As a young grad student, I remember going to a talk by Bennett where he explained how a Quantum Computer allows manipulation in a 2^N dimensional hilbert space, while the outputs measurements give you only N bits of information. The trick is to somehow encode the result in the final N bits.
I felt this was a much better layman explanation of what a quantum computer does than simply saying a quantum computer runs all possible paths in parallel.
> I felt this was a much better layman explanation of what a quantum computer does than simply saying a quantum computer runs all possible paths in parallel.
That comic is great I understand qubits a bit better now: it has 4 degrees of freedom but can be mapped onto the 2d surface of a sphere because of normalization (circle rule) and global phase symmetry which each take away one of the four DOF
I need a longer think on the interference/computation connection though
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.
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
I felt this was a much better layman explanation of what a quantum computer does than simply saying a quantum computer runs all possible paths in parallel.