Tutorial: Implement a Quantum Random Number Generator in Q#

A simple example of a quantum algorithm written in Q# is a quantum random number generator. This algorithm leverages the nature of quantum mechanics to produce a random number.

Prerequisites

Write a Q# operation

Q# operation code

  1. Replace the contents of the Program.qs file with the following code:
namespace Qrng {
    open Microsoft.Quantum.Convert;
    open Microsoft.Quantum.Math;
    open Microsoft.Quantum.Measurement;
    open Microsoft.Quantum.Canon;
    open Microsoft.Quantum.Intrinsic;
    
    operation SampleQuantumRandomNumberGenerator() : Result {
        using (q = Qubit())  {  // Allocate a qubit.
            H(q);               // Put the qubit to superposition. It now has a 50% chance of being 0 or 1.
            return MResetZ(q);  // Measure the qubit value.
        }
    }

}

As mentioned in our Understanding quantum computing article, a qubit is a unit of quantum information that can be in superposition. When measured, a qubit can only be either 0 or 1. However, during execution the state of the qubit represents the probability of reading either a 0 or a 1 with a measurement. This probabilistic state is known as superposition. We can use this probability to generate random numbers.

In our Q# operation, we introduce the Qubit datatype, native to Q#. We can only allocate a Qubit with a using statement. When it gets allocated, a qubit is always in the Zero state.

Using the H operation, we are able to put our Qubit in superposition. To measure a qubit and read its value, you use the M intrinsic operation.

By putting our Qubit in superposition and measuring it, our result will be a different value each time the code is invoked.

When a Qubit is de-allocated it must be explicitly set back to the Zero state, otherwise the simulator will report a runtime error. An easy way to achieve this is invoking Reset.

Visualizing the code with the Bloch sphere

In the Bloch sphere, the north pole represents the classical value 0 and the south pole represents the classical value 1. Any superposition can be represented by a point on the sphere (represented by an arrow). The closer the end of the arrow to a pole the higher the probability the qubit collapses into the classical value assigned to that pole when measured. For example, the qubit state represented by the red arrow below has a higher probability of giving the value 0 if we measure it.

A qubit state with a high probability of measuring zero

We can use this representation to visualize what the code is doing:

  • First we start with a qubit initialized in the state 0 and apply H to create a superposition in which the probabilities for 0 and 1 are the same.
Preparing a qubit in superposition
  • Then we measure the qubit and save the output:
Measuring a qubit and saving the output

Since the outcome of the measurement is completely random, we have obtained a random bit. We can call this operation several times to create integers. For example, if we call the operation three times to obtain three random bits, we can build random 3-bit numbers (that is, a random number between 0 and 7).

Creating a complete random number generator

Now that we have a Q# operation that generates random bits, we can use it to build a complete quantum random number generator. We can use the Q# command line applications or use a host program.

To create the full Q# command line application, add the following entry point to your Q# program:

operation SampleRandomNumberInRange(max : Int) : Int {
    mutable bits = new Result[0];
    for (idxBit in 1..BitSizeI(max)) {
        set bits += [SampleQuantumRandomNumberGenerator()];
    }
    let sample = ResultArrayAsInt(bits);
    return sample > max
           ? SampleRandomNumberInRange(max)
           | sample;
}

@EntryPoint()
operation SampleRandomNumber() : Int {
    let max = 50;
    Message($"Sampling a random number between 0 and {max}: ");
    return SampleRandomNumberInRange(max);
}

The executable will run the operation or function marked with the @EntryPoint() attribute on a simulator or resource estimator, depending on the project configuration and command-line options.

namespace Qrng {
    open Microsoft.Quantum.Convert;
    open Microsoft.Quantum.Math;
    open Microsoft.Quantum.Measurement;
    open Microsoft.Quantum.Canon;
    open Microsoft.Quantum.Intrinsic;
    
    operation SampleQuantumRandomNumberGenerator() : Result {
        using (q = Qubit())  {  // Allocate a qubit.
            H(q);               // Put the qubit to superposition. It now has a 50% chance of being 0 or 1.
            return MResetZ(q);  // Measure the qubit value.
        }
    }

    operation SampleRandomNumberInRange(max : Int) : Int {
        mutable bits = new Result[0];
        for (idxBit in 1..BitSizeI(max)) {
            set bits += [SampleQuantumRandomNumberGenerator()];
        }
        let sample = ResultArrayAsInt(bits);
        return sample > max
               ? SampleRandomNumberInRange(max)
               | sample;
    }
    
    @EntryPoint()
    operation SampleRandomNumber() : Int {
        let max = 50;
        Message($"Sampling a random number between 0 and {max}: ");
        return SampleRandomNumberInRange(max);
    }
}

In Visual Studio, simply press Ctrl + F5 to execute the script.

In VS Code, build the Program.qs the first time by typing the below in the terminal:

dotnet build

For subsequent runs, there is no need to build it again. To run it, type the following command and press enter:

dotnet run --no-build