Trying to learn about how to derive (& intuition) the complexity for a given algorithm as shown below. If there is any good reference or starting point that anyone can suggest that will be highly appreciated!
First, you need to get familiar with the notion of classical complexity and big-O notation. For this, I recommend:
- MIT 16.070 Big O notation lecture notes
- Computational Complexity: A Modern Approach
- The Complexity Zoo and links in the See Also section.
After getting a good grasp about classical complexity theory, you can start diving into quantum complexity theory. I recommend the following texts:
- Quantum Computational Complexity
- MIT 6.845 lecture notes. You may be tempted to skip the first few lectures from here, but I think all of them are worth reading to have a solid understanding of the fundamentals you'll need later on.
- Quantum Computing Since Democritus notes. There is also a book version, but that's not free. These notes may be a bit more informal, but very worth reading.