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Unit_tests.m
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Unit_tests.m
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(* ::Package:: *)
(*
Copyright 2019 UniversalQCompiler (https://github.com/Q-Compiler/UniversalQCompiler)
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
(*Switch off precision warnings*)
Off[N::meprec]
Off[Floor::meprec]
Off[Eigensystem::eivec0]
(*Helper methods for tests for tests*)
isZero[x_]:=Chop[x]==0;
isZeroMatrix[mat_]:=Tr[Abs[Flatten[Chop[mat]]]]==0;
isDiagonal[m_]:=Norm[Chop[DiagonalMatrix[Diagonal[m]]-m]]==0;
isIdentity[m_]:=Norm[Chop[m-IdentityMatrix[Length[m]]]]==0;
isIdentityUpToPhase[m_]:=If[Chop[FullSimplify[Norm[m[[1,1]]]]]==0,False,
If[Chop[FullSimplify[Norm[m[[1,1]]]-1]]==0,
Chop[FullSimplify[Norm[m/(m[[1,1]])-IdentityMatrix[Length[m]]]]]==0,
False
]
];
IsEqualUptoPhaseForUnitaries[a_,b_]:=Module[{},
If[Dimensions[a]==Dimensions[b], ,Return[False]];
Return[isIdentityUpToPhase[a . ConjugateTranspose[b]]]
]
(*Create a random n\[Times]m permutation matrix*)
randPermutMat[m_,n_]:=Module[{perm},(
perm=IdentityMatrix[n][[All,RandomSample[Range[m]]]];
perm=perm[[;;,1;;m]];
perm
)]
(*Input dimension instead of the number of qubits*)
CreateIsometryFromListDim[st_,M_]:=CreateOperationFromGateList[st,Log2[M]]
NCreateIsometryFromListDim[st_,M_]:=NCreateOperationFromGateList[st,Log2[M]]
(*Multiply the gates in the list representation st to get the matrix representaiton of the operator represented by st.
Note that n denotes the total number of qubits.
*)
MultiplyGates[st_,n_]:=CreateOperationFromGateList[st,n];
(*Numerically multiply the gates in the list representation st to get the matrix
representaiton of the operator represented by st. New version is faster than previous
*)
NMultiplyGates[st_,n_]:=NCreateOperationFromGateList[st,n]
(*Some functions for random numbers and matrices.
RR\[Rule]Random Real Number;
RC\[Rule]Random Complex Number;
RG[n]\[Rule]Random Complex Matrix of size n x n;
RU[n]\[Rule]Random Unitary Matrix of size n x n;
*)
RR:=RandomReal[NormalDistribution[0,1]];
RC:=RR+I*RR;
RG[n_]:=Table[RC,{n},{n}];
RU[n_]:=Orthogonalize[RG[n]];
(*Helpers for checking mathematical decompositions*)
checkIsoToUnitary[iso_]:=Module[{u},(
u=IsoToUnitary[iso];
isIdentity[u . ConjugateTranspose[u]]&&isZero[Norm[iso-u[[All,1;;Dimensions[iso][[2]]]]]]
)]
(*Tests for single methods for mathematical decompositions*)
testAppendColums:=Module[{},(
checkIsoToUnitary[PickRandomIsometry[2,4]]&&
checkIsoToUnitary[randPermutMat[2,4]]
)]
(*Unit tests for some basic methods*)
(*Helpers for checking basic methods*)
checkSimplifyGateLists[st_]:=Module[{u,stNew},(
stNew=SimplifyGateList[st];
isIdentityUpToPhase[ConjugateTranspose[CreateOperationFromGateList[st]] . CreateOperationFromGateList[stNew]]
)]
checkRzAngle[angle_]:=isIdentityUpToPhase[RzM[RzAngle[RzM[angle,1]],1] . ConjugateTranspose[RzM[angle,1]]]
checkRxAngle[angle_]:=isIdentityUpToPhase[RxM[RxAngle[RxM[angle,1]],1] . ConjugateTranspose[RxM[angle,1]]]
checkRyAngle[angle_]:=isIdentityUpToPhase[RyM[RyAngle[RyM[angle,1]],1] . ConjugateTranspose[RyM[angle,1]]]
(*Tests for checking basic methods*)
testSimplifyGateLists:=Module[{},(
If[
checkSimplifyGateLists[DecIsometry[PickRandomIsometry[2,4]]]&&
checkSimplifyGateLists[ColumnByColumnDec[N[randPermutMat[4,16]]]],
True
,
Print["Error in SimplifyGateLists"];
]
)]
testRzAngle:=Module[{},(
If[
checkRzAngle[0]&&checkRzAngle[0.]&&checkRzAngle[Pi/2]&&checkRzAngle[Pi/2.]&&
checkRzAngle[3Pi]&&checkRzAngle[3.Pi]&&checkRzAngle[0.456]&&checkRzAngle[4]
,
True
,
Print["Error in RzAngle"];
]
)]
testRxAngle:=Module[{},(
If[
checkRxAngle[0]&&checkRxAngle[0.]&&checkRxAngle[Pi/2]&&checkRxAngle[Pi/2.]&&
checkRxAngle[3Pi]&&checkRxAngle[3.Pi]&&checkRxAngle[0.456]&&checkRxAngle[4]
,
True
,
Print["Error in RxAngle"];
]
)]
testRyAngle:=Module[{},(
If[
checkRyAngle[0]&&checkRyAngle[0.]&&checkRyAngle[Pi/2]&&checkRyAngle[Pi/2.]&&
checkRyAngle[3Pi]&&checkRyAngle[3.Pi]&&checkRyAngle[0.456]&&checkRyAngle[4]
,
True
,
Print["Error in RyAngle"];
]
)]
(*All tests for basic methods*)
testAllBasicMethods:=Module[{},( If[
testSimplifyGateLists&&
testRzAngle&&
testRxAngle&&
