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// Copyright (c) Microsoft Corporation.// Licensed under the MIT License.namespaceMicrosoft.Quantum.Canon{openMicrosoft.Quantum.Intrinsic;openMicrosoft.Quantum.Arithmetic;openMicrosoft.Quantum.Arrays;openMicrosoft.Quantum.Diagnostics;openMicrosoft.Quantum.Math;/// # Summary/// Applies a multiply-controlled unitary operation $U$ that applies a/// unitary $V_j$ when controlled by n-qubit number state $\ket{j}$.////// $U = \sum^{N-1}_{j=0}\ket{j}\bra{j}\otimes V_j$.////// # Input/// ## unitaryGenerator/// A tuple where the first element `Int` is the number of unitaries $N$,/// and the second element `(Int -> ('T => () is Adj + Ctl))`/// is a function that takes an integer $j$ in $[0,N-1]$ and outputs the unitary/// operation $V_j$.////// ## index/// $n$-qubit control register that encodes number states $\ket{j}$ in/// little-endian format.////// ## target/// Generic qubit register that $V_j$ acts on.////// # Remarks/// `coefficients` will be padded with identity elements if/// fewer than $2^n$ are specified. This implementation uses/// $n-1$ auxiliary qubits.////// # References/// - [ *Andrew M. Childs, Dmitri Maslov, Yunseong Nam, Neil J. Ross, Yuan Su*,///      arXiv:1711.10980](https://arxiv.org/abs/1711.10980)operationMultiplexOperationsFromGenerator<'T>(unitaryGenerator:(Int,(Int->('T=>UnitisAdj+Ctl))),index:LittleEndian,target:'T):UnitisCtl+Adj{let(nUnitaries,unitaryFunction)=unitaryGenerator;letunitaryGeneratorWithOffset=(nUnitaries,0,unitaryFunction);ifLength(index!)==0{fail"MultiplexOperations failed. Number of index qubits must be greater than 0.";}ifnUnitaries>0{letauxiliary=[];AdjointMultiplexOperationsFromGeneratorImpl(unitaryGeneratorWithOffset,auxiliary,index,target);}}/// # Summary/// Implementation step of `MultiplexOperationsFromGenerator`./// # See Also/// - Microsoft.Quantum.Canon.MultiplexOperationsFromGeneratorinternaloperationMultiplexOperationsFromGeneratorImpl<'T>(unitaryGenerator:(Int,Int,(Int->('T=>UnitisAdj+Ctl))),auxiliary:Qubit[],index:LittleEndian,target:'T):Unit{body(...){letnIndex=Length(index!);letnStates=2^nIndex;let(nUnitaries,unitaryOffset,unitaryFunction)=unitaryGenerator;letnUnitariesLeft=MinI(nUnitaries,nStates/2);letnUnitariesRight=MinI(nUnitaries,nStates);letleftUnitaries=(nUnitariesLeft,unitaryOffset,unitaryFunction);letrightUnitaries=(nUnitariesRight-nUnitariesLeft,unitaryOffset+nUnitariesLeft,unitaryFunction);letnewControls=LittleEndian(Most(index!));ifnUnitaries>0{ifLength(auxiliary)==1andnIndex==0{// Termination case(ControlledAdjoint(unitaryFunction(unitaryOffset)))(auxiliary,target);}elifLength(auxiliary)==0andnIndex>=1{// Start caseletnewauxiliary=Tail(index!);ifnUnitariesRight>0{MultiplexOperationsFromGeneratorImpl(rightUnitaries,[newauxiliary],newControls,target);}within{X(newauxiliary);}apply{MultiplexOperationsFromGeneratorImpl(leftUnitaries,[newauxiliary],newControls,target);}}else{// Recursion that reduces nIndex by 1 and sets Length(auxiliary) to 1.letcontrols=[Tail(index!)]+auxiliary;usenewauxiliary=Qubit();useandauxiliary=Qubit[MaxI(0,Length(controls)-2)];within{ApplyAndChain(andauxiliary,controls,newauxiliary);}apply{ifnUnitariesRight>0{MultiplexOperationsFromGeneratorImpl(rightUnitaries,[newauxiliary],newControls,target);}within{(ControlledX)(auxiliary,newauxiliary);}apply{MultiplexOperationsFromGeneratorImpl(leftUnitaries,[newauxiliary],newControls,target);}}}}}adjointauto;controlled(controlRegister,...){MultiplexOperationsFromGeneratorImpl(unitaryGenerator,auxiliary+controlRegister,index,target);}adjointcontrolledauto;}/// # Summary/// Applies multiply-controlled unitary operation $U$ that applies a/// unitary $V_j$ when controlled by n-qubit number state $\ket{j}$.