Grover's algorithm (Algorithm 1, in Section 2)

Continuation of Q# practice (Bell state).

Grover's algorithm described in Section 2, Algorithm 1.

In this example, Oracle is expressed just with Toffoli (CCNOT) gate, and this is not a general implementation, as far as I understand.

In the literature, they constructed CCNOT with natively supported gates, but Q# has it, and I just used it (control and ancillary are a bit confusing to me though).

By running my sample code the numbers of measurements observed in 1000 trials are;

00:0, 01:0, 10:0, 11:1000

Unlike the previous one, the result is completely the same as the theory.

I feel I should split Q# and C# parts in a better way.

In any case, I am getting used to it, hopefully.

Sample codes are;

Q# (Program.qs)

/// # Summary

/// 

namespace Grover {

    open Microsoft.Quantum.Canon;

    open Microsoft.Quantum.Intrinsic;

    

    operation Grover() : (Int,Int,Int,Int) {

        Message("This is Q# implementation of Algorithm 1 in Quantum Algorithm Implementaions for Beginners");

        mutable n00 = 0;

        mutable n01 = 0;

        mutable n10 = 0;

        mutable n11 = 0;

        for(trial in 1..1000){

        using ( (qubit0, qubit1, qubit2) = (Qubit(), Qubit(),Qubit()) ){

            // qubit0: ancillar

            // qubit1, 2: x1, x2

            //Initializaiton

            X(qubit0);

            H(qubit0);

            H(qubit1);

            H(qubit2);

            // qubit0 is called ancillar, looking at the following site and the article, it should be the target

            // https://quantumcomputing.stackexchange.com/questions/3943/how-do-you-implement-the-toffoli-gate-using-only-single-qubit-and-cnot-gates

            CCNOT(qubit1,qubit2,qubit0); //Toffoli gate

            // Grover diffusion operator

            H(qubit1);

            X(qubit1);

            H(qubit1);

            H(qubit2);

            X(qubit2);

            CNOT(qubit2,qubit1);

            H(qubit1);

            X(qubit1);

            H(qubit1);

            X(qubit2);

            H(qubit2);

            let res0 = M(qubit1);

            let res1 = M(qubit2);

            if(res0 == Zero){

                if(res1 == Zero){

                    set n00 += 1;

                }else{

                    set n01 += 1;

                }

            }else{

                if(res1 == Zero){

                    set n10 += 1;

                }else{

                    set n11 += 1;

                }

            }

            Reset(qubit0);

            Reset(qubit1);

            Reset(qubit2);

        }

        }

        return(n00,n01,n10,n11);

    }

}

C# (Driver.cs)

using System;

using Microsoft.Quantum.Simulation.Core;

using Microsoft.Quantum.Simulation.Simulators;

namespace Grover

{

    class Driver

    {

        static void Main(string[] args)

        {

            

            using (var qsim = new QuantumSimulator())

            {

                long a,b,c,d;

                (a,b,c,d) = Grover.Run(qsim).Result;

                Console.WriteLine("{0},{1},{2},{3}",a,b,c,d);

            }

        }

    }

}