testRyAngle
,Print["All tests for the basic methods pass."],,
Print["testAllBasicMethods neither returned True nor False"]
]
)
]
(*Tests for (uniformly) multi controlled gates*)
(*Unit tests for MCGs*)
(*Helpers for checking the Decomposition of MCGs*)
(*Note: the matrix mat is required to be a unitary for this test.*)
checkApplyMCG[MCG_,mat_]:=Module[{mcg,invertMat,i,gates},
mcg=CreateMCG[MCG[[1]],Join[MCG[[2]],MCG[[3]]],MCG[[4]],MCG[[5]]];
(*Account for zero controls*)
gates={};
For[i=1,i<=MCG[[5]],i++,
If[MemberQ[MCG[[3]],i],
AppendTo[gates,RxM[Pi]],
AppendTo[gates,IdentityMatrix[2]];
];
];
invertMat=KroneckerProduct@@gates;
mcg=invertMat . mcg . invertMat;
isIdentityUpToPhase[mcg . mat . ConjugateTranspose[ApplyMCG[MCG,mat]]]
]
checkDecToffoliMultiControlUpToDiagonal[control_,target_,n_]:=Module[{i,st,mat},(
st=DecToffoliMultiControlUpToDiagonal[control,target,n];
mat=NMultiplyGates[st,n];
isDiagonal[mat . ConjugateTranspose[CreateMCToffoli[control,target,n]]]
)]
checkDecToffoliMultiControl[control_,target_,n_]:=Module[{i,st,mat},(
st=DecToffoliMultiControl[control,target,n];
mat=NMultiplyGates[st,n];
isIdentityUpToPhase[mat . ConjugateTranspose[CreateMCToffoli[control,target,n]]
]
)]
checkDecMCSpecialUnitary[su_,control_,target_,n_]:=Module[{i,st,mat},(
st=DecMCSpecialUnitary[su,control,target,n];
mat=NMultiplyGates[st,n];
isIdentityUpToPhase[mat . ConjugateTranspose[CreateMCG[su,control,target,n]]]
)]
checkDecMCG[u_,control_,target_,n_]:=Module[{i,st,mat},(
st=DecMCG[u,control,target,n];
mat=NMultiplyGates[st,n];
isIdentityUpToPhase[mat . ConjugateTranspose[CreateMCG[u,control,target,n]]]
)]
checkDecMCSpecialUnitaryUpToDiagonalWithDiagonal[u_,control_,target_,n_]:=Module[{i,st,mat},(
st=DecMCSpecialUnitaryUpToDiagonal[u,control,target,n,ReturnDiagonal->True];
mat=NMultiplyGates[st,n];
FullSimplify[isIdentityUpToPhase[mat . ConjugateTranspose[CreateMCG[u,control,target,n]]]]
)]
checkDecMCSpecialUnitaryUpToDiagonal[u_,control_,target_,n_]:=Module[{i,st,mat},(
st=DecMCSpecialUnitaryUpToDiagonal[u,control,target,n];
mat=NMultiplyGates[st,n];
FullSimplify[isDiagonal[mat . ConjugateTranspose[CreateMCG[u,control,target,n]]]]
)]
(*Tests for single methods for MGGs*)
testApplyMCG:=Module[{error},(
error=0;
If[Quiet[Check[checkApplyMCG[{RU[2],{1,2,4},{},3,5},RU[2^5]],error=1;False]] &&
Quiet[Check[checkApplyMCG[{RU[2],{2},{3,5},1,5},RU[2^5]],error=2;False]],True,
Print["Error in ApplyMCG[] with error message code ",error];False
]
)]
testDecToffoliMultiControlUpToDiagonal:=Module[{error},(
error=0;
If[Quiet[Check[checkDecToffoliMultiControlUpToDiagonal[{1,2,4},3,5],error=1;False]] &&
Quiet[Check[checkDecToffoliMultiControlUpToDiagonal[{1,2,4,5},3,7],error=2;False]],True,
Print["Error in DecToffoliMultiControlUpToDiagonal[] with error message code ",error];False
]
)]
testDecToffoliMultiControl:=Module[{error},(
error=0;
If[Quiet[Check[checkDecToffoliMultiControl[{1,3},2,3],error=1;False]] &&
Quiet[Check[checkDecToffoliMultiControl[{1,2,5},3,5],error=2;False]]&&
Quiet[Check[checkDecToffoliMultiControl[{1,2,3,4},5,6],error=3;False]],True,
Print["Error in DecToffoliMultiControl[] with error message code ",error];False
]
)]
testDecMCSpecialUnitary:=Module[{M,error},(
error=0;
M=RU[2];
M=M/Det[M]^(1/2);(*M is a random special unitary matrix*)
If[(*Quiet[Check[checkDecMCSpecialUnitary[N[-IdentityMatrix[2]],{1,2,3,4,5,6,8},7,8],error=1;False]] &&*)
Quiet[Check[checkDecMCSpecialUnitary[M,{1,2,3,4,5,6,7},8,8],error=2;False]],True,
Print["Error in DecMCSpecialUnitary[] with error message code ",error];False
]
)]
testDecMCG:=Module[{M,error},(
error=0;
M=RU[2];
If[Quiet[Check[checkDecMCG[-IdentityMatrix[2],{1,2,3,4},6,6],error=1;False]] &&
Quiet[Check[checkDecMCG[M,{1,2,5},4,5],error=2;False]] &&
Quiet[Check[checkDecMCG[M,{3},1,3],error=3;False]]&&
Quiet[Check[checkDecMCG[M,{3,1},2,3],error=4;False]],True,
Print["Error in DecMCG[] with error message code ",error];False
]
)]
(*Here it is enough to test for less than 8 controls, since otherwise we use the method DecMCSpecialUnitary[],
which is already tested above.*)
testDecMCSpecialUnitaryUpToDiagonalWithDiagonal:=Module[{M,error},(
error=0;
M=RU[2];
M=M/Det[M]^(1/2);(*M is a random special unitary matrix*)
