[BUG] TextbookQPE does not decompose successfully

[austingmhuang]

Expected Behavior:
We expect TextbookQPE().decompose_bloq() to execute without error

Actual Behavior:
When we combine GQSP with QPE, we get a ValueError when we try decompose_bloq()

from qualtran.bloqs.phase_estimation import RectangularWindowState, TextbookQPE
from qualtran.bloqs.hamiltonian_simulation.hamiltonian_simulation_by_gqsp import HamiltonianSimulationByGQSP
from qualtran.bloqs.chemistry.hubbard_model.qubitization import (
    get_walk_operator_for_hubbard_model,
)

walk_op = get_walk_operator_for_hubbard_model(2, 2, 1, 1)
hubbard_time_evolution_by_gqsp = HamiltonianSimulationByGQSP(walk_op, t=5, precision=1e-7)

textbook_qpe_w_gqsp = TextbookQPE(hubbard_time_evolution_by_gqsp, RectangularWindowState(3))

textbook_qpe_w_gqsp.decompose_bloq()

Raises:
ValueError: Cannot control channel with non-unitary operators: bloq.HamiltonianSimulationByGQSP

[mpharrigan]

After an initial look at this, the cirq-style .controlled_by method is doing some validation logic that fails for BloqAsCirqGate(HamiltonianSimulationByGQSP). I don't know why that validation logic fails. Really, we should be using native-qualtran idioms for "textbook" qpe

[mpharrigan]

I guess the issue was never updated, but it was pointed out to me that this is triggered by the issue in #1488

The cirq.Gate.controlled_by method wants to assert that the gate being controlled is unitary, so it tries to compute the unitary which causes it to start decomposing things and trying to find their unitary at each step. This fails outright in this case because we get to an AND AND^dag construction, whose parts aren't unitary. I saw this crop up somewhere else where the code just hung on the validation logic.

Anyways, I think this is fixed by implementing BloqAsCirqGate._has_unitary_ shortcut; and we can just say "yes if all thru registers" and it won't start recursing.

[mpharrigan]

(but I think we should also still use qualtran idioms for our textbook implementation of such an algorithm, and then we won't run into these interop-back-and-forth issues)