# qml.qaoa.mixers.x_mixer¶

x_mixer(wires: Union[Iterable, pennylane.wires.Wires])[source]

Creates a basic Pauli-X mixer Hamiltonian.

This Hamiltonian is defined as:

$H_M \ = \ \displaystyle\sum_{i} X_{i},$

where $$i$$ ranges over all wires, and $$X_i$$ denotes the Pauli-X operator on the $$i$$-th wire.

This is mixer is used in A Quantum Approximate Optimization Algorithm by Edward Farhi, Jeffrey Goldstone, Sam Gutmann [arXiv:1411.4028].

Parameters

wires (Iterable or Wires) – The wires on which the Hamiltonian is applied

Returns

Mixer Hamiltonian

Return type

Hamiltonian

Example

The mixer Hamiltonian can be called as follows:

>>> from pennylane import qaoa
>>> wires = range(3)
>>> mixer_h = qaoa.x_mixer(wires)
>>> print(mixer_h)
(1) [X0]
+ (1) [X1]
+ (1) [X2]


Using PennyLane

Development

API