ] := WickMeasurement[k_Integer][in:WickState[{fac_?NumericQ, cvr_?MatrixQ}, rest___]] := Module[ {aa, bb, new}, {aa, bb} = WickMeasurementKernel[k, Length[cvr]/2]; - new = theWickMeasurement[aa, bb, cvr]; + new = theWickMeasurement[{aa, bb}, cvr]; $MeasurementOut[k] = $MeasurementOut[0]; KeyDrop[$MeasurementOut, 0]; WickState[{1, new}, rest] @@ -1067,7 +1037,7 @@ WickMeasurement[mat_?MatrixQ][in:WickState[{fac_?NumericQ, cvr_?MatrixQ}, rest__ { vv = First[mat], aa, bb, new }, {aa, bb} = WickMeasurementKernel[N @ vv]; - new = theWickMeasurement[aa, bb, cvr]; + new = theWickMeasurement[{aa, bb}, cvr]; $MeasurementOut[vv] = $MeasurementOut[0]; KeyDrop[$MeasurementOut, 0]; WickState[{1, new}, rest] @@ -1084,12 +1054,12 @@ WickMeasurement[mat_?MatrixQ][in_WickState] := (* NOTE: The dressed fermion modes associated with different rows in matrix mat do not have to be mutually orthogonal. Only required is that each row gives a proper dressed fermion mode, independently of other rows. *) -theWickMeasurement[aa_?MatrixQ, bb_?MatrixQ, cvr_?MatrixQ] := Module[ +theWickMeasurement[{aa_?MatrixQ, bb_?MatrixQ}, cvr_?MatrixQ] := Module[ { dd = -aa, id, mm, pp }, id = One[Dimensions @ cvr]; mm = id + dd.cvr; - pp = Quiet[Sqrt[Det @ mm]/2, {Det::luc}]; + pp = Quiet[Sqrt[Det @ mm]/2, {Det::luc}]; (* prefactor = 1/2 *) If[ RandomReal[] < Re[pp], (* Re[...] to quickly handle numerical errors. *) $MeasurementOut[0] = 1, $MeasurementOut[0] = 0; @@ -1127,10 +1097,10 @@ WickMeasurementOdds[mat_?MatrixQ][cvr_?MatrixQ] := Module[ theWickMeasurementOdds[vec_?VectorQ][cvr_?MatrixQ] := Module[ { aa, bb, dd, mm, pp }, {aa, bb} = WickMeasurementKernel[N @ vec]; - dd = -aa; - mm = One[Dimensions @ cvr] + dd.cvr; - pp = Quiet[Sqrt[Det @ mm]/2, {Det::luc}]; - {1- pp, pp} + mm = One[Dimensions @ cvr] - aa.cvr; (* D = -A *) + pp = Quiet[Sqrt[Det @ mm]/2, {Det::luc}]; (* prefactor = 1/2 *) + pp = Ramp[Re @ pp]; (* Ramp and Re to quickly handle numerical errors. *) + {Ramp[1 - pp], pp} ] (**** ****) @@ -1156,15 +1126,11 @@ WickMeasurementKernel[k_Integer, n_Integer] := { {2n, 2n} ] } +(* NOTE: This is intended for WickMeasurement (rather than WickMap), and returns only matrices A and B (but not D). *) -WickMeasurementKernel[kk:{___Integer}, n_Integer] := - Map[WickMeasurementKernel[#, n]&, kk] - - -(* For measurement outcome = 1 *) WickMeasurementKernel[vec_?VectorQ] := Module[ { n = Length[vec]/2, - xx, yy, aa, bb, trs }, + xx, yy, aa, bb, nn, trs }, xx = Re[N @ vec]; (* Notice N[...]; otherwise, it may take very long *) yy = Im[N @ vec]; (* verify the dressed fermion mode *) @@ -1175,11 +1141,11 @@ WickMeasurementKernel[vec_?VectorQ] := Module[ (* The Cartan-Dieudonné theorem *) trs = HouseholderMatrix[xx]; trs = HouseholderMatrix[trs.yy, 2] . trs; - {aa, bb} = WickMeasurementKernel[1, n]; - {Transpose[trs].aa.trs, Transpose[trs].bb.trs} + {aa, bb} = WickMeasurementKernel[1, n]; (* nn is ignored *) + { Transpose[trs].aa.trs, + Transpose[trs].bb.trs } ] - -WickMeasurementKernel[mat_?MatrixQ] := Map[WickMeasurementKernel, mat] +(* NOTE: This is