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CDKMRippleCarryAdder

class CDKMRippleCarryAdder(num_state_qubits, kind='full', name='CDKMRippleCarryAdder')[source]

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

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 CircuitInstructions for each instruction.

Return type

QuantumCircuitData

extension_lib = 'include "qelib1.inc";'
global_phase

Return the global phase of the circuit in radians.

header = 'OPENQASM 2.0;'
instances = 129
layout

Return any associated layout information anout the circuit

This attribute contains an optional TranspileLayout object. This is typically set on the output from transpile() or 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() function, an initial layout which permutes the qubits based on the selected physical qubits on the Target, and a final layout which is an output permutation caused by SwapGates 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_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 -- When circuit is not scheduled.

parameters

The parameters defined in the circuit.

This attribute returns the Parameter objects in the circuit sorted alphabetically. Note that parameters instantiated with a ParameterVector are still sorted numerically.

Examples

The snippet below shows that insertion order of parameters does not matter.

>>> 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 unituitive when it comes to numbers. The literal "10" comes before "2" in strict alphabetical sorting.

>>> 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 can be used.


>>> 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 objects in the circuit.

prefix = 'circuit'
qubits

Returns a list of quantum bits in the order that the registers were added.