Merge branch 'master' of https://github.com/QuantumUtils/quantum-utils-mathematica

Author: Christopher J. Wood

doc/api-doc/GRAPE.nb

@@ -72,7 +72,7 @@
 		ObservableListQ,FunctionListQ,
 		DistributionQ
 	},
-	$Usages
+	$QSimUsages
 ];
 
 
@@ -91,7 +91,7 @@
 		StepSize,PollingInterval,InitialState,SimulationOutput,SequenceMode,NumericEvaluation,ForceSuperoperator,
 		TimeVector,Superoperators,Unitaries,States,Functions,Observables
 	},
-	$Usages
+	$QSimUsages
 ];
 
 
@@ -112,7 +112,7 @@
 		GetPulseShapeMatrix,
 		GetStepSize,GetPollingInterval,DivideEvenly,MakeMultipleOf
 	},
-	$Usages
+	$QSimUsages
 ];
 
 
@@ -121,7 +121,7 @@
 
 
 Unprotect[PulseSim];
-AssignUsage[PulseSim,$Usages];
+AssignUsage[PulseSim,$QSimUsages];
 
 
 PulseSim::badControlDim = "The internal Hamiltonian dimension, `1`, is neither equal to nor a multiple of (one of) the control Hamiltonian dimension(s), `2`.";
@@ -132,7 +132,7 @@
 
 
 Unprotect[DrawSequence];
-AssignUsage[DrawSequence,$Usages];
+AssignUsage[DrawSequence,$QSimUsages];
 
 
 (* ::Section:: *)
@@ -909,7 +909,7 @@
 (*We give each kind of pulse its own width weight for aesthetics.*)
 
 
-DrawSequence[seq_?PulseSequenceQ]:=
+DrawSequence[seq_?PulseSequenceQ,opt:OptionsPattern[Graphics]]:=
 	Module[{shapedFrac=0.3,uFrac=0.07,sFrac=0.07,driftFrac=0.63,width=500,height=100,widths},
 		widths=shapedFrac*(ShapedPulseQ/@seq)/.{True->1,False->0};
 		widths=widths+uFrac*(UnitaryPulseQ/@seq)/.{True->1,False->0};
@@ -921,7 +921,7 @@
 			Arrow[{{0,0},{width,0}},-width/20],
 			Text["t",{width+width/15,0}],
 			Table[DrawPulse[seq[[k]],widths[[k]],height*0.8,Total[Take[widths,k]]-widths[[k]]],{k,Length[seq]}]
-		}]
+		},opt]
 	]
 
 

doc/api-doc/Perturbation.nb

@@ -36,7 +36,7 @@
 $QuantumChannelUsages = LoadUsages[FileNameJoin[{$QUDocumentationPath, "api-doc", "QuantumChannel.nb"}]];
 
 
-(* ::Section::Closed:: *)
+(* ::Section:: *)
 (*Usage Declarations*)
 
 
@@ -66,10 +66,10 @@
 
 
 (* ::Subsection::Closed:: *)
-(*Channel Functions*)
+(*Channel Functions and Metrics*)
 
 
-Unprotect[GateFidelity,AverageGateFidelity,EntanglementFidelity,ChannelVolume, Unitarity];
+Unprotect[GateFidelity,AverageGateFidelity,EntanglementFidelity,ChannelVolume,Unitarity,DiamondNormDistance];
 
 
 AssignUsage[ProcessFidelity,$QuantumChannelUsages];
@@ -84,12 +84,13 @@
 (*Predicates*)
 
 
-Unprotect[CompletelyPositiveQ,TracePreservingQ,HermitianPreservingQ,UnitalQ,PauliChannelQ];
+Unprotect[CompletelyPositiveQ,TracePreservingQ,HermitianPreservingQ,UnitaryQ,UnitalQ,PauliChannelQ];
 
