Exercise - Create a quantum random number generator - Training

10 minutes

In this section, you implement the second phase of your quantum random number generator: combining multiple random bits to form a larger number to use as a valid and secure password. This phase builds on the random bit generator that you already created. You'll need to write some classical code for this phase.

First, let's see how classical code fits in with Q#.

Can I write classical code in Q#?

Yes, you can. Quantum computers perform specialized tasks. You don't use a quantum computer for everything because, for many tasks, classical computers work fine.

Just like a graphics processing unit (GPU) or other specialized hardware, you want to use a quantum computer for the tasks they're best suited for. In this case, you want to produce purely random bits.

This is why Q# also enables you to write classical code that resembles programming languages you already know.

Let's see how we can use Q# features to build a complete random number generator.

Define the random number generator logic

Before we continue, let's outline what the logic of a random number generator should be, provided we have a random bit generator:

Define max as the maximum number you want to generate.
Define the number of random bits that you need to generate. This is done by calculating how many bits, nBits, we need to express integers up to max.
Generate a random bit string that's nBits in length.
If the bit string represents a number greater than max, go back to step three.
Otherwise, the process is complete. Return the generated number as an integer.

As an example, let's set max to 12. That is, 12 is the largest number you want to use as a secure password.

You need ${\lfloor ln(12) / ln(2) + 1 \rfloor}$, or 4 bits to represent a number between 0 and 12. (For brevity, we'll skip how to derive this equation.)

Let's say you generate the bit string ${1101_{\ binary}}$, which is equivalent to ${13_{\ decimal}}$. Because 13 is greater than 12, you repeat the process.

Next, you generate the bit string ${0110_{\ binary}}$, which is equivalent to ${6_{\ decimal}}$. Because 6 is less than 12, the process is complete.

The QRNG will return number 6 as your password. In practice, set a larger number as the maximum because lower numbers are easy to crack by just trying all possible passwords. In fact, to increase the difficulty of guessing or cracking your password, you could use ASCII code to convert binary to text and to generate a password by using numbers, symbols, and mixed-case letters.

Now you can be sure that your passwords are truly random. Space fleet data and their facilities are protected with the highest security standards.

With our logic in place, you're now ready to build a complete random number generator.

Create the SampleRandomNumberInRange operation

Here, you expand on the QuantumRNG project to build larger random numbers.

Add the required libraries

For the complete random number generator, you need to include two other libraries: Microsoft.Quantum.Math and Microsoft.Quantum.Convert. Add the following open directives to Program.qs, like this:

namespace QuantumRNG {

    open Microsoft.Quantum.Canon;
    open Microsoft.Quantum.Intrinsic;
    open Microsoft.Quantum.Measurement;
    open Microsoft.Quantum.Math;
    open Microsoft.Quantum.Convert;

    @EntryPoint()
    operation GenerateRandomBit() : Result {
        // Allocate a qubit.
        use q = Qubit();
        // Put the qubit to superposition.
        H(q);
        // It now has a 50% chance of being measured 0 or 1.
        // Measure the qubit value.
        return M(q);
    }
}

Define the operation

Here, you define the SampleRandomNumberInRange operation. This operation repeatedly calls the GenerateRandomBit operation to build a string of bits.

Modify Program.qs like this:

namespace QuantumRNG {

    open Microsoft.Quantum.Canon;
    open Microsoft.Quantum.Intrinsic;
    open Microsoft.Quantum.Measurement;
    open Microsoft.Quantum.Math;
    open Microsoft.Quantum.Convert;

    operation GenerateRandomBit() : Result {
        // Allocate a qubit.
        use q = Qubit(); 
        // Put the qubit to superposition.
        H(q);
        // It now has a 50% chance of being measured 0 or 1.
        // Measure the qubit value.
        return M(q);
    }

    operation SampleRandomNumberInRange(max : Int) : Int {
        mutable output = 0; 
        repeat {
            mutable bits = []; 
            for idxBit in 1..BitSizeI(max) {
                set bits += [GenerateRandomBit()]; 
            }
            set output = ResultArrayAsInt(bits);
        } until (output <= max);
        return output;
    }
}

Let's take a moment to review the new code.

Recall that we need to calculate the number of bits we need to express integers up to max. The Microsoft.Quantum.Math library provides the BitSizeI function to accomplish this task.

The SampleRandomNumberInRange operation uses a repeat loop to generate random numbers until it generates one that's equal to or less than max.

The for loop inside repeat works exactly the same as a for loop in other programming languages.

In this example, output and bits are mutable variables. A mutable variable is one that can change during the computation. You use the set directive to change a mutable variable's value.

The ResultArrayAsInt function comes from the Microsoft.Quantum.Convert library. This function converts the bit string to a positive integer.

Define the entry point

Your program can now generate random numbers. Here, you define the entry point for your program.

Modify Program.qs like this:

namespace QuantumRNG {

    open Microsoft.Quantum.Canon;
    open Microsoft.Quantum.Intrinsic;
    open Microsoft.Quantum.Measurement;
    open Microsoft.Quantum.Math;
    open Microsoft.Quantum.Convert;

    operation GenerateRandomBit() : Result {
        // Allocate a qubit.
        use q = Qubit();
        // Put the qubit to superposition.
        H(q);
        // It now has a 50% chance of being measured 0 or 1.
        // Measure the qubit value.
        return M(q);
    }

    operation SampleRandomNumberInRange(max : Int) : Int {
        mutable output = 0; 
        repeat {
            mutable bits = []; 
            for idxBit in 1..BitSizeI(max) {
                set bits += [GenerateRandomBit()]; 
            }
            set output = ResultArrayAsInt(bits);
        } until (output <= max);
        return output;
    }

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

The let directive declares variables that don't change during the computation. For learning purposes, here we define the maximum value as 50.

Note

This code snippet does not currently run on any available Azure Quantum hardware targets, as the callable ResultArrayAsInt requires a QPU with full computation profile.

Learn module code that does not feature such a notice is executable on current hardware targets.

Run the program

Let's try out our new random number generator!

In Visual Studio Code, run dotnet run from the integrated terminal:
```
dotnet run
```
Here's sample output:
```
Sampling a random number between 0 and 50:
42
```
The computation might produce numbers that are greater than 50. But the repeat loop retries the operation until it produces a number that's 50 or less.
As an optional step, run the program again like this:
```
dotnet run --no-build
```
(If you make changes to the code, you need to omit the --no-build argument to rebuild your program.)

Here's sample output:
```
Sampling a random number between 0 and 50: 
10
```

Congratulations! Now you know how to combine classical logic with Q# to create a quantum random number generator.

Bonus exercise

Modify the program to also require the generated random number to be greater than some minimum number, min, instead of zero.

In the next unit, you'll learn more about the structure Q# programs in general and the basic building blocks of quantum computing.

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