Q 샤프

Q 샤프(Q#)는 양자 알고리즘을 표현하기 위해 사용되는 도메인 특화 언어이다. 양자 개발 키트의 일부로서 마이크로소프트가 처음 공개하였다. 다음의 소스 코드는 공식 마이크로소프트 Q# 라이브러리 저장소에서 가져온 멀티플렉서이다. // Copyright (c) Microsoft Corporation. // Licensed under the MIT License. namespace Microsoft.Quantum.Canon { open Microsoft.Quantum.Intrinsic; open Microsoft.Quantum.Arithmetic; open Microsoft.Quantum.Arrays; open Microsoft.Quantum.Diagnostics; open Microsoft.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) operation MultiplexOperationsFromGenerator<'T>(unitaryGenerator : (Int, (Int -> ('T => Unit is Adj + Ctl))), index: LittleEndian, target: 'T) : Unit is Ctl + Adj { let (nUnitaries, unitaryFunction) = unitaryGenerator; let unitaryGeneratorWithOffset = (nUnitaries, 0, unitaryFunction); if Length(index!) == 0 { fail "MultiplexOperations failed. Number of index qubits must be greater than 0."; } if nUnitaries > 0 { let auxiliary = []; Adjoint MultiplexOperationsFromGeneratorImpl(unitaryGeneratorWithOffset, auxiliary, index, target); } } /// # Summary /// Implementation step of `MultiplexOperationsFromGenerator`. /// # See Also /// - Microsoft.Quantum.Canon.MultiplexOperationsFromGenerator internal operation MultiplexOperationsFromGeneratorImpl<'T>(unitaryGenerator : (Int, Int, (Int -> ('T => Unit is Adj + Ctl))), auxiliary: Qubit[], index: LittleEndian, target: 'T) : Unit { body (...) { let nIndex = Length(index!); let nStates = 2^nIndex; let (nUnitaries, unitaryOffset, unitaryFunction) = unitaryGenerator; let nUnitariesLeft = MinI(nUnitaries, nStates / 2); let nUnitariesRight = MinI(nUnitaries, nStates); let leftUnitaries = (nUnitariesLeft, unitaryOffset, unitaryFunction); let rightUnitaries = (nUnitariesRight - nUnitariesLeft, unitaryOffset + nUnitariesLeft, unitaryFunction); let newControls = LittleEndian(Most(index!)); if nUnitaries > 0 { if Length(auxiliary) == 1 and nIndex == 0 { // Termination case (Controlled Adjoint (unitaryFunction(unitaryOffset)))(auxiliary, target); } elif Length(auxiliary) == 0 and nIndex >= 1 { // Start case let newauxiliary = Tail(index!); if nUnitariesRight > 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. let controls = [Tail(index!)] + auxiliary; use newauxiliary = Qubit(); use andauxiliary = Qubit[MaxI(0, Length(controls) - 2)]; within { ApplyAndChain(andauxiliary, controls, newauxiliary); } apply { if nUnitariesRight > 0 { MultiplexOperationsFromGeneratorImpl(rightUnitaries, [newauxiliary], newControls, target); } within { (Controlled X)(auxiliary, newauxiliary); } apply { MultiplexOperationsFromGeneratorImpl(leftUnitaries, [newauxiliary], newControls, target); } } } } } adjoint auto; controlled (controlRegister, ...) { MultiplexOperationsFromGeneratorImpl(unitaryGenerator, auxiliary + controlRegister, index, target); } adjoint controlled auto; } /// # 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. operation MultiplexOperationsBruteForceFromGenerator<'T>(unitaryGenerator : (Int, (Int -> ('T => Unit is Adj + Ctl))), index: LittleEndian, target: 'T) : Unit is Adj + Ctl { let nIndex = Length(index!); let nStates = 2^nIndex; let (nUnitaries, unitaryFunction) = unitaryGenerator; for idxOp in 0..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.MultiplexOperationsFromGenerator function MultiplexerFromGenerator(unitaryGenerator : (Int, (Int -> (Qubit[] => Unit is Adj + Ctl)))) : ((LittleEndian, Qubit[]) => Unit is Adj + Ctl) { return MultiplexOperationsFromGenerator(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.MultiplexOperationsBruteForceFromGenerator function MultiplexerBruteForceFromGenerator(unitaryGenerator : (Int, (Int -> (Qubit[] => Unit is Adj + Ctl)))) : ((LittleEndian, Qubit[]) => Unit is Adj + Ctl) { return MultiplexOperationsBruteForceFromGenerator(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. internal operation ApplyAndChain(auxRegister : Qubit[], ctrlRegister : Qubit[], target : Qubit) : Unit is Adj { if Length(ctrlRegister) == 0 { X(target); } elif Length(ctrlRegister) == 1 { CNOT(Head(ctrlRegister), target); } else { EqualityFactI(Length(auxRegister), Length(ctrlRegister) - 2, "Unexpected number of auxiliary qubits"); let controls1 = ctrlRegister[0..0] + auxRegister; let controls2 = Rest(ctrlRegister); let targets = auxRegister + [target]; ApplyToEachA(ApplyAnd, Zipped3(controls1, controls2, targets)); } } } “Introduction to Q#” (PDF). University of Washington.  QuantumWriter. “The Q# Programming Language”. 《docs.microsoft.com》 (미국 영어). 2017년 12월 11일에 확인함.  “Announcing the Microsoft Quantum Development Kit” (미국 영어). 2017년 12월 11일에 확인함.  Q 샤프 - 공식 웹사이트 (영어) qsharp-language - 깃허브