qml.qaoa.cost.bit_driver

bit_driver(wires, b)

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 * Z(0) + 1 * Z(1) + 1 * Z(2)

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