[ahelwer]

There are algorithms which involve advanced mathematics on classical computers, too. You don't have to understand them to understand how classical computers work. I've never bothered to learn the general number field sieve, and similarly I've never bothered to learn Shor's.

I say if you understand gates as unitary matrix multiplication, representing multiple qbits with the tensor product, entanglement, and projective measurement, you basically understand quantum computing. Throw in an algorithm or two to convince yourself of the benefits.

[chilukrn]

True, but: 1. Any serious quantum computing course/book will have Shor's algorithm in the first few chapters (in fact there are not a lot of quantum algorithms which have clear advantage over classical ones). One can teach quite a bit of useful classical algos (sort, binary search, tree/graph-based) without going into mathematics like FFT or jpeg coding.

2. Again valid, but IMHO measurements (and PoVMs) can lead to deep rabbit holes, and I found myself digging in much deeper.

Probably I should read easier expositions to see how effectively they teach. (I come from a EE+physics background, so I do gravitate to math-heavy rigorous explanations)