Comment by amemi
4 hours ago
Don't let the terminology intimidate you. The interesting ideas in quantum computing are far more dependent upon a foundation in linear algebra rather than a foundation in mathematical analysis.
When I started out, I was under the assumption that I had to understand at least the undergraduate real analysis curriculum before I could grasp quantum algorithms. In reality, for the main QC algorithms you see discussed, you don't need to understand completeness; you can just treat a Hilbert space as a finite-dimensional vector space with a complex inner product.
For those unfamiliar with said concepts from linear algebra, there is a playlist [1] often recommended here which discusses them thoroughly.
[1] https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2x...
Yeah all the names and terminology really do make it seem harder than it is. Took me a long time and I’m still learning. 2d Hilbert space is same as 2d Euclidean space but each dimension has 2 degrees of freedom (real + imaginary). Might even think of it as 4d space, for vector imagining purposes, but that would probably be wrong and someone would call you out