CDKMRippleCarryAdder

class qiskit.circuit.library.CDKMRippleCarryAdder(num_state_qubits, kind='full', name='CDKMRippleCarryAdder')

Bases: Adder

A ripple-carry circuit to perform in-place addition on two qubit registers.

As an example, a ripple-carry adder circuit that performs addition on two 3-qubit sized registers with a carry-in bit (kind="full") is as follows:

        ┌──────┐                                     ┌──────┐
 cin_0: ┤2     ├─────────────────────────────────────┤2     ├
        │      │┌──────┐                     ┌──────┐│      │
   a_0: ┤0     ├┤2     ├─────────────────────┤2     ├┤0     ├
        │      ││      │┌──────┐     ┌──────┐│      ││      │
   a_1: ┤  MAJ ├┤0     ├┤2     ├─────┤2     ├┤0     ├┤  UMA ├
        │      ││      ││      │     │      ││      ││      │
   a_2: ┤      ├┤  MAJ ├┤0     ├──■──┤0     ├┤  UMA ├┤      ├
        │      ││      ││      │  │  │      ││      ││      │
   b_0: ┤1     ├┤      ├┤  MAJ ├──┼──┤  UMA ├┤      ├┤1     ├
        └──────┘│      ││      │  │  │      ││      │└──────┘
   b_1: ────────┤1     ├┤      ├──┼──┤      ├┤1     ├────────
                └──────┘│      │  │  │      │└──────┘
   b_2: ────────────────┤1     ├──┼──┤1     ├────────────────
                        └──────┘┌─┴─┐└──────┘
cout_0: ────────────────────────┤ X ├────────────────────────
                                └───┘

Here MAJ and UMA gates correspond to the gates introduced in [1]. Note that in this implementation the input register qubits are ordered as all qubits from the first input register, followed by all qubits from the second input register.

Two different kinds of adders are supported. By setting the kind argument, you can also choose a half-adder, which doesn’t have a carry-in, and a fixed-sized-adder, which has neither carry-in nor carry-out, and thus acts on fixed register sizes. Unlike the full-adder, these circuits need one additional helper qubit.

The circuit diagram for the fixed-point adder (kind="fixed") on 3-qubit sized inputs is

        ┌──────┐┌──────┐                ┌──────┐┌──────┐
   a_0: ┤0     ├┤2     ├────────────────┤2     ├┤0     ├
        │      ││      │┌──────┐┌──────┐│      ││      │
   a_1: ┤      ├┤0     ├┤2     ├┤2     ├┤0     ├┤      ├
        │      ││      ││      ││      ││      ││      │
   a_2: ┤      ├┤  MAJ ├┤0     ├┤0     ├┤  UMA ├┤      ├
        │      ││      ││      ││      ││      ││      │
   b_0: ┤1 MAJ ├┤      ├┤  MAJ ├┤  UMA ├┤      ├┤1 UMA ├
        │      ││      ││      ││      ││      ││      │
   b_1: ┤      ├┤1     ├┤      ├┤      ├┤1     ├┤      ├
        │      │└──────┘│      ││      │└──────┘│      │
   b_2: ┤      ├────────┤1     ├┤1     ├────────┤      ├
        │      │        └──────┘└──────┘        │      │
help_0: ┤2     ├────────────────────────────────┤2     ├
        └──────┘                                └──────┘

It has one less qubit than the full-adder since it doesn’t have the carry-out, but uses a helper qubit instead of the carry-in, so it only has one less qubit, not two.

References:

[1] Cuccaro et al., A new quantum ripple-carry addition circuit, 2004. arXiv:quant-ph/0410184

[2] Vedral et al., Quantum Networks for Elementary Arithmetic Operations, 1995. arXiv:quant-ph/9511018

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.
• kind (str) – The kind of adder, can be 'full' for a full adder, 'half' for a half adder, or 'fixed' for a fixed-sized adder. A full adder includes both carry-in and carry-out, a half only carry-out, and a fixed-sized adder neither carry-in nor carry-out.
• name (str) – The name of the circuit object.

Raises

ValueError – If num_state_qubits is lower than 1.

Attributes

name

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

my_circuit