 
 AssignUsage[CompletelyPositiveQ,$QuantumChannelUsages];
 AssignUsage[TracePreservingQ,$QuantumChannelUsages];
 AssignUsage[HermitianPreservingQ,$QuantumChannelUsages];
+AssignUsage[UnitaryQ,$QuantumChannelUsages];
 AssignUsage[UnitalQ,$QuantumChannelUsages];
 AssignUsage[PauliChannelQ,$QuantumChannelUsages];
 
@@ -109,7 +110,7 @@
 AssignUsage[FunctionChannel,$QuantumChannelUsages];
 
 
-(* ::Subsection:: *)
+(* ::Subsection::Closed:: *)
 (*Error Messages*)
 
 
@@ -148,7 +149,7 @@
 Begin["`Private`"];
 
 
-(* ::Subsection:: *)
+(* ::Subsection::Closed:: *)
 (*Predicates*)
 
 
@@ -163,7 +164,7 @@
 KrausPairQ[set_]:=And[First[Dimensions[set]]===2,AllQ[KrausSingleQ,set]]
 KrausSingleQ[set_]:=AllQ[MatrixQ,set]
 KrausQ[set_]:=Or[KrausPairQ[set],KrausSingleQ[set]];
-KrausUnitaryQ[set_]:=And[KrausSingleQ[set],Length[set]===1]
+KrausUnitaryQ[set_]:=And[KrausSingleQ[set],Length[set]===1,UnitaryMatrixQ[First@set,Tolerance->10^(-12)]]
 
 
 StinespringPairQ[set_]:=And[Length[set]==2,AllQ[MatrixQ,set]];
@@ -214,8 +215,8 @@
 		choi=First[Choi[chan]],
 		assum=And[$Assumptions,OptionValue[Assumptions]],
 		eigen,boole},
-	If[NumericQ[choi],	
-		PositiveSemidefiniteMatrixQ[choi],
+	If[AllQ[NumericQ,Flatten[choi]],	
+		PositiveSemidefiniteMatrixQ[choi,Tolerance->10^(-12)],
 		eigen=Simplify[Eigenvalues[choi],Assumptions->assum];
 		boole=FullSimplify[And@@NonNegative[eigen],Assumptions->assum];
 		Which[
@@ -238,17 +239,32 @@
 
 TracePreservingQ[chan_QuantumChannel,opts:OptionsPattern[CompletelyPositiveQ]]:=
 	With[{
-	op=PartialTr[
-			First[Choi[chan,Basis->"Col"]],
-			{InputDim[chan],OutputDim[chan]},{2}],
-	assum=And[$Assumptions,OptionValue[Assumptions]],
-	id=IdentityMatrix[InputDim[chan]]},
-		AllMatchQ[0,
+		op=PartialTr[First[Choi[chan,Basis->"Col"]],{InputDim[chan],OutputDim[chan]},{2}],
+		assum=And[$Assumptions,OptionValue[Assumptions]],
+		id=IdentityMatrix[InputDim[chan]]
+	},
+		AllQ[FullSimplify[#*#\[Conjugate],Assumptions->assum]<10.^-12&,
 			FullSimplify[Flatten[op-id],Assumptions->assum]
 		]		
 	]
 
 
+
+UnitaryQ[chan_QuantumChannel,opts:OptionsPattern[CompletelyPositiveQ]]:=Or[
+	(ChannelRep/.ChannelParameters[chan])===Unitary,
+	And[
+		TracePreservingQ[chan,Assumptions->OptionValue[Assumptions]],
+		Module[{unitarity=FullSimplify[Unitarity[chan],And[$Assumptions,OptionValue[Assumptions]]]},
+			If[NumericQ[unitarity],
+				Abs[unitarity-1]<10^-12,
+				TrueQ[unitarity==1]
+			]
+		],
+		CompletelyPositiveQ[chan,Assumptions->OptionValue[Assumptions]]
+	]
+];
+
+
 UnitalQ[chan_QuantumChannel,opts:OptionsPattern[CompletelyPositiveQ]]:=
 	With[{
 	op=PartialTr[
@@ -434,7 +450,7 @@
 	]]
 