intended for WickMeasurement (rather than WickMap), and does NOT calculate the NormSquare of vec for an efficient simulation of the measurement process. Furthermore, it returns only matrices A and B (but not D). *) (**** ****) @@ -1193,84 +1159,86 @@ RandomWickMeasurement[n_Integer] := WickMeasurement @ RandomNambuMeasurement[n] -(**** ****) +(**** ****) -WickMap::usage = "WickMap[mat] or WickMap[mat, True] represents a projective quantum operation \[Rho] \[RightTeeArrow] Sum[p[i]**\[Rho]**p[i], {i, m}] + Sum[(1-p[i])**\[Rho]**(1-p[i]), {j, m}], where m is the number of rows in mat, p[i]:=Dagger[b[i]]**b[i] are projection operators, and b[i]:=Sum[mat[[i,j]] c[j], {j, 2n}] are the dressed Dirac fermion modes consisting of n bare Majorana fermion modes c[j].\nWickMap[mat, False] represents \[Rho] \[RightTeeArrow] Sum[p[i]**\[Rho]**p[i], {i, m}]." +WickMapKernel::usage = "WickMapKernel[type, mat] returns {A, B, D, nrm}, where A, B and D are 2n\[Times]2n real matrices and nrm is a list of prefactors. The 4n\[Times]4n matrix {{A, B}, {-Transpose[B], A}} gives the Gaussian kernel of the Grassmann representation of the Gaussian map \[Rho] \[RightTeeArrow] Sum[L[k]**\[Rho]**Dagger[L[k]], {k, m}]. For type=1, L[k] are linear superpositin of Majorana operators. For type=2, L[k] are bilinear combination of Majorana operators." -WickMap::null = "The quantum operation returns the null state." - -(* alias *) -WickMap[jmp_WickJump, ___][in_WickState] = jmp[in] +(* L[k] := b[k] *) +WickMapKernel[1, mat_?MatrixQ] := Module[ + {aa, bb, nn}, + {aa, bb, nn} = Transpose @ Map[WickFlopKernel, mat]; + aa = SparseArray[aa]; + {aa, SparseArray @ bb, aa, nn} +] +(* L[k] := Dagger[a[k]]**a[k] *) +WickMapKernel[2, kk:{___Integer}, n_Integer] := Module[ + {aa, bb}, + {aa, bb} = Transpose @ Map[WickMeasurementKernel[#, n]&, kk]; + aa = SparseArray[aa]; + {aa, SparseArray @ bb, -aa, ConstantArray[1/2, Length @ kk]} +] -WickMap[kk:{___Integer}] := WickMap[kk, True] +(* L[k] := Dagger[b[k]]**b[k], b[i] := Sum[mat[[i, j]]**c[j], {j, 2n}] *) +WickMapKernel[2, mat_?MatrixQ] := Module[ + { nn = Map[NormSquare, mat], + aa, bb }, + {aa, bb} = Transpose @ Map[WickMeasurementKernel, mat]; + aa = SparseArray[aa]; + {aa, SparseArray @ bb, -aa, 2*nn^2} + (* Notice the power of 2 (rathern than just nn) and the factor of 2. *) +] +(* NOTE: This is intended for WickMap (rather than WickMeasurement), and returns all matrices A, B, and D as well as the squared norms of rows of matrix mat. *) -WickMap[WickMeasurement[k_Integer, ___], flag___] := - WickMap[{k}, flag] +(**** ****) -WickMap[WickMeasurement[kk:{___Integer}, ___], flag___] := - WickMap[kk, flag] -WickMap[kk:{___Integer}, flag:(True|False)][ - WickState[{_?NumericQ, cvr_?MatrixQ}, rest___] -] := WickState[{1, WickMap[kk, flag] @ cvr}, rest] +(**** ****) -WickMap[kk:{___Integer}, flag:(True|False)][cvr_?MatrixQ] := Module[ - {aa, bb }, - {aa, bb} = Transpose @ WickMeasurementKernel[kk, Length[cvr]/2]; - theWickMap[aa, bb, cvr, flag] -] +WickMap::usage = "WickMap[mat] or WickMap[mat, True] represents a projective quantum operation \[Rho] \[RightTeeArrow] Sum[p[i]**\[Rho]**p[i], {i, m}] + Sum[(1-p[i])**\[Rho]**(1-p[i]), {j, m}], where m is the number of rows in mat, p[i]:=Dagger[b[i]]**b[i] are projection operators, and b[i]:=Sum[mat[[i,j]] c[j], {j, 2n}] are the dressed Dirac fermion modes consisting of n bare Majorana fermion modes c[j].