Add another implementation for the "increment" function in the discrete quantum walk tutorial

[TomerGoldfriend]

The tutorial on Discrete Quantum Walks demonstrates an example of a quantum walk on a circle. The quantum_step_clockwise quantum function is implemented as a QFT-adder, however, there are other implementations available for such quantum operation, e.g., by applying a cascade of multi-controlled-X gates.

The goal of this issue is to add another implementation for the quantum_step_clockwise quantum function in the aforementioned tutorial.

Detailed guidelines:

1. Within the section "Example: Symmetric Quantum Walk on a Circle" in the notebook do the following:
   • Add a text explaining that in this example we will construct an implementation for the "clockwise_step"/"increment" function, which is different from the QFT-based implementation presented above.
   • Add a cell defining a new quantum function with the following declaration: qfunc increment(x: QArray[QBit]).
   • Use the new function in the specific example treated in the section.
   • Modify the synthesis constraints: optimize over depth with a relevant constraint over the width.
2. Under the "Technical Notes" section, add a short explanation about the implementation.
3. Make sure to generate a qmod (using the write_qmod function) for the modified example.
4. Make sure the notebook looks well, does not have any typos / mistakes, and is running properly.
5. Follow the contribution guidelines to open a pull request.

If you have any questions or comments, you can ask them here in the issue, or in our slack community, and the Classiq team will be happy to assist.

Happy quantum coding!

[TomerGoldfriend]

@AbdullahKazi500 Please see the description above. Let us know if you have any questions.

[AbdullahKazi500]

sure let me have a look

[AbdullahKazi500]

@TomerGoldfriend I have started the work on this

[TomerGoldfriend]

Great @AbdullahKazi500 ! let us know if you have any questions.