definition of _add_ctrled is too restrictive

[NoureldinYosri]

The second return return value of get_ctrl_system is _add_ctrled which is defined as

https://github.com/quantumlib/Qualtran/blob/a4365b26a01956bb0341f12e673176e3a66ab33b/qualtran/_infra/bloq.py#L384C33-L389

This definition is too restrictive since it assumes that no new registers may be created which is not true. for example And().controlled() should be MultiAnd which creates an extra junk register.

[mpharrigan]

I think this is out of scope for the notion of a "controlled" operation.

Controlled(A) = $\ket{0}\bra{0}\otimes I + \ket{1}\bra{1} \otimes A$

[mpharrigan]

@NoureldinYosri can you provide more context on your use case

[mpharrigan]

I wrote some more here: #1304 (comment)

The contract (irrespective of whether the registers are RIGHT or THRU) is that the controlled version can only add new registers that comport with CtrlSpec.qdtypes. The system has no idea what to do with the extra junk registers. If you wanted to encode the idea that "this junk needs to get cleaned up by And^dag" you'd use something like #1221