>You realize quantum computing is ultimately just a few linear algebra operations right?

Quantum systems have wavefunctions though, which collapse to a state. And before collapse, these can interfere. The math of this involves way more than normal linear algebra. Especially when you consider the things we've simplified away -- e.g. how exactly the wave function collapses. (We just say it's 'abrupt' and kinda leave it there. But it's possible this has implications for quantum computing, once we think in quantum theory terms rather than CS.)