The Coxeter symmetries of high-level general sequential computation in the invertible-digital and quantum domains

The article investigates high-level general invertible-sequential processing in the digital and quantum domains. In particular it is shown that (i) invertible digital-sequential processes, constructed using a standard general-inversion procedure, and (ii) sequential quantum processes, determine Coxeter groups. In each case the groups are seen to define all processes that may be constructed from the, given, elemental processes of the sequences. Explicit forms of the presentations of the Coxeter groups are given for all cases. The quantum processes are seen to define unitary representations of the associated Coxeter groups in tensor-product qubit spaces.