I personally found this chapter very confusing, even with a good working knowledge of quantum computing - specifically the part about paths interfering destruct

I personally found this chapter very confusing, even with a good working knowledge of quantum computing - specifically the part about paths interfering destructively and canceling each other out. After a lot of thought and asking around I finally figured out what was going on with that diagram and wrote it up in a blog post: https://ahelwer.ca/post/2020-12-06-sum-over-paths/ https://ahelwer.ca/post/2020-12-06-sum-over-paths/ Basically there are two ways of looking at the model of quantum computation, commonly called the standard (or Schrödinger) and sum-over-paths (or Feynman) methods. In the standard method you keep a 2^n-sized state vector of amplitudes around and multiply it against matrices (gates). In the sum-over-paths method you only focus on specific amplitudes and trace them back through the gates, drawing in all the other amplitudes that contributed to the final amplitude value. In the end it's a basic time/space tradeoff - simulating quantum computers with the standard method takes less time but more space, and the sum-over-paths method takes more time but less space. Another advantage of the sum-over-paths method is you can actually see quantum interference happening when a negative & positive amplitude cancel each other out, which is just sort of swallowed up by the standard method. This is what the diagram is trying to illustrate.