Bases: Adder

A circuit that uses QFT to perform in-place addition on two qubit registers.

For registers with $$n$$ qubits, the QFT adder can perform addition modulo $$2^n$$ (with kind="fixed") or ordinary addition by adding a carry qubits (with kind="half").

As an example, a non-fixed_point QFT adder circuit that performs addition on two 2-qubit sized registers is as follows:

 a_0:   ─────────■──────■────────────────────────■────────────────
│      │                        │
a_1:   ─────────┼──────┼────────■──────■────────┼────────────────
┌──────┐ │P(π)  │        │      │        │       ┌───────┐
b_0:   ┤0     ├─■──────┼────────┼──────┼────────┼───────┤0      ├
│      │        │P(π/2)  │P(π)  │        │       │       │
b_1:   ┤1 qft ├────────■────────■──────┼────────┼───────┤1 iqft ├
│      │                        │P(π/2)  │P(π/4) │       │
cout_0: ┤2     ├────────────────────────■────────■───────┤2      ├
└──────┘                                         └───────┘


References:

[1] T. G. Draper, Addition on a Quantum Computer, 2000. arXiv:quant-ph/0008033

[2] Ruiz-Perez et al., Quantum arithmetic with the Quantum Fourier Transform, 2017. arXiv:1411.5949

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

প্যারামিটার:
• 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 'half' for a half adder or 'fixed' for a fixed-sized adder. A half adder contains a carry-out to represent the most-significant bit, but the fixed-sized adder doesn't and hence performs addition modulo 2 ** num_state_qubits.

• name (str) -- The name of the circuit object.

রেইজেস:

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).

রিটার্নস:

a list-like object containing the CircuitInstructions for each instruction.

রিটার্ন টাইপ:

QuantumCircuitData

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

Return the global phase of the circuit in radians.

instances = 127#
layout#

Return any associated layout information about 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.

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.

রিটার্নস:

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.

রিটার্নস:

List of integers representing instruction start times. The index corresponds to the index of instruction in QuantumCircuit.data.

রেইজেস:

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 unintuitive 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])
])

রিটার্নস:

The sorted Parameter objects in the circuit.

prefix = 'circuit'#
qubits#

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