Q Sharp

// 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));            let controls1 = ctrlRegister[0..0] + auxRegister;            let controls2 = Rest(ctrlRegister);            let targets = auxRegister + [target];            ApplyToEachA(ApplyAnd, Zipped3(controls1, controls2, targets));        }    }}