If[Quiet[Check[checkDecMCSpecialUnitaryUpToDiagonalWithDiagonal[N[-IdentityMatrix[2]],{1,2,3,4},5,5],error=1;False]] &&
Quiet[Check[checkDecMCSpecialUnitaryUpToDiagonalWithDiagonal[M,{1,2,5},4,5],error=2;False]] &&
Quiet[Check[checkDecMCSpecialUnitaryUpToDiagonalWithDiagonal[M,{3},1,3],error=3;False]]&&
Quiet[Check[checkDecMCSpecialUnitaryUpToDiagonalWithDiagonal[M,{},1,3],error=4;False]]&&
Quiet[Check[checkDecMCSpecialUnitaryUpToDiagonalWithDiagonal[M,{3,1},2,3],error=5;False]]&&
(*Also check the method for analytic calculations:*)
Quiet[Check[checkDecMCSpecialUnitaryUpToDiagonalWithDiagonal[IdentityMatrix[2],{1,2,3},4,4],error=6;False]],
True,
Print["Error in DecMCGspecialUnitaryUpToDiagonal[] (with option returning the diagonal gate) with error message code ",error];False
]
)]
(*Here it is enough to test for less than 8 controls, since otherwise we use the method DecMCSpecialUnitary[],
which is already tested above.*)
testDecMCGspecialUnitaryUpToDiagonal:=Module[{M,error},(
error=0;
M=RU[2];
M=M/Det[M]^(1/2);(*M is a random special unitary matrix*)
If[Quiet[Check[checkDecMCSpecialUnitaryUpToDiagonal[N[-IdentityMatrix[2]],{1,2,3,4},5,5],error=1;False]] &&
Quiet[Check[checkDecMCSpecialUnitaryUpToDiagonal[M,{1,2,5},4,5],error=2;False]] &&
Quiet[Check[checkDecMCSpecialUnitaryUpToDiagonal[M,{3},1,3],error=3;False]]&&
Quiet[Check[checkDecMCSpecialUnitaryUpToDiagonal[M,{},1,3],error=4;False]]&&
Quiet[Check[checkDecMCSpecialUnitaryUpToDiagonal[M,{3,1},2,3],error=5;False]]&&
(*Also check the method for analytic calculations:*)
Quiet[Check[checkDecMCSpecialUnitaryUpToDiagonal[N[IdentityMatrix[2]],{1,2,3},4,4],error=6;False]],
True,
Print["Error in DecMCGspecialUnitaryUpToDiagonal[] with error message code ",error];False
]
)]
(*Test all Methods for MCG*)
testAllMCGMethods:=Module[{},( If[
testApplyMCG&&
testDecToffoliMultiControlUpToDiagonal&&
testDecToffoliMultiControl&&
testDecMCG &&
testDecMCSpecialUnitary&&
testDecMCSpecialUnitaryUpToDiagonalWithDiagonal&&
testDecMCGspecialUnitaryUpToDiagonal
,Print["All tests for MCGs pass."],,
Print["testAllMCGMethods neither returned True nor False"]
]
)
]
(*Unit tests for UCGs*)
checkApplyUCG[UCG_,mat_]:=Module[{ucg},(
ucg=CreateUCG[UCG[[1]],UCG[[2]],UCG[[3]],UCG[[4]]];
Chop[Norm[ucg . mat-ApplyUCG[UCG,mat]]]==0
)]
(*Helpers for checking the Decomposition of UCGs*)
checkDecUCGUpToDiagonalWithDiagonal[u_,control_,target_,n_]:=Module[{i,st,mat,dia},(
st=DecUCGUpToDiagonal[u,control,target,n,ReturnDiagonal->True];
dia=st[[-1]];
mat=ApplyDiag[{dia[[2]],dia[[3]],n},MultiplyGates[Drop[st,-1],n]];
FullSimplify[isIdentityUpToPhase[mat . ConjugateTranspose[CreateUCG[u,control,target,n]]]]
)]
checkDecUCGUpToDiagonal[u_,control_,target_,n_]:=Module[{i,st,mat},(
st=DecUCGUpToDiagonal[u,control,target,n];
mat=MultiplyGates[st,n];
FullSimplify[isDiagonal[mat . ConjugateTranspose[CreateUCG[u,control,target,n]]]]
)]
(*checks UC Z-rotations (set rotAxis=3) and Y-rotations (set rotAxis=2)*)
RotGate[\[Alpha]_,i_]:=
MatrixExp[I \[Alpha]/2 PauliMatrix[i]]
Options[checkDecUCZY] = {DecUCYWithCZ -> False};
checkDecUCZY[angles_,control_,target_,n_,rotAxis_,OptionsPattern[]]:=Module[{i,st,mat,op,str,m},(
If[rotAxis==3,
st=DecUCZ[angles,control,target,n],
If[OptionValue[DecUCYWithCZ],
st=DecUCY[angles,control,target,n,TwoQubitGate->"Cz"],
st=DecUCY[angles,control,target,n]
];
];
mat=MultiplyGates[st,n];
m={};
For[i=1,i<= Length[angles],i++,AppendTo[m,RotGate[angles[[i]],rotAxis]]];
isIdentityUpToPhase[mat . ConjugateTranspose[CreateUCG[m,control,target,n]]]
)]
(*Tests for methods for UGGs*)
testApplyUCG:=Module[{i,m0,m1,m2,m3,error},(
error=0;
(*generate set with unitaries*)
m0={};
For[i=1,i<= 2^3,i++,AppendTo[m0,IdentityMatrix[2]]];
m1={};
For[i=1,i<= 2^4,i++,AppendTo[m1,N[IdentityMatrix[2]]]];
m2={{{0,1},{1,0}}};
For[i=1,i<= 2^3-1,i++,AppendTo[m2,RU[2]]];
If[Quiet[Check[checkApplyUCG[{m0,{1,2,3},4,4},RU[2^4]],error=1;False]] &&
Quiet[Check[checkApplyUCG[{m1,{1,2,3,5},4,5},RU[2^5]],error=2;False]] &&
Quiet[Check[checkApplyUCG[{m1,{1,2,5},4,5},RU[2^5]],error=3;False]]&&
Quiet[Check[checkApplyUCG[{m1,{1,5,2},4,5},RU[2^5]],error=4;False]]&&
Quiet[Check[checkApplyUCG[{m1,{5,1,2},4,6},RU[2^6]],error=5;False]]&&
