Arithmetic circuit library: multipliers

[mantcep]

Summary

Part of qiskit-community/qiskit-advocate-mentorship-program#12 with @Cryoris and @ManjulaGandhi.

Add a new circuit library submodule to perform classical multiplication of two equally-sized
qubit registers including:

• RGQFTMultiplier (from https://arxiv.org/pdf/1411.5949.pdf)
• HRSCumulativeMultiplier (from https://arxiv.org/pdf/1805.12445.pdf)

Details and comments

Example:

from qiskit.circuit import QuantumCircuit
from qiskit.circuit.library import RGQFTMultiplier
from qiskit.quantum_info import Statevector

num_state_qubits = 2

# a encodes |11> = 3
a = QuantumCircuit(num_state_qubits)
a.x(range(num_state_qubits))

# b encodes |11> = 3
b = QuantumCircuit(num_state_qubits)
b.x(range(num_state_qubits))

# multiplier on 2-bit numbers
multiplier = RGQFTMultiplier(num_state_qubits)

# add the state preparations to the front of the circuit
multiplier.compose(a, [0, 1], inplace=True, front=True)
multiplier.compose(b, [2, 3], inplace=True, front=True)

# simulate and get the state of all qubits
sv = Statevector(multiplier)
counts = sv.probabilities_dict(decimals=10)
state = list(counts.keys())[0]  # we only have a single state

# skip both input registers
result = state[:-2*num_state_qubits]
print(result)  # '1001' = 9 = 3 * 3

[Cryoris]

LGTM thanks for the contribution @mantcep!

[mantcep]

Thanks @Cryoris, really appreciate your help on the PR 🙂