 
-(* ::Subsection:: *)
+(* ::Subsection::Closed:: *)
 (*Transforming Representations*)
 
 
@@ -681,7 +697,7 @@
 TransformChannel[Kraus->Unitary,op_,opts:OptionsPattern[TransformChannel]]:=First[op]
 
 
-(* ::Subsubsection:: *)
+(* ::Subsubsection::Closed:: *)
 (*From Choi*)
 
 
@@ -1018,7 +1034,7 @@
 
 
 (* ::Subsection::Closed:: *)
-(*Fidelity and Volume*)
+(*Channel Functions and Metrics*)
 
 
 ChannelVolume[chan_QuantumChannel]:=Det[MatrixPower[Part[Super[chan,Basis->"Pauli"],1,2;;All,2;;All],1/2]];
@@ -1062,10 +1078,27 @@
 
 Unitarity[chan_QuantumChannel] :=
 	With[{
-		Eu = First[Super[chan, Basis -> "Pauli"]][[2;;, 2;;]]
+		Eu = First[Super[chan, Basis -> "Weyl"[InputDim[chan]]]][[2;;, 2;;]]
 	},
-	Tr[Eu\[HermitianConjugate].Eu] / (First @ Dimensions @ Eu)
+	Chop[Tr[Eu\[HermitianConjugate].Eu]] / (First @ Dimensions @ Eu)
+]
+
+
+DiamondNormDistance[U_?SquareMatrixQ]:=Module[{eiglist, minangle},
+	eiglist = Sort[Arg[Eigenvalues[U]]];
+	minangle = Min[\[Pi],2\[Pi]-Max@Differences[{##, #1 + 2 \[Pi]} & @@ eiglist]];
+	2*Sin[minangle/2]
+];
+DiamondNormDistance[U_?SquareMatrixQ,V_?SquareMatrixQ]:=DiamondNormDistance[U\[ConjugateTranspose].V]
+GetFirstKraus[chan_]:=If[
+	ChannelRep[chan]===Unitary,
+	First@chan,
+	With[{K=First@Kraus@chan},
+		If[KrausSingleQ[K],First@K,First@First@K]
+	]
 ]
+DiamondNormDistance[U_QuantumChannel?UnitaryQ]:=DiamondNormDistance@GetFirstKraus[U]
+DiamondNormDistance[U_QuantumChannel?UnitaryQ,V_QuantumChannel?UnitaryQ]:=DiamondNormDistance[GetFirstKraus[U],GetFirstKraus[V]]
 
 
 (* ::Subsection::Closed:: *)
@@ -1175,8 +1208,8 @@
 
 Protect[Choi,Super,Chi,Kraus,Stinespring,Unitary,SysEnv];
 Protect[QuantumChannel,ChannelRep,InputDim,OutputDim,Basis];
-Unprotect[GateFidelity,AverageGateFidelity,EntanglementFidelity,ChannelVolume];
-Protect[CompletelyPositiveQ,TracePreservingQ,HermitianPreservingQ,UnitalQ,PauliChannelQ];
+Unprotect[GateFidelity,AverageGateFidelity,EntanglementFidelity,ChannelVolume,Unitarity,DiamondNormDistance];
+Protect[CompletelyPositiveQ,TracePreservingQ,HermitianPreservingQ,UnitaryQ,UnitalQ,PauliChannelQ];
 Unprotect[ComChannel,AComChannel,LindbladDissipator,Lindblad,PartialTrChannel,FunctionChannel];
 
 

doc/api-doc/QSim.nb

@@ -582,32 +582,42 @@
 (*Matrix Bases*)
 
 
-(* ::Subsubsection:: *)
+(* ::Subsubsection::Closed:: *)
 (*Named Bases*)
 
 
 $POBasis=(PauliMatrix/@Range[0,3]);
 $PauliBasis=(PauliMatrix/@Range[0,3])/Sqrt[2];
+$WeylBasis[d_]:=Flatten[Table[RotateLeft[DiagonalMatrix[Table[Exp[2\[Pi]*I*n*b/d],{n,0,d-1}]],a]/Sqrt[d],{a,0,d-1},{b,0,d-1}],1];
+
+
+$NamedBasis={"Pauli"->$PauliBasis,"PO"->$POBasis,"Weyl"[d_]:>$WeylBasis[d]};
 