Quiet[Check[checkApplyUCG[{m2,{2,3,4},1,6},RU[2^6]],error=6;False]],
True,
Print["Error in ApplyUCG[] with error message code ",error];False
]
)]
testDecUCG:=Module[{i,m0,m1,m2,m3,error},(
error=0;
(*generate set with unitaries*)
m0={};
For[i=1,i<= 2^2,i++,AppendTo[m0,IdentityMatrix[2]]];
m1={};
For[i=1,i<= 2^4,i++,AppendTo[m1,N[IdentityMatrix[2]]]];
m2={{{0,1},{1,0}}};
For[i=1,i<= 2^3-1,i++,AppendTo[m2,RU[2]]];
(*
m3={};
For[i=1,i<= 2^7,i++,AppendTo[m3,RU[2]]];
*)
If[Quiet[Check[checkDecUCGUpToDiagonalWithDiagonal[m0,{1,3},2,3],error=1;False]] &&
Quiet[Check[checkDecUCGUpToDiagonalWithDiagonal[m1,{1,2,3,5},4,5],error=2;False]] &&
Quiet[Check[checkDecUCGUpToDiagonalWithDiagonal[m2,{2,4,3},1,6],error=3;False]] (*&&
Quiet[Check[checkDecUCGUpToDiagonalWithDiagonal[m3,{1,2,3,5,6,7,8},4,8],error=4;False]]
*),
True,
Print["Error in DecUCG[] with error message code ",error];False
]
)]
testDecUCGUpToDiagonal:=Module[{i,m0,m1,m2,m3,error},(
error=0;
(*generate set with unitaries*)
m0={};
For[i=1,i<= 2^2,i++,AppendTo[m0,IdentityMatrix[2]]];
m1={};
For[i=1,i<= 2^4,i++,AppendTo[m1,N[IdentityMatrix[2]]]];
m2={{{0,1},{1,0}}};
For[i=1,i<= 2^3-1,i++,AppendTo[m2,RU[2]]];
(*
m3={};
For[i=1,i<= 2^7,i++,AppendTo[m3,RU[2]]];
*)
If[Quiet[Check[checkDecUCGUpToDiagonal[m0,{1,2},3,3],error=1;False]] &&
Quiet[Check[checkDecUCGUpToDiagonal[m1,{1,2,3,5},4,5],error=2;False]] &&
Quiet[Check[checkDecUCGUpToDiagonal[m2,{4,2,3},1,6],error=3;False]] (*&&
Quiet[Check[checkDecUCGUpToDiagonal[m3,{1,2,3,5,6,7,8},4,8],error=4;False]]
*),
True,
Print["Error in DecUCGUpToDiagonal[] with error message code ",error];False
]
)]
testDecUCZY:=Module[{i,m1,m2,error},(
error=0;
(*generate angles for UCZ*)
m1={};
For[i=1,i<= 2^4,i++,AppendTo[m1,0]];
m2={};
For[i=1,i<= 2^4,i++,AppendTo[m2,RandomReal[]]];
If[Quiet[Check[checkDecUCZY[m1,{1,3,5,6},2,6,3],error=1;False]] &&
Quiet[Check[checkDecUCZY[m1,{1,3,5,6},2,6,2],error=2;False]]&&
Quiet[Check[checkDecUCZY[m1,{6,3,5,1},2,6,2,DecUCYWithCZ -> True],error=3;False]]&&
Quiet[Check[checkDecUCZY[m2,{1,2,4,5},3,6,3],error=4;False]]&&
Quiet[Check[checkDecUCZY[m2,{1,2,4,5},3,6,2],error=5;False]]&&
Quiet[Check[checkDecUCZY[m2,{1,4,2,5},3,6,2,DecUCYWithCZ -> True],error=6;False]],
True,
Print["Error in DecUCGZ[] with error message code ",error];False
]
)]
(*Test UGGs*)
testUCGs:=If[testApplyUCG&&testDecUCG &&testDecUCGUpToDiagonal&& testDecUCZY,Print["All tests for UCGs pass."],,Print["testUCGs neither returned True nor False"]]
(*Unit tests for diagonal gates*)
checkApplyDiag[diagGate_,mat_]:=Module[{diag},(
diag=DiagMat[diagGate[[1]],diagGate[[2]],diagGate[[3]]];
Chop[Norm[diag . mat-ApplyDiag[diagGate,mat]]]==0
)
]
(*Helpers for checking decomposition of diagonal gates*)
checkDecDiagGate[dia_]:=Module[{st,m},(
st=DecDiagGate[dia];
m=MultiplyGates[st,Log2[Length[dia]]];
isIdentityUpToPhase[ConjugateTranspose[DiagonalMatrix[dia]] . m]
)
]
(*Test for Diagonal gates*)
testApplyDiag:=Module[{error},(
error=0;
If[Quiet[Check[checkApplyDiag[{Exp[I RandomReal[{0,2Pi},2^1]],{2},2},RU[2^2]],error=1;False]]&&
Quiet[Check[checkApplyDiag[{Exp[I RandomReal[{0,2Pi},2^2]],{1,3},3},RU[2^3]],error=2;False]]&&
Quiet[Check[checkApplyDiag[{Exp[I RandomReal[{0,2Pi},2^3]],{3,1,4},5},IdentityMatrix[2^5]],error=3;False]]
,
True,
Print["Error in ApplyDiag[] with error message code ",error];False
]
)]
testDecDiagGate:=Module[{error},(
error=0;
If[Quiet[Check[checkDecDiagGate[Exp[I RandomReal[{0,2Pi},2^1]]],error=1;False]]&&
Quiet[Check[checkDecDiagGate[Exp[I RandomReal[{0,2Pi},2^2]]],error=2;False]]&&
Quiet[Check[checkDecDiagGate[Exp[I RandomReal[{0,2Pi},2^3]]],error=3;False]]&&
Quiet[Check[checkDecDiagGate[ConstantArray[1,2^3]],error=4;False]],
True,
Print["Error in DecDiagGate[] with error message code ",error];False
]
)]
(*Test all methods for diagonal gates*)
testAllDiagGateMethods:=Module[{},(
If[testDecDiagGate && testApplyDiag,Print["All tests for diagonal gates pass."],,
Print["testAllDiagGateMethods neither returned True nor False"]
]
)
]
(*Unit tests for column-by-column decomposition*)
(*Helpers for checking the CC-decomposition*)
checkColumnByColumnDec[v_]:=Module[{i,st,iso,st2,iso2},(
st=ColumnByColumnDec[v];
