How does one obtain amplitude information in Q#?

Question

Is it possible to obtain amplitude information (in lexicographic ordering) for a particular qubit register in Q#?

For example, in the following code:

operation GetProbabilityAmplitude() : Double[]
{
    body
    {
        mutable result = new Double[4];
        using (register = Qubit[2])
        {
            H(register[0]);
            CNOT(register[0], register[1]);
            // ...put the amplitude doubles in the result array
        }
        return result;
    }
}

The doubles in result should be {0.5,0.0,0.0,0.5}. I looked quite a bit for it in the documentation but couldn't find anything about getting the amplitudes.

Answer 1

Yes, it is possible to obtain this information, but only for troubleshooting purposes, not for using it in the code.

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Dump functions dump the status of the target machine into a file or to the console output. If the program is executed on the full-state simulator, this status will include the wave function of the whole system (for DumpMachine) or of the register (for DumpRegister).

So you could do the following:

using (register = Qubit[2]) {
    H(register[0]);
    CNOT(register[0], register[1]);
    DumpMachine("");
    // to avoid ReleasedQubitsAreNotInZeroState exception
    ResetAll(register);
}

and get the following amplitudes (each one is a complex number):

Ids:    [1;0;]
Wavefunction:
0:      0.707107        0
1:      0       0
2:      0       0
3:      0.707107        0

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Note that this does not allow you to implement the GetProbabilityAmplitude() function which you requested. If you are running a Q# program on a simulator, it will let you see the wave function but it will not let you make any decisions in the program based on that information. The intent is twofold: to facilitate debugging on a simulator while not allowing to implement any logic which would be impossible to execute on a quantum computer. Since the execution on a quantum computer won't give the program direct access to the quantum state, it's better not to rely on this feature in the code.

Answer 2

I never looked at Q# but it looks like by using Dump functions you can output it. Hope this helps.