HRSCumulativeMultiplier

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

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):

  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.

References:

[1] Häner et al., Optimizing Quantum Circuits for Arithmetic, 2018. arXiv:1805.12445

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 (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 | None) – Half adder circuit to be used for performing multiplication. The CDKMRippleCarryAdder is used as default if no adder is provided.
• name (str) – The name of the circuit object.

Raises

NotImplementedError – If num_result_qubits is not default and a custom adder is provided.

Attributes

name

from qiskit import QuantumCircuit

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

my_circuit