--- title: RGQFTMultiplier (v0.46) description: API reference for qiskit.circuit.library.RGQFTMultiplier in qiskit v0.46 source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/qiskit/0.46/qiskit.circuit.library.RGQFTMultiplier --- # RGQFTMultiplier *class* `qiskit.circuit.library.RGQFTMultiplier(num_state_qubits, num_result_qubits=None, name='RGQFTMultiplier')` [GitHub](https://github.com/qiskit/qiskit/tree/stable/0.46/qiskit/circuit/library/arithmetic/multipliers/rg_qft_multiplier.py) 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: ```python 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](https://arxiv.org/pdf/1411.5949.pdf) **Parameters** - **num\_state\_qubits** ([*int*](https://docs.python.org/3/library/functions.html#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** ([*int*](https://docs.python.org/3/library/functions.html#int) *| None*) – 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*](https://docs.python.org/3/library/stdtypes.html#str)) – The name of the circuit object. ## Attributes ### ancillas Returns a list of ancilla bits in the order that the registers were added. ### calibrations Return calibration dictionary. The custom pulse definition of a given gate is of the form `{'gate_name': {(qubits, params): schedule}}` ### clbits Returns a list of classical bits in the order that the registers were added. ### data Return the circuit data (instructions and context). **Returns** a list-like object containing the [`CircuitInstruction`](/docs/api/qiskit/0.46/qiskit.circuit.CircuitInstruction "qiskit.circuit.CircuitInstruction")s for each instruction. **Return type** QuantumCircuitData ### extension\_lib Default value: `'include "qelib1.inc";'` ### global\_phase Return the global phase of the current circuit scope in radians. ### header Default value: `'OPENQASM 2.0;'` ### instances Default value: `456` ### layout Return any associated layout information about the circuit This attribute contains an optional [`TranspileLayout`](/docs/api/qiskit/0.46/qiskit.transpiler.TranspileLayout "qiskit.transpiler.TranspileLayout") object. This is typically set on the output from [`transpile()`](/docs/api/qiskit/0.46/compiler#qiskit.compiler.transpile "qiskit.compiler.transpile") or [`PassManager.run()`](/docs/api/qiskit/0.46/qiskit.transpiler.PassManager#run "qiskit.transpiler.PassManager.run") to retain information about the permutations caused on the input circuit by transpilation. There are two types of permutations caused by the [`transpile()`](/docs/api/qiskit/0.46/compiler#qiskit.compiler.transpile "qiskit.compiler.transpile") function, an initial layout which permutes the qubits based on the selected physical qubits on the [`Target`](/docs/api/qiskit/0.46/qiskit.transpiler.Target "qiskit.transpiler.Target"), and a final layout which is an output permutation caused by [`SwapGate`](/docs/api/qiskit/0.46/qiskit.circuit.library.SwapGate "qiskit.circuit.library.SwapGate")s inserted during routing. ### metadata 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. ### num\_ancillas Return the number of ancilla qubits. ### num\_clbits Return number of classical bits. ### num\_parameters The number of parameter objects in the circuit. ### num\_qubits Return number of qubits. ### num\_result\_qubits The number of result qubits to limit the output to. **Returns** The number of result qubits. ### num\_state\_qubits The number of state qubits, i.e. the number of bits in each input register. **Returns** The number of state qubits. ### op\_start\_times Return a list of operation start times. This attribute is enabled once one of scheduling analysis passes runs on the quantum circuit. **Returns** List of integers representing instruction start times. The index corresponds to the index of instruction in `QuantumCircuit.data`. **Raises** [**AttributeError**](https://docs.python.org/3/library/exceptions.html#AttributeError) – When circuit is not scheduled. ### parameters The parameters defined in the circuit. This attribute returns the [`Parameter`](/docs/api/qiskit/0.46/qiskit.circuit.Parameter "qiskit.circuit.Parameter") objects in the circuit sorted alphabetically. Note that parameters instantiated with a [`ParameterVector`](/docs/api/qiskit/0.46/qiskit.circuit.ParameterVector "qiskit.circuit.ParameterVector") are still sorted numerically. **Examples** The snippet below shows that insertion order of parameters does not matter. ```python >>> 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. ```python >>> 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() ┌─────────────────────────────┐ q: ┤ U(angle_1,angle_2,angle_10) ├ └─────────────────────────────┘ >>> circuit.parameters ParameterView([Parameter(angle_1), Parameter(angle_10), Parameter(angle_2)]) ``` To respect numerical sorting, a [`ParameterVector`](/docs/api/qiskit/0.46/qiskit.circuit.ParameterVector "qiskit.circuit.ParameterVector") can be used. ```python ``` ```python >>> 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 ParameterView([ ParameterVectorElement(x[0]), ParameterVectorElement(x[1]), ParameterVectorElement(x[2]), ParameterVectorElement(x[3]), ..., ParameterVectorElement(x[11]) ]) ``` **Returns** The sorted [`Parameter`](/docs/api/qiskit/0.46/qiskit.circuit.Parameter "qiskit.circuit.Parameter") objects in the circuit. ### prefix Default value: `'circuit'` ### qubits Returns a list of quantum bits in the order that the registers were added.