\nWickMap[mat, False] represents \[Rho] \[RightTeeArrow] Sum[p[i]**\[Rho]**p[i], {i, m}]." +WickMap::null = "The quantum operation returns the null state." -WickMap[mat_?MatrixQ] := WickMap[mat, True] +WickMap /: +MakeBoxes[map:WickMap[{aa_?ArrayQ, bb_?ArrayQ, dd_?ArrayQ, nn_?VectorQ}, flag_], fmt_] := + BoxForm`ArrangeSummaryBox[ + WickMap, msr, None, + { BoxForm`SummaryItem @ { "Bare modes: ", Length[First @ aa]/2 }, + BoxForm`SummaryItem @ { "Kraus elements: ", Length[nn] }, + BoxForm`SummaryItem @ { "Completion: ", flag } + }, + { BoxForm`SummaryItem @ { "Block A: ", ArrayShort /@ aa }, + BoxForm`SummaryItem @ { "Block B: ", ArrayShort /@ bb }, + BoxForm`SummaryItem @ { "Block D: ", ArrayShort /@ dd } + }, + fmt, + "Interpretable" -> Automatic + ] -WickMap[WickMeasurement[mat_?MatrixQ, ___], flag___] := - WickMap[mat, flag] +(* conversion *) +WickMap[jmp_WickJump, ___] := + WickMap[WickMapKernel[1, First @ jmp], False] -WickMap[mat_?MatrixQ, flag:(True|False)][ - WickState[{_?NumericQ, cvr_?MatrixQ}, rest___] -] := WickState[{1, WickMap[mat, flag] @ cvr}, rest] +(* conversion *) +WickMap[msr_WickMeasurement, flag___] := + WickMap[WickMapKernel[2, First @ msr], flag] -WickMap[mat_?MatrixQ, flag:(True|False)][cvr_?MatrixQ] := Module[ - {aa, bb }, - {aa, bb} = Transpose @ WickMeasurementKernel[mat]; - theWickMap[aa, bb, cvr, flag] -] +(* default flag *) +WickMap[spec_] = WickMap[spec, False] -theWickMap[aa_?ArrayQ, bb_?ArrayQ, cvr_?MatrixQ, True] := Module[ - { m = Length[aa], - k, an, bn, dd, mm, id, pp }, - id = ConstantArray[One[Dimensions @ cvr], Length @ aa]; - dd = -aa; - mm = id + dd.cvr; - Quiet[pp = Sqrt[Det /@ mm]/2, Det::luc]; - pp = Ramp[Re @ pp]; (* Ramp and Re to quickly handle numerical errors. *) - pp = Join[Ramp[1 - pp], pp]; - k = RandomChoice[pp -> Range[2m]]; - If[ k <= m, - (* projection by a**Dagger[a] *) - $WickMapOut = {k, 0}; - an = -aa[[k]]; - bn = bb[[k]], - (* projection by Dagger[a]**a *) - k -= m; - $WickMapOut = {k, 1}; - an = aa[[k]]; - bn = bb[[k]] - ]; - dd = -an; - mm = One[Dimensions @ dd] + dd.cvr; - an + bn.cvr.Inverse[mm].Transpose[bn] -] +(* On WickState *) +WickMap[spec_, flag_][WickState[{_?NumericQ, cvr_?MatrixQ}, rest___]] := + WickState[{1, WickMap[spec, flag] @ cvr}, rest] -theWickMap[aa_?ArrayQ, bb_?ArrayQ, cvr_?MatrixQ, False] := Module[ - { m = Length[aa], - k, dd, mm, id, pp }, +(* On the covariance matrix *) +WickMap[{aa_?ArrayQ, bb_?ArrayQ, dd_?ArrayQ, nn_?VectorQ}, False][cvr_?MatrixQ] := Module[ + { m = Length[nn], + mm, id, pp, k }, id = ConstantArray[One[Dimensions @ cvr], m]; - dd = -aa; mm = id + dd.cvr; - Quiet[pp = Sqrt[Det /@ mm]/2, Det::luc]; - pp = Ramp[Re @ pp]; (* Ramp and Re to quickly handle numerical