qml.qaoa.cost.bit_driver

bit_driver(wires, b)[source]

Returns the bit-driver cost Hamiltonian.

This Hamiltonian is defined as:

\[H \ = \ (-1)^{b + 1} \displaystyle\sum_{i} Z_i\]

where \(Z_i\) is the Pauli-Z operator acting on the \(i\)-th wire and \(b \ \in \ \{0, \ 1\}\). This Hamiltonian is often used when constructing larger QAOA cost Hamiltonians.

Parameters
  • wires (Iterable or Wires) – The wires on which the Hamiltonian acts

  • b (int) – Either \(0\) or \(1\). Determines whether the Hamiltonian assigns lower energies to bitstrings with a majority of bits being \(0\) or a majority of bits being \(1\), respectively.

Returns

Return type

Hamiltonian

Example

>>> wires = range(3)
>>> hamiltonian = qaoa.bit_driver(wires, 1)
>>> print(hamiltonian)
(1.0) [Z0] + (1.0) [Z1] + (1.0) [Z2]