Computation beyond unitary matrices Just out of curiosity, if the classical computation is about permutation matrices and quantum computing is about unitary matrices (of which the permutation matrices are a subgroup), then will there be any computation paradigm beyond unitary matrices?
Circuits made out of general linear operators are $PP$-complete. See the PostBQP paper by Scott Aaronson  or Schuch's paper on the computational power of PEPS and tensor network contraction.