////// $U = \sum^{N-1}_{j=0}\ket{j}\bra{j}\otimes V_j$.////// # Input/// ## unitaryGenerator/// A tuple where the first element `Int` is the number of unitaries $N$,/// and the second element `(Int -> ('T => () is Adj + Ctl))`/// is a function that takes an integer $j$ in $[0,N-1]$ and outputs the unitary/// operation $V_j$.////// ## index/// $n$-qubit control register that encodes number states $\ket{j}$ in/// little-endian format.////// ## target/// Generic qubit register that $V_j$ acts on.////// # Remarks/// `coefficients` will be padded with identity elements if/// fewer than $2^n$ are specified. This version is implemented/// directly by looping through n-controlled unitary operators.operationMultiplexOperationsBruteForceFromGenerator<'T>(unitaryGenerator:(Int,(Int->('T=>UnitisAdj+Ctl))),index:LittleEndian,target:'T):UnitisAdj+Ctl{letnIndex=Length(index!);letnStates=2^nIndex;let(nUnitaries,unitaryFunction)=unitaryGenerator;foridxOpin0..MinI(nStates,nUnitaries)-1{(ControlledOnInt(idxOp,unitaryFunction(idxOp)))(index!,target);}}/// # Summary/// Returns a multiply-controlled unitary operation $U$ that applies a/// unitary $V_j$ when controlled by n-qubit number state $\ket{j}$.////// $U = \sum^{2^n-1}_{j=0}\ket{j}\bra{j}\otimes V_j$.////// # Input/// ## unitaryGenerator/// A tuple where the first element `Int` is the number of unitaries $N$,/// and the second element `(Int -> ('T => () is Adj + Ctl))`/// is a function that takes an integer $j$ in $[0,N-1]$ and outputs the unitary/// operation $V_j$.////// # Output/// A multiply-controlled unitary operation $U$ that applies unitaries/// described by `unitaryGenerator`.////// # See Also/// - Microsoft.Quantum.Canon.MultiplexOperationsFromGeneratorfunctionMultiplexerFromGenerator(unitaryGenerator:(Int,(Int->(Qubit[]=>UnitisAdj+Ctl)))):((LittleEndian,Qubit[])=>UnitisAdj+Ctl){returnMultiplexOperationsFromGenerator(unitaryGenerator,_,_);}/// # Summary/// Returns a multiply-controlled unitary operation $U$ that applies a/// unitary $V_j$ when controlled by n-qubit number state $\ket{j}$.////// $U = \sum^{2^n-1}_{j=0}\ket{j}\bra{j}\otimes V_j$.////// # Input/// ## unitaryGenerator/// A tuple where the first element `Int` is the number of unitaries $N$,/// and the second element `(Int -> ('T => () is Adj + Ctl))`/// is a function that takes an integer $j$ in $[0,N-1]$ and outputs the unitary/// operation $V_j$.////// # Output/// A multiply-controlled unitary operation $U$ that applies unitaries/// described by `unitaryGenerator`.////// # See Also/// - Microsoft.Quantum.Canon.MultiplexOperationsBruteForceFromGeneratorfunctionMultiplexerBruteForceFromGenerator(unitaryGenerator:(Int,(Int->(Qubit[]=>UnitisAdj+Ctl)))):((LittleEndian,Qubit[])=>UnitisAdj+Ctl){returnMultiplexOperationsBruteForceFromGenerator(unitaryGenerator,_,_);}/// # Summary/// Computes a chain of AND gates////// # Description/// The auxiliary qubits to compute temporary results must be specified explicitly./// The length of that register is `Length(ctrlRegister) - 2`, if there are at least/// two controls, otherwise the length is 0.internaloperationApplyAndChain(auxRegister:Qubit[],ctrlRegister:Qubit[],target:Qubit):UnitisAdj{ifLength(ctrlRegister)==0{X(target);}elifLength(ctrlRegister)==1{CNOT(Head(ctrlRegister),target);}else{EqualityFactI(Length(auxRegister),Length(ctrlRegister));letcontrols1=ctrlRegister[0..0]+auxRegister;letcontrols2=Rest(ctrlRegister);lettargets=auxRegister+[target];ApplyToEachA(ApplyAnd,Zipped3(controls1,controls2,targets));}}}

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