errors. *) + pp = Quiet[Sqrt[Det /@ mm], Det::luc]; + pp = nn*Ramp[Re @ pp]; + (* NOTE: Ramp and Re to quickly handle numerical errors. *) If[ ArrayZeroQ[pp], Message[WickMap::null]; $WickMapOut = Indeterminate; @@ -1281,6 +1249,34 @@ theWickMap[aa_?ArrayQ, bb_?ArrayQ, cvr_?MatrixQ, False] := Module[ aa[[k]] + bb[[k]].cvr.Inverse[mm[[k]]].Transpose[bb[[k]]] ] +(* On the covariance matrix *) +WickMap[{aa_?ArrayQ, bb_?ArrayQ, dd_?ArrayQ, nn_?VectorQ}, True][cvr_?MatrixQ] := Module[ + { m = Length[nn], + ak, bk, dk, mm, id, pp, k }, + id = ConstantArray[One[Dimensions @ cvr], m]; + mm = id + dd.cvr; + pp = Quiet[Sqrt[Det /@ mm]/2, Det::luc]; + (* NOTE: A factor of 1/2 because this case is supposed to be the measurement of a fermion mode. *) + pp = Ramp[Re @ pp]; + pp = Join[nn*Ramp[1-pp], nn*pp]; + (* NOTE: More precisely, here needs to be an additional factor 2 because the prefactors nn from WickMapKernel[2, ...] already contains the factor of 1/2. It is ignored because it is a global factor anyway. *) + k = RandomChoice[pp -> Range[2m]]; + If[ k <= m, + (* projection by a**Dagger[a] *) + $WickMapOut = {k, 0}; + ak = -aa[[k]]; + dk = -dd[[k]], + (* projection by Dagger[a]**a *) + k -= m; + $WickMapOut = {k, 1}; + ak = aa[[k]]; + dk = dd[[k]]; + ]; + bk = bb[[k]]; + mm = One[Dimensions @ dk] + dk.cvr; + ak + bk.cvr.Inverse[mm].Transpose[bk] +] + (**** ****) @@ -1288,47 +1284,46 @@ theWickMap[aa_?ArrayQ, bb_?ArrayQ, cvr_?MatrixQ, False] := Module[ WickMapOdds::usage = "WickMapOdds[mat][in] returns the probabilities for the projective process \[Rho] \[RightTeeArrow] p[i]**\[Rho]**p[i], where p[i]:=Dagger[b[i]]**b[i] and b[i]:=Sum[mat[[[i,j]] c[j], {j, 2n}] are the dressed Dirac fermion modes consisting of bare Majorana fermion modes c[j]." -WickMapOdds[kk:{___Integer}] := WickMapOdds[kk, True] - -WickMapOdds[WickMeasurement[k_Integer, ___], flag___] := - WickMapOdds[{k}, flag] - -WickMapOdds[WickMeasurement[kk:{___Integer}, ___], flag___] := - WickMapOdds[kk, flag] - -WickMapOdds[kk:{___Integer}, flag:(True|False)][in_WickState] := - WickMapOdds[kk, flag][ in[[1, 2]] ] +(* conversion *) +WickMapOdds[jmp_WickJump, ___] := + WickMapOdds[WickMapKernel[1, First @ jmp], False] -WickMapOdds[kk:{___Integer}, flag:(True|False)][cvr_?MatrixQ] := Module[ - {aa, bb}, - {aa, bb} = Transpose @ WickMeasurementKernel[kk, Length[cvr]/2]; - theWickMapOdds[aa, bb, cvr, flag] -] +(* conversion *) +WickMapOdds[WickMeasurement[mat_?MatrixQ, ___], flag___] := + WickMapOdds[WickMapKernel[2, mat], flag] +(* default flag *) +WickMapOdds[spec_] = WickMapOdds[spec, False] -WickMapOdds[mat_?MatrixQ] := WickMapOdds[mat, True] +(* canonicalize *) +WickMapOdds[{_?ArrayQ, _?ArrayQ, dd_?ArrayQ, nn_?VectorQ}, flag_] := + WickMapOdds[{dd, nn}, flag] -WickMapOdds[WickMeasurement[mat_?MatrixQ, ___], rest___] := - WickMapOdds[mat, rest] +(* On WickState *) +WickMapOdds[WickMeasurement[kk:{__Integer}, ___], flag_][in_WickState] := + WickMapOdds[WickMapKernel[2, kk, FermionCount @ in], flag][in] -WickMapOdds[mat_?MatrixQ, flag:(True|False)][in_WickState] := - WickMapOdds[mat, flag][ in[[1, 2]] ] +(* On WickState *) +WickMapOdds[spec_, flag_][WickState[{_?NumericQ, cvr_?MatrixQ}, rest___]] := + WickMapOdds[spec, flag][cvr] -WickMapOdds[mat_?MatrixQ, flag:(True|False)][cvr_?MatrixQ] := Module[ - {aa, bb}, - {aa, bb} = Transpose @ WickMeasurementKernel[mat]; - theWickMapOdds[aa, bb, cvr, flag] +(* On covariance matrix *) +WickMapOdds[{dd_?ArrayQ, nn_?VectorQ}, False][cvr_?MatrixQ] := Module[ + { mm, id, pp }, + id = ConstantArray[One[Dimensions @ cvr], Length @ nn]; + mm = id + dd.cvr; + pp = Quiet[Sqrt[Det /@ mm], Det::luc]; + pp = nn*Ramp[Re @ pp]; + Normalize[pp, Norm[#, 1]&] ] - -theWickMapOdds[aa_?ArrayQ, bb_?ArrayQ, cvr_?MatrixQ, flag:(True|False)] := Module[ - { dd = -aa, - mm, id, pp }, - id = ConstantArray[One[Dimensions @ cvr], Length @ aa]; +WickMapOdds[{dd_?ArrayQ, nn_?VectorQ}, True][cvr_?MatrixQ] := Module[ + { mm, id, pp }, + id = ConstantArray[One[Dimensions @ cvr], Length @ nn]; mm = id + dd.cvr; pp = Quiet[Sqrt[Det /@ mm]/2, Det::luc]; pp = Ramp[Re @ pp]; - pp = If[flag, Join[Ramp[1-pp], pp], pp]; + pp = Join[nn*Ramp[1-pp], nn*pp]; Normalize[pp, Norm[#, 1]&] ] @@ -1717,17 +1712,40 @@ MakeBoxes[op:WickNonunitary[{ham_?MatrixQ, dmp_?MatrixQ, gmm_?NumericQ}, rest___ "Interpretable" -> Automatic ] -(* conversion *) -WickNonunitary[{ham_NambuHermitian, dmp_NambuHermitian, gmm_}, rest___] := - WickNonunitary[{WickHermitian @ ham, WickHermitian @ dmp, gmm}, rest] +(* canonicalization *) +WickNonunitary[{ham_NambuHermitian, more__}, rest___] := + WickNonunitary[{First @ WickHermitian @ ham, more}, rest] (* CONVENTION: (1/2) (a^\dag, a) H (a, a^\dag) = (i/4) c A c. *) (* canonicalization *) -WickNonunitary[{ham_WickHermitian, dmp_WickHermitian, gmm_}, rest___] := - WickNonunitary[{First @ ham, First @ dmp, gmm}, rest] +WickNonunitary[{ham_WickHermitian, more__}, rest___] := + WickNonunitary[{First @ ham, more}, rest] + +(* canonicalization *) +WickNonunitary[{ham_, dmp_NambuHermitian, gmm___}, rest___] := + WickNonunitary[{ham, First @ WickHermitian @ dmp, gmm}, rest] +(* CONVENTION: (1/2) (a^\dag, a) H (a, a^\dag) = (i/4) c A c. *) + +(* canonicalization *) +WickNonunitary[{ham_, dmp_WickHermitian, gmm___}, rest___] := + WickNonunitary[{ham, First @ dmp, gmm}, rest] + +(* conversion *) +WickNonunitary[{ham_?MatrixQ, WickMeasurement[kk:{__Integer}, ___]}, rest___] := Module[ + { msr = One[Dimensions @ ham] }, + msr = WickMeasurement[NambuMeasurement @ msr[[kk]]]; + WickNonunitary[{ham, msr}, rest] +] + +(* conversion *) +WickNonunitary[{ham_, jmp:(_WickJump|_WickMeasurement)}, rest___] := Module[ + {dmp, gmm}, + {dmp, gmm} = WickDampingOperator[jmp]; + WickNonunitary[{ham, dmp, gmm}, rest] +] (* shortcut *) -WickNonunitary[{ham_, dmp_}, rest___] := +WickNonunitary[{ham_?MatrixQ, dmp_?MatrixQ}, rest___] := WickNonunitary[{ham, dmp, 0}, rest] WickNonunitary /: @@ -1849,7 +1867,11 @@ WickDampingOperator[WickMeasurement[msr_?MatrixQ, ___]] := Module[ (**** ****) -WickSimulate::usage = "WickSimulate[in, ham, jmp, {nt, dt}] solves the quantum master