# RGQFTMultiplier¶

class RGQFTMultiplier(num_state_qubits, num_result_qubits=None, name='RGQFTMultiplier')[source]

Bases: qiskit.circuit.library.arithmetic.multipliers.multiplier.Multiplier

A QFT multiplication circuit to store product of two input registers out-of-place.

Multiplication in this circuit is implemented using the procedure of Fig. 3 in [1], where weighted sum rotations are implemented as given in Fig. 5 in [1]. QFT is used on the output register and is followed by rotations controlled by input registers. The rotations transform the state into the product of two input registers in QFT base, which is reverted from QFT base using inverse QFT. As an example, a circuit that performs a modular QFT multiplication on two 2-qubit sized input registers with an output register of 2 qubits, is as follows:

  a_0: ────────────────────────────────────────■───────■──────■──────■────────────────
│       │      │      │
a_1: ─────────■───────■───────■───────■──────┼───────┼──────┼──────┼────────────────
│       │       │       │      │       │      │      │
b_0: ─────────┼───────┼───────■───────■──────┼───────┼──────■──────■────────────────
│       │       │       │      │       │      │      │
b_1: ─────────■───────■───────┼───────┼──────■───────■──────┼──────┼────────────────
┌──────┐ │P(4π)  │       │P(2π)  │      │P(2π)  │      │P(π)  │       ┌───────┐
out_0: ┤0     ├─■───────┼───────■───────┼──────■───────┼──────■──────┼───────┤0      ├
│  qft │         │P(2π)          │P(π)          │P(π)         │P(π/2) │  iqft │
out_1: ┤1     ├─────────■───────────────■──────────────■─────────────■───────┤1      ├
└──────┘                                                              └───────┘


References:

[1] Ruiz-Perez et al., Quantum arithmetic with the Quantum Fourier Transform, 2017. arXiv:1411.5949

Parameters
• num_state_qubits (int) – The number of qubits in either input register for state $$|a\rangle$$ or $$|b\rangle$$. The two input registers must have the same number of qubits.

• num_result_qubits (Optional[int]) – The number of result qubits to limit the output to. If number of result qubits is $$n$$, multiplication modulo $$2^n$$ is performed to limit the output to the specified number of qubits. Default value is 2 * num_state_qubits to represent any possible result from the multiplication of the two inputs.

• name (str) – The name of the circuit object.

Attributes

ancillas

Returns a list of ancilla bits in the order that the registers were added.

Return type

List[AncillaQubit]

calibrations

Return calibration dictionary.

The custom pulse definition of a given gate is of the form

{‘gate_name’: {(qubits, params): schedule}}

Return type

dict

clbits

Returns a list of classical bits in the order that the registers were added.

Return type

List[Clbit]

data

Return the circuit data (instructions and context).

Returns

a list-like object containing the tuples for the circuit’s data.

Each tuple is in the format (instruction, qargs, cargs), where instruction is an Instruction (or subclass) object, qargs is a list of Qubit objects, and cargs is a list of Clbit objects.

Return type

QuantumCircuitData

extension_lib = 'include "qelib1.inc";'
global_phase

Return the global phase of the circuit in radians.

Return type

Union[ParameterExpression, float]

instances = 9

The user provided metadata associated with the circuit

The metadata for the circuit is a user provided dict of metadata for the circuit. It will not be used to influence the execution or operation of the circuit, but it is expected to be passed between all transforms of the circuit (ie transpilation) and that providers will associate any circuit metadata with the results it returns from execution of that circuit.

Return type

dict

num_ancillas

Return the number of ancilla qubits.

Return type

int

num_clbits

Return number of classical bits.

Return type

int

num_parameters

Convenience function to get the number of parameter objects in the circuit.

Return type

int

num_qubits

Return number of qubits.

Return type

int

num_result_qubits

The number of result qubits to limit the output to.

Return type

int

Returns

The number of result qubits.

num_state_qubits

The number of state qubits, i.e. the number of bits in each input register.

Return type

int

Returns

The number of state qubits.

parameters

Convenience function to get the parameters defined in the parameter table.

Return type

ParameterView

prefix = 'circuit'
qubits

Returns a list of quantum bits in the order that the registers were added.

Return type

List[Qubit]