Whatever a person can compute by following rules, a simple machine can compute, reading and writing symbols on a tape. And a single machine, given a description of any other on its tape, can do whatever that machine does: one universal machine can compute anything that can be computed at all.
Every physical system that can be built can be perfectly simulated by a universal computer working by finite means – but only by a quantum one. A universal quantum computer can do whatever any physical machine can do, and some things far faster than any classical computer could.