 
-$NamedBasis={"Pauli"->$PauliBasis,"PO"->$POBasis};
+(*We need to be fancier than MemberQ because of possible dimension arguments*)
+NamedBasisMemberQ[basis_]:=(basis/.Thread[RuleDelayed[Keys[$NamedBasis],True]])===True
 
 
 CheckNamedBasis[basis_]:=
-	If[MemberQ[Keys[$NamedBasis],basis],
+	If[NamedBasisMemberQ[basis],
 		basis/.$NamedBasis,
 		basis]
 
 
 $POBasisLabels={"I","X","Y","Z"};
 $PauliBasisLabels={"I","X","Y","Z"}/Sqrt[2];
+$WeylBasisLabels[d_]:=Flatten[Table["W["<>ToString[a]<>","<>ToString[b]<>"]",{a,0,d-1},{b,0,d-1}],1]
 
 
-$NamedBasisLabels={"Pauli"->$PauliBasisLabels,"PO"->$POBasisLabels};
+$NamedBasisLabels={"Pauli"->$PauliBasisLabels,"PO"->$POBasisLabels,"Weyl"[d_]:>$WeylBasisLabels[d]};
+
+
+(*We need to be fancier than MemberQ because of possible dimension arguments*)
+NamedBasisLabelsMemberQ[basis_]:=(basis/.Thread[RuleDelayed[Keys[$NamedBasisLabels],True]])===True
 
 
 CheckNamedBasisLabels[basis_]:=
-	If[MemberQ[Keys[$NamedBasisLabels],basis],
+	If[NamedBasisLabelsMemberQ[basis],
 		basis/.$NamedBasisLabels,
 		basis]
 
@@ -711,7 +721,7 @@
 		Which[
 			basis==="Col",funcs[[1]][args],
 			basis==="Row",funcs[[2]][args],
-			MemberQ[Keys[$NamedBasis],basis],funcs[[3]][(basis/.$NamedBasis),args],
+			NamedBasisMemberQ[basis],funcs[[3]][(basis/.$NamedBasis),args],
 			True,funcs[[3]][basis,args]]]
 
 
@@ -769,7 +779,7 @@
 	Which[
 		basis==="Row",BasisMatrixCol["Row",arg],
 		ListQ[basis],BasisMatrixCol[basis,arg],
-		MemberQ[Keys[$NamedBasis],basis],BasisMatrixCol[basis/.$NamedBasis,arg],
+		NamedBasisMemberQ[basis],BasisMatrixCol[basis/.$NamedBasis,arg],
 		True,Message[BasisMatrix::input]
 	]
 BasisMatrix[Rule[basis_,"Col"],arg___]:=ConjugateTranspose@BasisMatrix[Rule["Col",basis],arg]
@@ -801,7 +811,7 @@
 
 
 BasisMatrixColList[basis_,op_]:=
-	If[MemberQ[Keys[$NamedBasis],basis],
+	If[NamedBasisMemberQ[basis],
 		BasisMatrixColList[basis/.$NamedBasis,op],
 		Message[BasisMatrix::keys]
 	]
@@ -831,8 +841,9 @@
 
 BasisTransformation[op_,Rule[basis1_,basis2_]]:=
 	BasisTransformation[
-		BasisTransformation[op,Rule[basis1,"Col"],
-		Rule["Col",basis2]]]
+		BasisTransformation[op,Rule[basis1,"Col"]],
+		Rule["Col",basis2]
+	]
 
 
 (* ::Subsection::Closed:: *)

doc/api-doc/QuantumChannel.nb

@@ -875,8 +875,8 @@
 	]]];
 
 
-(* ::Subsection:: *)
-(*Channel Functions*)
+(* ::Subsection::Closed:: *)
+(*Channel Functions and Metrics*)
 
