DraperQFTAdder

class DraperQFTAdder(num_state_qubits, kind='fixed', name='DraperQFTAdder')

Bases: qiskit.circuit.library.arithmetic.adders.adder.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

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 '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.

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 tuples for the circuit’s data.

Each tuple is in the format (instruction, qargs, cargs), where instruction is an Instruction (or subclass) object, qargs is a list of Qubit objects, and cargs is a list of Clbit objects.

Return type

QuantumCircuitData

extension_lib = 'include "qelib1.inc";'

global_phase

Return the global phase of the circuit in radians.

header = 'OPENQASM 2.0;'

instances = 16

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

Convenience function to get 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.

Return type

int

Returns

The number of state qubits.

parameters

Convenience function to get the parameters defined in the parameter table.

prefix = 'circuit'

qubits

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