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HRSCumulativeMultiplier

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

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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.

See also

The MultiplierGate objects 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, 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

Parameters

  • num_state_qubits (int) – 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 | 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.
  • 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

Type: str

A human-readable name for the circuit.

Example

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