 
 Module[{a,b,chan1,chan2},
@@ -923,6 +923,13 @@
 ];
 
 
+TestCase[$RegisteredTests, "QuantumChannel:DiamondNormDistance",
+	And[
+		Module[{\[Theta]},FullSimplify[DiamondNormDistance[Unitary[MatrixExp[-I \[Theta] {{0,1},{1,0}}/2]]]-2*Sin[\[Theta]/2],Assumptions->0<=\[Theta]<2\[Pi]]==0]
+	]
+]
+
+
 TestCase[$RegisteredTests, "QuantumChannel:Unitarity",
 	And[
 		Unitarity[
@@ -994,6 +1001,21 @@
 	]];
 
 
+TestCase[$RegisteredTests,"QuantumChannel:UnitaryQ",
+	Module[{a,b,p0,p1,p2,p3},
+	And[
+		UnitaryQ[Unitary[{{0,1},{1,0}}]],
+		UnitaryQ[Kraus[{{{Cos[a],Sin[a]},{-Sin[a],Cos[a]}}}],Assumptions->a\[Element]Reals],
+		UnitaryQ[Kraus[{{{a,b},{-b\[Conjugate],a\[Conjugate]}}}],Assumptions->Abs[a]^2+Abs[b]^2==1],
+		Not@UnitaryQ[Kraus[{{{a,b},{-b\[Conjugate],a\[Conjugate]}}}],Assumptions->Abs[a]^2+Abs[b]^2==2],
+		Not@UnitaryQ[Chi[DiagonalMatrix[{p0,p1,p2,p3}]]],
+		UnitaryQ[Chi[DiagonalMatrix[{2,0,0,0}]]],
+		UnitaryQ[Kraus[{{{-0.15655368690078914`+ 0.3430921066545964` I,-0.2348331888076826`- 0.05351542084751404` I,0.15434364097586445` -0.7761828151024415` I,0.4126091294603258` +0.05692281573291967` I},{-0.20161584271439267`+ 0.19817760822741248` I,-0.16484366732378541`- 0.4753872264482968` I,-0.3635752839999726`+ 0.43813126093787663` I,0.5287549284414077` +0.2513612431126086` I},{0.8487976714138722` +0.03598473246540806` I,-0.10339410593987132`- 0.09547646392229023` I,0.10895450613616803` -0.029258702335285096` I,0.05717734865987785` +0.49238715504781155` I},{-0.042404220777264696`- 0.23303418445576338` I,-0.6832106295507965`- 0.44971119932859627` I,-0.12711459846245918`- 0.14382980174948` I,-0.4835653853512809`- 0.06480284622646271` I}}}]],
+		Not@UnitaryQ[Kraus[{{{0.062322322567051225` +0.4499103526192444` I,-0.0030534708049662967`+ 0.7475381561426192` I,-0.36536281946601035`- 0.3184085336398186` I},{-0.7251449050775644`- 0.06243481298569527` I,0.39685356189665594` +0.36971092879610457` I,0.2807315180487294` +0.31189365989100587` I},{0.5135328388272068` -0.0157285386936368` I,-0.03753268853883381`+ 0.3815622600004384` I,0.7607430120380767` +0.10152952864202755` I}}/Sqrt[2],{{-0.3385280862506501`- 0.11148473131686024` I,-0.09839679668003078`- 0.20068656570790783` I,0.7898784700625915` +0.44621168158367813` I},{0.47420455444381676` -0.7834563570746536` I,0.11075193848722416` +0.007811711947949143` I,0.2662964187271937` -0.2794376133502603` I},{0.18364835205881913` +0.023861043414192033` I,-0.444049899273856`- 0.8605438077054051` I,-0.14114688592590158`- 0.08980830675081206` I}}/Sqrt[2]}]]
+	]]
+	];
+
+
 TestCase[$RegisteredTests,"QuantumChannel:UnitalQ",
 	And[
 		Not@UnitalQ[