Basic Unary Iteration / QROM

[mpharrigan]

unary iteration / qrom bloqs support a lot of features (multi-dimensional select; break) that obscure the key points of the design. They're also written cirq-style where each target op op[l] is a bundle of gates instead of one bloq per index. Writing an idiomatic "basic" 1d unary iteration and/or qrom bloq would be very instructive.

[mpharrigan]

A sketch of how this might look

class Set(Bloq):
  datum: int
  bitsize: int

  return Signature.build(x=bitsize)

  def decompose(bb, x):
    for bit in iter_bits(self.datum):
       if bit:
         bb.Add(XGate()

class ApplyL(Bloq):
  ops: List[Bloq]
  selection_bitsize: int = field(validator=len(ops) fits)
  target_bitsize: int

  return Signature.build(ctrl=1, selection=self.selection_bitsize, target=self.target_bitsize)

  def decompose(bb, ctrl, selection, target):
    selection = selection.split()
    l = 0
    for ...:
        # construct and ladder
        _, add_ctrl_op = self.ops[l].get_ctrl_system()
        s, target = add_ctrl_op(ctrl = [current selection bit], {'x': target})
        l += 1
        # unconstruct and ladder

qrom = ApplyL([Set(d, target_bitsize) for d in data], selection_bitsize, target_bitsize)

[tanujkhattar]

This should go in a tutorial notebook. We shouldn't have two QROM implementations.

[tanujkhattar]

After ApplyLthBloq and UnaryIterationGate, I think this can be closed. The "basic" unary iteration can be accessed using the ApplyLthBloq interface and power users can derive from UnaryIterationGate for more control.