qml.qaoa.mixers.x_mixer¶

x_mixer(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 * X(0) + 1 * X(1) + 1 * X(2)