iso=NCreateIsometryFromListDim[st,Dimensions[v][[1]]];
st2=ColumnByColumnDec[v,FirstColumn->"StatePreparation"];
iso2=NCreateIsometryFromListDim[st2,Dimensions[v][[1]]];
isIdentityUpToPhase[ConjugateTranspose[v] . iso]&&isIdentityUpToPhase[ConjugateTranspose[v] . iso2]
)
]
checkColumnByColumnDecExact[v_]:=Module[{i,st,iso},(
st=ColumnByColumnDec[v,Simp->False];
iso=NCreateIsometryFromListDim[st,Dimensions[v][[1]]];
isIdentityUpToPhase[ConjugateTranspose[v] . iso]
)
]
(*Test methods for CC-decomposition*)
testColumnByColumnDec:=Module[{error,v1,v2,v3,vExact1},(
error=0;
v1=CreateOperationFromGateList[{Ancilla[0,1],Rx[1,2],CNOT[1,2],Rz[1,1],Rz[1,1]}];
v2=CreateOperationFromGateList[NGateList[{Ancilla[0,1],Rx[1,3],CNOT[3,1],Rz[1,3],Rz[1,1],CNOT[2,3],Ry[1,1]}]];
v3=CreateOperationFromGateList[NGateList[{Ancilla[0,1],Ancilla[0,4],Rx[1,3],CNOT[3,1],Rz[2.5,3],Rz[0.7,1],CNOT[2,3],Ry[0.4,1],Rz[0.4,1],Ry[\[Pi]/2,2],Rz[\[Pi],2],CNOT[2,4]}]];
vExact1=CreateOperationFromGateList[{Ancilla[0,1],Rx[Pi/4,2],Rx[Pi/4,1],CNOT[1,2],CNOT[3,2],CNOT[2,3],CNOT[3,1]}];
If[Quiet[Check[checkColumnByColumnDec[PickRandomIsometry[2^2,2^4]],error=1;False]]&&
Quiet[Check[checkColumnByColumnDec[PickRandomIsometry[2^3,2^3]],error=2;False]]&&
Quiet[Check[checkColumnByColumnDec[randPermutMat[2^1,2^2]],error=3;False]]&&
Quiet[Check[checkColumnByColumnDec[N[randPermutMat[2^2,2^3]]],error=4;False]]&&
Quiet[Check[checkColumnByColumnDec[PickRandomIsometry[1,2^2]],error=5;False]]&&
Quiet[Check[checkColumnByColumnDec[v1],error=6;False]]&&
Quiet[Check[checkColumnByColumnDec[v2],error=7;False]]&&
Quiet[Check[checkColumnByColumnDec[v3],error=8;False]]&&
Quiet[Check[checkColumnByColumnDecExact[vExact1],error=9;False]]&&
Quiet[Check[checkColumnByColumnDecExact[randPermutMat[8,8]],error=10;False]]
(*&&
Quiet[Check[checkColumnByColumnDec[PickRandomIsometry[2^3,2^3]],error=6;False]]&&
Quiet[Check[checkColumnByColumnDec[PickRandomIsometry[2^4,2^4]],error=7;False]]*),
True,
Print["Error in ColumnByColumnDec[] with error message code ",error];False
]
)]
(*Test CC-decomposition*)
testCCDec:=If[testDecUCGUpToDiagonal&&testColumnByColumnDec,Print["All tests for the column-by-column decomposition pass."],,
Print["ttestCCDec neither returned True nor False"]]
(*Unit tests for DecIsometry*)
(*Helpers for testing DecIsometry*)
checkDecIsometry[v_]:=Module[{i,st,iso,st2,iso2},(
st=DecIsometry[v];
iso=NCreateIsometryFromListDim[st,Dimensions[v][[1]]];
isIdentityUpToPhase[ConjugateTranspose[v] . iso]
)
]
(*Tests for DecIsometry*)
testDecIsometry:=Module[{error,v1,v2,v3},(
error=0;
v1=CreateOperationFromGateList[{Ancilla[0,1],Rx[Pi,2],CNOT[1,2],Rz[Pi,1],Rz[Pi,1]}];
v2=CreateOperationFromGateList[NGateList[{Ancilla[0,1],Rx[1,3],CNOT[3,1],Rz[1,3],Rz[1,1],CNOT[2,3],Ry[1,1]}]];
v3=CreateOperationFromGateList[NGateList[{Ancilla[0,1],Ancilla[0,4],Rx[1,3],CNOT[3,1],Rz[2.5,3],Rz[0.7,1],CNOT[2,3],Ry[0.4,1],Rz[0.4,1],Ry[\[Pi]/2,2],Rz[\[Pi],2],CNOT[2,4]}]];
If[Quiet[Check[checkDecIsometry[PickRandomIsometry[2^2,2^4]],error=1;False]]&&
Quiet[Check[checkDecIsometry[PickRandomIsometry[2^1,2^2]],error=2;False]]&&
Quiet[Check[checkDecIsometry[randPermutMat[2^1,2^2]],error=3;False]]&&
Quiet[Check[checkDecIsometry[N[randPermutMat[2^2,2^3]]],error=4;False]]&&
Quiet[Check[checkDecIsometry[PickRandomIsometry[1,2^2]],error=5;False]]&&
Quiet[Check[checkDecIsometry[PickRandomIsometry[2^4,2^4]],error=6;False]]&&
Quiet[Check[checkDecIsometry[v1],error=7;False]]&&
Quiet[Check[checkDecIsometry[v2],error=8;False]]&&
Quiet[Check[checkDecIsometry[v3],error=9;False]]
,
True,
Print["Error in DecIsometry[] with error message code ",error];False
]
)]
testIsometryDecompositions:=If[testDecIsometry,Print["All tests for DecIsometry pass."],,
Print["testIsometryDecompositions neither returned True nor False"]]
(*Unit tests for Isometries on a small number of qubits*)
(*Helpers for checking the methods for isoemtries on a small number of qubits*)
checkStatePrep1Qubit[s_]:=Module[{i,st,iso},(
st=StatePrep1Qubit[s];
iso=NCreateIsometryFromListDim[st,Dimensions[s][[1]]];
isIdentityUpToPhase[ConjugateTranspose[s] . iso]
)
]
checkStatePrep2Qubits[s_]:=Module[{i,st,iso},(
st=StatePrep2Qubits[s];
iso=NCreateIsometryFromListDim[st,Dimensions[s][[1]]];
