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class qiskit.circuit.library.RGQFTMultiplier(num_state_qubits, num_result_qubits=None, name='RGQFTMultiplier')

GitHub(opens in a new tab)

Bases: 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/2) │  iqft │
out_1:1     ├─────────■───────────────■──────────────■─────────────■───────┤1
       └──────┘                                                              └───────┘


[1] Ruiz-Perez et al., Quantum arithmetic with the Quantum Fourier Transform, 2017. arXiv:1411.5949(opens in a new tab)


  • num_state_qubits (int(opens in a new tab)) – The number of qubits in either input register for state a|a\rangle or b|b\rangle. The two input registers must have the same number of qubits.
  • num_result_qubits (int(opens in a new tab) | None) – The number of result qubits to limit the output to. If number of result qubits is nn, multiplication modulo 2n2^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(opens in a new tab)) – The name of the circuit object.



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


Return calibration dictionary.

The custom pulse definition of a given gate is of the form {'gate_name': {(qubits, params): schedule}}


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


Return the circuit data (instructions and context).


a list-like object containing the CircuitInstructions for each instruction.

Return type



Default value: 'include "";'


Return the global phase of the current circuit scope in radians.

Default value: 'OPENQASM 2.0;'


Default value: 474


Return any associated layout information about the circuit

This attribute contains an optional TranspileLayout object. This is typically set on the output from transpile() or to retain information about the permutations caused on the input circuit by transpilation.

There are two types of permutations caused by the transpile() function, an initial layout which permutes the qubits based on the selected physical qubits on the Target, and a final layout which is an output permutation caused by SwapGates inserted during routing.


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 the number of ancilla qubits.


Return number of classical bits.


The number of parameter objects in the circuit.


Return number of qubits.


The number of result qubits to limit the output to.


The number of result qubits.


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


The number of state qubits.


Return a list of operation start times.

This attribute is enabled once one of scheduling analysis passes runs on the quantum circuit.


List of integers representing instruction start times. The index corresponds to the index of instruction in


AttributeError(opens in a new tab) – When circuit is not scheduled.


The parameters defined in the circuit.

This attribute returns the Parameter objects in the circuit sorted alphabetically. Note that parameters instantiated with a ParameterVector are still sorted numerically.


The snippet below shows that insertion order of parameters does not matter.

>>> from qiskit.circuit import QuantumCircuit, Parameter
>>> a, b, elephant = Parameter("a"), Parameter("b"), Parameter("elephant")
>>> circuit = QuantumCircuit(1)
>>> circuit.rx(b, 0)
>>> circuit.rz(elephant, 0)
>>> circuit.ry(a, 0)
>>> circuit.parameters  # sorted alphabetically!
ParameterView([Parameter(a), Parameter(b), Parameter(elephant)])

Bear in mind that alphabetical sorting might be unintuitive when it comes to numbers. The literal “10” comes before “2” in strict alphabetical sorting.

>>> from qiskit.circuit import QuantumCircuit, Parameter
>>> angles = [Parameter("angle_1"), Parameter("angle_2"), Parameter("angle_10")]
>>> circuit = QuantumCircuit(1)
>>> circuit.u(*angles, 0)
>>> circuit.draw()
>>> circuit.parameters
ParameterView([Parameter(angle_1), Parameter(angle_10), Parameter(angle_2)])

To respect numerical sorting, a ParameterVector can be used.

>>> from qiskit.circuit import QuantumCircuit, Parameter, ParameterVector
>>> x = ParameterVector("x", 12)
>>> circuit = QuantumCircuit(1)
>>> for x_i in x:
...     circuit.rx(x_i, 0)
>>> circuit.parameters
    ParameterVectorElement(x[0]), ParameterVectorElement(x[1]),
    ParameterVectorElement(x[2]), ParameterVectorElement(x[3]),
    ..., ParameterVectorElement(x[11])


The sorted Parameter objects in the circuit.


Default value: 'circuit'


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

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