Issues with existing Select/Prepare Oracles

[fdmalone]

This might be a misunderstanding on my part, but currently we expect that the SelectOracle and PrepareOracle selection registers should match up (in terms of bitsizes) (this is assumed in #508), AND that the selection registers (from prepare) are those registers that we want to reflect about for constructing the walk operator. However, this leads to some awkward cases:

1. We typically perform a state preparation over a register (sigma) for alias sampling which needs to be reflected on, so it should be a selection register. Now Select would require this register as part of its signature (but won't act on it) and require knowledge of the bitsize.
2. For sparse state preparation we use a flat register to index non-zero matrix elements and the store the indices in another register (called $|ind_j\rangle$), this ind register doesn't need to be reflected on BUT the ind_j register is used a selection register for SELECT, so again there's some inconsistency.

A possible workaround would be to define black boxes which partition the incoming registers and only select the ones absolutely necessary for the gate, and then prepare should probably define a registers_for_reflection?

[fdmalone]

cc @tanujkhattar @mpharrigan

[mpharrigan]

What's the essence of the problem? We use PREPARE to create a state but certain parts of that state are reflect-only or use-as-index-only? And the current system assumes the prepared state is both the thing we want to reflect and the indices used for select?

[mpharrigan]

is my understanding of the issue (close to) correct?

[fdmalone]

yes that's right