isIdentityUpToPhase[ConjugateTranspose[s] . iso]
)
]
checkStatePrep3Qubits[s_,class_]:=Module[{i,st,iso},(
st=StatePrep3Qubits[s];
iso=NCreateIsometryFromListDim[st,Dimensions[s][[1]]];
isIdentityUpToPhase[ConjugateTranspose[s] . iso] &&
(CNOTCount[st]==class)
)
]
checkDecIso12[v_,analytic_:False]:=Module[{i,st,iso},(
st=DecIso12[v];
If[analytic,
iso=CreateIsometryFromListDim[st,Dimensions[v][[1]]];
isIdentityUpToPhase[ConjugateTranspose[v] . N[iso]]
,
iso=NCreateIsometryFromListDim[st,Dimensions[v][[1]]];
isIdentityUpToPhase[ConjugateTranspose[v] . iso]
]
)
]
(*Test methods for isometries on a small number of qubits*)
testStatePrep1Qubit:=Module[{error},(
error=0;
If[Quiet[Check[checkStatePrep1Qubit[PickRandomPsi[2]],error=1;False]]&&
Quiet[Check[checkStatePrep1Qubit[FPickRandomPsi[2,4]],error=2;False]]&&
Quiet[Check[checkStatePrep1Qubit[I*{{0},{1}}],error=3;False]]&&
Quiet[Check[checkStatePrep1Qubit[{{1},{0}}],error=4;False]]&&
Quiet[Check[checkStatePrep1Qubit[CreateOperationFromGateList[{Ancilla[0,1],Rz[1/3,1],Rz[1/3,1]}]],error=5;False]]
,
True,
Print["Error in statePrep1Qubit[] with error message code ",error];False
]
)]
testStatePrep2Qubits:=Module[{error,psi},(
error=0;
If[Quiet[Check[checkStatePrep2Qubits[PickRandomPsi[4]],error=1;False]]&&
Quiet[Check[checkStatePrep2Qubits[FPickRandomPsi[4,4]],error=2;False]]&&
(psi = {\!\(\*
TagBox[
RowBox[{"(",
TagBox[GridBox[{
{
FractionBox["1",
SqrtBox["2"]]}
},
GridBoxAlignment->{"Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}, "Items" -> {}, "ItemsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {Offset[0.27999999999999997`], {Offset[0.5599999999999999]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {Offset[0.2], {Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}, "Items" -> {}, "ItemsIndexed" -> {}}],
Column], ")"}],
Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]\),\!\(\*
TagBox[
RowBox[{"(",
TagBox[GridBox[{
{"0"}
},
GridBoxAlignment->{"Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}, "Items" -> {}, "ItemsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {Offset[0.27999999999999997`], {Offset[0.5599999999999999]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {Offset[0.2], {Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}, "Items" -> {}, "ItemsIndexed" -> {}}],
Column], ")"}],
Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]\),\!\(\*
TagBox[
RowBox[{"(",
TagBox[GridBox[{
{"0"}
},
GridBoxAlignment->{"Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}, "Items" -> {}, "ItemsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {Offset[0.27999999999999997`], {Offset[0.5599999999999999]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {Offset[0.2], {Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}, "Items" -> {}, "ItemsIndexed" -> {}}],
Column], ")"}],
Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]\),\!\(\*
TagBox[
RowBox[{"(",
TagBox[GridBox[{
{
FractionBox["1",
SqrtBox["2"]]}
},
GridBoxAlignment->{"Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}, "Items" -> {}, "ItemsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {Offset[0.27999999999999997`], {Offset[0.5599999999999999]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {Offset[0.2], {Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}, "Items" -> {}, "ItemsIndexed" -> {}}],
Column], ")"}],
Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]\)};
Quiet[Check[checkStatePrep2Qubits[psi],error=3;False]])&&
Quiet[Check[checkStatePrep2Qubits[CreateOperationFromGateList[{Ancilla[0,1],Ancilla[0,2],Rz[1/3,1],Rz[1/3,1],CNOT[2,1],Rz[1/3,1],Rz[1/3,2]}]],error=4;False]]
,
True,
Print["Error in statePrep2Qubits[] with error message code ",error];False
]
)]
testStatePrep3Qubits := Module[{state,TestBoolean, theta, ru},
TestBoolean = True;
(*class 0*)
state = Transpose[{Flatten[KroneckerProduct[PickRandomPsi[2],PickRandomPsi[2], PickRandomPsi[2]]]}];
If[checkStatePrep3Qubits[state,0], ,Print["3 qubit state preparation failed on a Class 0 state"]; TestBoolean = False];
state = NCreateIsometryFromListDim[{Ancilla[0,3],Ancilla[0,2],Ancilla[0,1],Rz[0.8,1],Rx[0.1,2],Rx[0.8,3],Rx[0.4,1],Ry[0.4, 3]}, 8];
