Improved decomposition for OutMultiplier

[dwierichs]

Context:
Currently, OutMultiplier is implemented via doubly-controlled sequences of PhaseAdders and QFTs.

Description of the Change:
Implement the "textbook" variant of multiplication as performed by hand. This uses SemiAdders instead.

Benefits:
Significantly cheaper quantum cost of OutMultiplier, as long as num_y_wires zeroed auxiliary wires are available.
See below for an example.

Possible Drawbacks:
N/A

Related GitHub Issues:

import pennylane as qml
from pennylane.templates.subroutines.arithmetic.out_multiplier import _out_multiplier_decomposition, _out_multiplier_with_adders

qml.decomposition.enable_graph()
k = 4
x_wires = list(range(k))
y_wires = list(range(k, 2*k))
out_wires = list(range(2*k, 4*k))
work_wires = list(range(4*k, 5*k))

gate_set_phase_adder = {
    "QFT",
    "Adjoint(QFT)",
    "C(PhaseShift)",
    "CNOT",
    "PauliX",
}

gate_set_adder = {
    "Toffoli",
    "TemporaryAND",
    "Adjoint(TemporaryAND)",
    "CNOT", 
    "Hadamard",
}

@qml.transforms.decompose(gate_set=gate_set_phase_adder)
@qml.qnode(qml.device("null.qubit", wires=5*k))
def func_phase_adder(k):
    _out_multiplier_decomposition(x_wires, y_wires, out_wires, work_wires=work_wires, mod=None)

@qml.transforms.decompose(gate_set=gate_set_adder)
@qml.qnode(qml.device("null.qubit", wires=5*k))
def func_adder(k):
    _out_multiplier_with_adders(x_wires, y_wires, out_wires, work_wires=work_wires, mod=None)

>>> print("Resources for phase-adder implementation:")
>>> print(qml.specs(func_phase_adder)(k)["resources"].gate_types)
>>> print("Resources for adder implementation:")
>>> print(qml.specs(func_adder)(k)["resources"].gate_types)
Resources for phase-adder implementation:
{'QFT': 1, '2C(PhaseShift)': 2025, 'Adjoint(QFT)': 1}
Resources for adder implementation:
{'TemporaryAND': 16, 'CNOT': 72, 'Toffoli': 20, 'Adjoint(TemporaryAND)': 16}