equation for a non-interacting dissipative fermionic many-body system by using the Monte Carlo simulation method (alos known as the quantum jump approach or quantum trajectory method). The model is specified by the single-particle Hamiltonian ham in the WickHermitian form and the quantum jump operators are specified by jmp in the WickJump form. The simulation starts from the initial state IN in the WickState at time 0 and goes nt time steps of size dt." +$WickMinorSteps::usage = "$WickMinorSteps is a parameter that controls the behavior of WickSimulate by setting the number of minor steps for the non-unitary gate to make between major steps of update the quantum state." + +$WickMinorSteps = 10; + +WickSimulate::usage = "WickSimulate[in, ham, jmp, {\[Tau], dt}] solves the quantum master equation for a non-interacting dissipative fermionic many-body system by using the Monte Carlo simulation method (alos known as the quantum jump approach or quantum trajectory method). The model is specified by the single-particle Hamiltonian ham in the WickHermitian form and the quantum jump operators are specified by jmp in the WickJump form. The simulation starts from the initial state IN in the WickState at time 0 and runs to time \[Tau] in steps of size dt." WickSimulate::ham = "The Hamiltonian matrix `` needs to be numeric." @@ -1871,22 +1893,21 @@ WickSimulate[ in_WickState, ham_WickHermitian, jmp:(_WickJump | _WickMeasurement), - {nT_Integer, dt_}, + {tau_?NumericQ, dt_?NumericQ}, opts:OptionsPattern[] ] := Module[ - { n = OptionValue["Samples"], + { ns = OptionValue["Samples"], progress = 0, - dmp, gmm, non, map, data, more }, + non, map, data, more }, - {dmp, gmm} = WickDampingOperator[jmp]; - non = WickNonunitary[{ham, dmp, gmm}]; + non = WickNonunitary[{ham, jmp}]; map = WickMap[jmp, False]; PrintTemporary[ProgressIndicator @ Dynamic @ progress]; data = Table[ - progress = k / N[n]; - theWickSimulate[in, non, map, {nT, dt}], - {k, n} + progress = k / N[ns]; + theWickSimulate[in, non, map, {tau, dt}], + {k, ns} ]; If[ OptionValue["SaveData"], @@ -1899,29 +1920,26 @@ WickSimulate[ False ] -theWickSimulate[in_WickState, non_WickNonunitary, map_WickMap, {nT_Integer, dt_}] := +theWickSimulate[in_WickState, non_WickNonunitary, map_WickMap, {tau_, dt_}] := Module[ - { n = FermionCount[non], + { t = dt, res = {in}, new = in, - out, prb, t }, - t = 1; - While[ t <= nT, + out, prb }, + While[ t <= tau, prb = RandomReal[]; - (* non-unitary evolution *) - out = nonUnitaryEvolution[non, new, {dt, dt/10}]; + out = nonUnitaryEvolution[non, new, {dt, dt/$WickMinorSteps}]; If[ prb < NormSquare[out], new = Normalize @ out; AppendTo[res, new]; - t += 1; + t += dt; Continue[] ]; - (* quantum jumps *) new = map[new]; AppendTo[res, new]; - t += 1; + t += dt; ]; Return[res] ] @@ -1959,31 +1977,39 @@ WickMonitor[in_WickState, ham_?NambuMatrixQ, rest___] := WickMonitor[ in_WickState, ham_WickHermitian, - {nT_Integer, dt_?NumericQ}, + {tau_?NumericQ, dt_?NumericQ}, opts___?OptionQ -] := WickMonitor[in, ham, - WickMeasurement[Range @ FermionCount @ in], - {nT, dt}, - opts +] := Module[ + { n = FermionCount[in], + map }, + map = WickMap[WickMapKernel[2, Range @ n, n], True]; + WickMonitor[in, ham, map, {tau, dt}, opts] ] WickMonitor[ in_WickState, ham_WickHermitian, msr_WickMeasurement, - {nT_Integer, dt_?NumericQ}, + {tau_?NumericQ, dt_?NumericQ}, + opts:OptionsPattern[] +] := WickMonitor[in, ham, WickMap[msr, True], {tau, dt}, opts] + +WickMonitor[ + in_WickState, + ham_WickHermitian, + map_WickMap, + {tau_?NumericQ, dt_?NumericQ}, opts:OptionsPattern[] ] := Module[ { n = OptionValue["Samples"], progress = 0, - map = WickMap[msr], uni, data, more }, uni = WickUnitary @ MatrixExp[N @ First[ham]*dt]; PrintTemporary[ProgressIndicator @ Dynamic @ progress]; data = Table[ progress = k / N[n]; - theWickMonitor[in, uni, map, {nT, dt}], + theWickMonitor[in, uni, map, {tau, dt}], {k, n} ]; @@ -2001,27 +2027,27 @@ theWickMonitor[ in_WickState, uni_WickUnitary, map_WickMap, - {nT_Integer, dt_?NumericQ} + {tau_?NumericQ, dt_?NumericQ} ] := Module[ - { n = Length[First @ map], (* the number of projective measurements *) - t = 1, + { t = dt, res = {in}, new = in, - nrm }, - nrm = Exp[-n*dt]; (* squared norm *) - (* NOTE: Effectively, the input WickMeasurement is normalized. *) - While[ t <= nT, + gmm }, + gmm = 2 * Total @ map[[1, 4]]; + (* NOTE: Here, the additional factor 2 is required because the prefactors map[[1, 4]] from WickMapKernel[2, ...] already contains the factor of 1/2 associated with projection Dagger[b]**b. *) + gmm = Exp[-gmm*dt]; + While[ t <= tau, (* non-unitary (yet practically unitary) evolution *) - If[ RandomReal[] < nrm, + If[ RandomReal[] < gmm, new = uni[new]; AppendTo[res, new]; - t += 1; + t += dt; Continue[] ]; (* quantum jumps *) new = map[new]; AppendTo[res, new]; - t += 1; + t += dt; ]; Return[res] ] @@ -2185,6 +2211,18 @@ MakeBoxes[msr:NambuMeasurement[mat_?MatrixQ, ___], fmt_] := Module[ ] ] +NambuMeasurement /: +Dagger @ NambuMeasurement[mat_?MatrixQ, rest___] := NambuMeasurement[ + ArrayFlatten[ + Reverse /@ Conjugate @ PartitionInto[mat, {1, 2}] + ], + rest +] + +NambuMeasurement /: +Times[z_, NambuMeasurement[mm_, rest___]] := + NambuMeasurement[z * mm, rest] + NambuMeasurement /: Normalize[NambuMeasurement[mat_?MatrixQ, rest___], ___] := NambuMeasurement[Normalize /@ mat, rest] diff --git a/Q3/PacletInfo.wl b/Q3/PacletInfo.wl index 1d8d4090a..4b4842fb4 100644 --- a/Q3/PacletInfo.wl +++ b/Q3/PacletInfo.wl @@ -1,6 +1,6 @@ Paclet[ "Name" -> "Q3", - "Version" -> "3.7.7", + "Version" -> "3.8.0", "WolframVersion" -> "12.3+", "Updating" -> Automatic, "Loading" -> "Startup", diff --git a/RELEASES.md b/RELEASES.md index b00f1676f..165ae68ac 100644 --- a/RELEASES.md +++ b/RELEASES.md @@ -1,5 +1,11 @@ # Release Notes +## 3.8.0 + +- Significantly improved computational speed of WickMonitor and WickSimulate. +- Changes: The input arguments syntax of WickMonitor and WickSimulate +- New: $WickMinorStep + ## 3.7.7 - Improved: WickSimulate supports quadratic projection operators as quantum jump operators through WickMeasurement.