If[checkStatePrep3Qubits[state,0], ,Print["3 qubit state preparation failed on a Class 0 state"]; TestBoolean = False];
(*class 1*)
state = Transpose[{Flatten[KroneckerProduct[PickRandomPsi[2],PickRandomPsi[4]]]}];
If[checkStatePrep3Qubits[state,1], ,Print["3 qubit state preparation failed on a Class 1 state"]; TestBoolean = False];
state = NCreateIsometryFromListDim[{Ancilla[0,3],Ancilla[0,2],Ancilla[0,1],Rz[0.8,1],Rx[0.1,2],Rx[0.8,3],Ry[0.8,1],Rz[0.1,2],CNOT[1, 2],Rx[0.4,1],Ry[0.4,3],Ry[0.8,1],Rx[0.1,2],Rx[0.8,3]},8];
If[checkStatePrep3Qubits[state,1], ,Print["3 qubit state preparation failed on a Class 1 state"]; TestBoolean = False];
(*class 2*)
theta = RandomVariate[UniformDistribution[{0, \[Pi]/2}]];ru = RU[2]; state = Transpose[{Cos[theta] *Flatten[KroneckerProduct[ru[[All,1]],PickRandomPsi[2], PickRandomPsi[2]]]+ Sin[theta]*Flatten[KroneckerProduct[ru[[All,2]],PickRandomPsi[2], PickRandomPsi[2]]]}];
If[checkStatePrep3Qubits[state,2], ,Print["3 qubit state preparation failed on a Class 2 state, with the orthogonal factors on the first qubit"]; TestBoolean = False];
theta = RandomVariate[UniformDistribution[{0, \[Pi]/2}]];ru = RU[2]; state = Transpose[{Cos[theta] *Flatten[KroneckerProduct[PickRandomPsi[2],ru[[All,1]], PickRandomPsi[2]]]+ Sin[theta]*Flatten[KroneckerProduct[PickRandomPsi[2],ru[[All,2]], PickRandomPsi[2]]]}];
If[checkStatePrep3Qubits[state,2], ,Print["3 qubit state preparation failed on a Class 2 state, with the orthogonal factors on the second qubit"]; TestBoolean = False];
theta = RandomVariate[UniformDistribution[{0, \[Pi]/2}]];ru = RU[2]; state = Transpose[{Cos[theta] *Flatten[KroneckerProduct[PickRandomPsi[2], PickRandomPsi[2],ru[[All,1]]]]+ Sin[theta]*Flatten[KroneckerProduct[PickRandomPsi[2], PickRandomPsi[2],ru[[All,2]]]]}];
If[checkStatePrep3Qubits[state,2], ,Print["3 qubit state preparation failed on a Class 2 state, with the orthogonal factors on the third qubit"]; TestBoolean = False];
state = NCreateIsometryFromListDim[{Ancilla[0,3],Ancilla[0,2],Ancilla[0,1],Rz[0.8,1],Rx[0.1,2],Rx[0.8,3],Ry[0.8,1],Rz[0.1,2],CNOT[1,2],Rx[0.4,2],Ry[0.4,3],CNOT[2,3],Ry[0.9,3],Ry[0.8,1],Rx[0.1,2],Rx[0.8,3]},8];
If[checkStatePrep3Qubits[state,2], ,Print["3 qubit state preparation failed on a Class 2 state"]; TestBoolean = False];
state = NCreateIsometryFromListDim[{Ancilla[0,3],Ancilla[0,2],Ancilla[0,1],Rz[0.8,1],Rx[0.1,2],Rx[0.8,3],Ry[0.8,1],Rz[0.1,2],CNOT[1, 2],Rx[0.4,1],Ry[0.4,3],CNOT[3,1],Ry[0.8,1],Rx[0.1,2],Rx[0.8,3]},8];
If[checkStatePrep3Qubits[state,2], ,Print["3 qubit state preparation failed on a Class 2 state"]; TestBoolean = False];
(*class 3*)
state = PickRandomPsi[8];
If[checkStatePrep3Qubits[state,3], ,Print["3 qubit state preparation failed on a random 3 qubit state (assumed to be class 3)"]; TestBoolean = False];
TestBoolean
]
testDecIso12:=Module[{error,v1},
error=0;
v1=CreateOperationFromGateList[{Ancilla[0,1],Rx[1,2],CNOT[1,2],Rz[1,1],Rz[1,1]}];
If[Quiet[Check[checkDecIso12[PickRandomIsometry[2,4]],error=1;False]]&&
Quiet[Check[checkDecIso12[v1,True],error=2;False]]
,
True,
Print["Error in DecIso12[] with error message code ",error];False
]
]
(*Test Isometries on a small number of qubits*)
testIsoSmall:=If[testStatePrep1Qubit && testStatePrep2Qubits && testStatePrep3Qubits && testDecIso12 ,Print["All tests for the isometries on a small number of qubits pass."],,
Print["testIsoSmall neither returned True nor False"]]
(*Unit tests for decomposition of single-qubit unitaries*)
(*Unit tests for decomposition of two-qubit unitaries*)
(*Helpers for testing ZYZDec, XYXDec, ZXZDec, XZXDec, YXYDec,YZYDec*)
checkZYZDec[u_] := Module[{st},
st = ZYZDec[u,1];
If[isIdentityUpToPhase[MultiplyGates[st,1] . ConjugateTranspose[u]],
Return[True],
Print["ZYZDec failed on input\n", MatrixFormOp[u]];
Return[False]
];
]
checkXYXDec[u_] := Module[{st},
st = XYXDec[u,1];
If[isIdentityUpToPhase[MultiplyGates[st,1] . ConjugateTranspose[u]],
Return[True],
Print["ZYZDec failed on input\n", MatrixFormOp[u]];
Return[False]
];
]
checkZXZDec[u_] := Module[{st},
st = ZXZDec[u,1];
If[isIdentityUpToPhase[MultiplyGates[st,1] . ConjugateTranspose[u]],
Return[True],
Print["ZXZDec failed on input\n", MatrixFormOp[u]];
Return[False]
];
]
