---
title: HRSCumulativeMultiplier (latest version)
description: API reference for qiskit.circuit.library.HRSCumulativeMultiplier in the latest version of qiskit
source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/qiskit/qiskit.circuit.library.HRSCumulativeMultiplier
---

# HRSCumulativeMultiplier

*class* `qiskit.circuit.library.HRSCumulativeMultiplier(num_state_qubits, num_result_qubits=None, adder=None, name='HRSCumulativeMultiplier')`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/circuit/library/arithmetic/multipliers/hrs_cumulative_multiplier.py#L21-L145)

Bases: `Multiplier`

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

Circuit uses the approach from \[1]. As an example, a multiplier circuit that performs a non-modular multiplication on two 3-qubit sized registers with the default adder is as follows (where `Adder` denotes the `CDKMRippleCarryAdder`):

```text
  a_0: ────■─────────────────────────
           │
  a_1: ────┼─────────■───────────────
           │         │
  a_2: ────┼─────────┼─────────■─────
       ┌───┴────┐┌───┴────┐┌───┴────┐
  b_0: ┤0       ├┤0       ├┤0       ├
       │        ││        ││        │
  b_1: ┤1       ├┤1       ├┤1       ├
       │        ││        ││        │
  b_2: ┤2       ├┤2       ├┤2       ├
       │        ││        ││        │
out_0: ┤3       ├┤        ├┤        ├
       │        ││        ││        │
out_1: ┤4       ├┤3       ├┤        ├
       │  Adder ││  Adder ││  Adder │
out_2: ┤5       ├┤4       ├┤3       ├
       │        ││        ││        │
out_3: ┤6       ├┤5       ├┤4       ├
       │        ││        ││        │
out_4: ┤        ├┤6       ├┤5       ├
       │        ││        ││        │
out_5: ┤        ├┤        ├┤6       ├
       │        ││        ││        │
aux_0: ┤7       ├┤7       ├┤7       ├
       └────────┘└────────┘└────────┘
```

Multiplication in this circuit is implemented in a classical approach by performing a series of shifted additions using one of the input registers while the qubits from the other input register act as control qubits for the adders.

> **See also**
>
> The [`MultiplierGate`](/docs/api/qiskit/qiskit.circuit.library.MultiplierGate "qiskit.circuit.library.MultiplierGate") object represents a multiplication, like this circuit class, but allows the compiler to select the optimal decomposition based on the context. Specific implementations can be set via the [`HLSConfig`](/docs/api/qiskit/qiskit.transpiler.passes.HLSConfig "qiskit.transpiler.passes.HLSConfig"), e.g. this circuit can be chosen via `Multiplier=["cumulative_h18"]`.

References:

\[1] Häner et al., Optimizing Quantum Circuits for Arithmetic, 2018. [arXiv:1805.12445](https://arxiv.org/pdf/1805.12445.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.
- **adder** ([*QuantumCircuit*](/docs/api/qiskit/qiskit.circuit.QuantumCircuit "qiskit.circuit.quantumcircuit.QuantumCircuit") *| None*) – Half adder circuit to be used for performing multiplication. The CDKMRippleCarryAdder is used as default if no adder is provided.
- **name** ([*str*](https://docs.python.org/3/library/stdtypes.html#str)) – The name of the circuit object.

**Raises**

[**NotImplementedError**](https://docs.python.org/3/library/exceptions.html#NotImplementedError) – If `num_result_qubits` is not default and a custom adder is provided.

## Attributes

### name

Type: `str`

A human-readable name for the circuit.

**Example**

```python
from qiskit import QuantumCircuit

qc = QuantumCircuit(2, 2, name="my_circuit")
print(qc.name)
```

```text
my_circuit
```