checkXZXDec[u_] := Module[{st},
st = XZXDec[u,1];
If[isIdentityUpToPhase[MultiplyGates[st,1] . ConjugateTranspose[u]],
Return[True],
Print["XZXDec failed on input\n", MatrixFormOp[u]];
Return[False]
];
]
checkYXYDec[u_] := Module[{st},
st = YXYDec[u,1];
If[isIdentityUpToPhase[MultiplyGates[st,1] . ConjugateTranspose[u]],
Return[True],
Print["YXYDec failed on input\n", MatrixFormOp[u]];
Return[False]
];
]
checkYZYDec[u_] := Module[{st},
st = YZYDec[u,1];
If[isIdentityUpToPhase[MultiplyGates[st,1] . ConjugateTranspose[u]],
Return[True],
Print["YZYDec failed on input\n", MatrixFormOp[u]];
Return[False]
];
]
(*Tests for ZYZDec and XYXDec*)
testZYZDec := Module[{isWorking},
isWorking=checkZYZDec[PickRandomIsometry[2,2]]&&checkZYZDec[{{0,1},{1,0}}]&&checkZYZDec[N[{{0,1},{1,0}}]]&&checkZYZDec[CreateOperationFromGateList[{Rz[Pi/2,1]}]]&&
checkZYZDec[CreateOperationFromGateList[{Ry[Pi/3,1]}]]&&checkZYZDec[CreateOperationFromGateList[{Ry[Pi/3,1]}]];
If[Not[isWorking],
Print["ZYZDec failed"]];
isWorking
];
testXYXDec := Module[{isWorking},
isWorking=checkXYXDec[PickRandomIsometry[2,2]]&&checkXYXDec[{{0,1},{1,0}}]&&checkXYXDec[N[{{0,1},{1,0}}]]
&&checkXYXDec[CreateOperationFromGateList[{Rz[Pi/3,1]}]]&&
checkXYXDec[CreateOperationFromGateList[{Ry[Pi/3,1]}]]&&checkXYXDec[CreateOperationFromGateList[{Ry[Pi/3,1]}]];
If[Not[isWorking],
Print["ZYZDec failed"]];
isWorking
];
testZXZDec := Module[{isWorking},
isWorking=checkZXZDec[PickRandomIsometry[2,2]]&&checkZXZDec[{{0,1},{1,0}}]&&checkZXZDec[N[{{0,1},{1,0}}]]
&&checkZXZDec[CreateOperationFromGateList[{Rz[Pi/3,1]}]]&&
checkZXZDec[CreateOperationFromGateList[{Ry[Pi/3,1]}]]&&checkZXZDec[CreateOperationFromGateList[{Ry[Pi/3,1]}]];
If[Not[isWorking],
Print["ZXZDec failed"]];
isWorking
];
testXZXDec := Module[{isWorking},
isWorking=checkXZXDec[PickRandomIsometry[2,2]]&&checkXZXDec[{{0,1},{1,0}}]&&checkXZXDec[N[{{0,1},{1,0}}]]
&&checkXZXDec[CreateOperationFromGateList[{Rz[Pi/3,1]}]]&&
checkXZXDec[CreateOperationFromGateList[{Ry[Pi/3,1]}]]&&checkXZXDec[CreateOperationFromGateList[{Ry[Pi/3,1]}]];
If[Not[isWorking],
Print["XZXDec failed"]];
isWorking
];
testYXYDec := Module[{isWorking},
isWorking=checkYXYDec[PickRandomIsometry[2,2]]&&checkYXYDec[{{0,1},{1,0}}]&&checkYXYDec[N[{{0,1},{1,0}}]]
&&checkYXYDec[CreateOperationFromGateList[{Rz[Pi/3,1]}]]&&
checkYXYDec[CreateOperationFromGateList[{Ry[Pi/3,1]}]]&&checkYXYDec[CreateOperationFromGateList[{Ry[Pi/3,1]}]];
If[Not[isWorking],
Print["XZXDec failed"]];
isWorking
];
testYZYDec := Module[{isWorking},
isWorking=checkYZYDec[PickRandomIsometry[2,2]]&&checkYZYDec[{{0,1},{1,0}}]&&checkYZYDec[N[{{0,1},{1,0}}]]
&&checkYZYDec[CreateOperationFromGateList[{Rz[Pi/3,1]}]]&&
checkYZYDec[CreateOperationFromGateList[{Ry[Pi/3,1]}]]&&checkYZYDec[CreateOperationFromGateList[{Ry[Pi/3,1]}]];
If[Not[isWorking],
Print["XZXDec failed"]];
isWorking
];
(*All tests for single-qubit unitaries*)
testDecSingleQubit := Module[{out},
If[testZYZDec && testXYXDec&& testZXZDec && testXZXDec&& testYXYDec&& testYZYDec
,
Print["All tests for ZYZDec, XYXDec, ZXZDec, XZXDec, YXYDec and YZYDec pass."];
out=True;
,
Print["Error(s) in ZYZDec, XYXDec, ZXZDec, XZXDec, YXYDec or YZYDec"];
out=False;
,
Print["testDecSingleQubit neither returned True nor False"]
];
out
]
(*Helpers for testing Dec2Qubit *)
checkDec2QubitGateUpToDiagonal[u_] := Module[{diag, st},
st = DecUnitary2Qubits[u,{1,2}, UpToDiagonal-> True];
If[isIdentityUpToPhase[NMultiplyGates[st,2] . ConjugateTranspose[u]],
Return[True],
Print["Dec2Qubit with option UpToDiagonal->True failed on input\n", MatrixFormOp[u]];
Return[False]
];
]
(*Helpers for testing Dec2Qubit *not* up to a diagonal *)
checkDecUnitary2Qubits[u_,numCNOT_:Null] := Module[{diag, st,out,isCNOTCOUNTCorrect},
st = DecUnitary2Qubits[u,{1,2}, UpToDiagonal->False];
isCNOTCOUNTCorrect=If[numCNOT===Null,True,CNOTCount[st]==numCNOT];
If[isIdentityUpToPhase[NMultiplyGates[st,2] . ConjugateTranspose[u]]&&isCNOTCOUNTCorrect,
out=True,
If[isIdentityUpToPhase[NMultiplyGates[st,2] . ConjugateTranspose[u]],,Print["Dec2Qubit failed on input\n", MatrixForm[u]]];
If[isCNOTCOUNTCorrect,,Print["Dec2Qubit outputs wrong number of C-NOT gates on input\n", MatrixForm[u]]];
out=False
];
out