openfermion.ops.MajoranaOperator

A linear combination of products of Majorana operators.

openfermion.ops.MajoranaOperator(
    term=None, coefficient=1.0
)

A system of N fermionic modes can be described using 2N Majorana operators \(\gamma_1, \ldots, \gamma_{2N}\) as an alternative to using N fermionic annihilation operators. The algebra of Majorana operators amounts to the relation

\[ \{\gamma_i, \gamma_j\} = \gamma_i \gamma_j + \gamma_j \gamma_i = 2 \delta_{ij} \]

Note that this implies \(\gamma_i^2 = 1\).

The MajoranaOperator class stores a linear combination of products of Majorana operators. Each product is represented as a tuple of integers representing the indices of the operators. As an example, MajoranaOperator((2, 3, 5), -1.5) initializes an operator with a single term which represents the operator \(-1.5 \gamma_2 \gamma_3 \gamma_5\). MajoranaOperators can be added, subtracted, multiplied, and divided by scalars. They can be compared for approximate numerical equality using ==.

term Tuple[int]

The indices of a Majorana operator term to start off with

coefficient complex

The coefficient of the term

terms A dictionary from term, represented by a tuple of integers, to the coefficient of the term in the linear combination.

Methods

commutes_with

View source

commutes_with(
    other
)

Test commutation with another MajoranaOperator

from_dict

View source

@staticmethod
from_dict(
    terms
)

Initialize a MajoranaOperator from a terms dictionary.

Args
terms A dictionary from Majorana term to coefficient

with_basis_rotated_by

View source

with_basis_rotated_by(
    transformation_matrix
)

Change to a basis of new Majorana operators.

The input to this method is a real orthogonal matrix \(O\). It returns a new MajoranaOperator which is equivalent to the old one but rewritten in terms of a new basis of Majorana operators. Let the original Majorana operators be denoted by \(\gamma_i\) and the new operators be denoted by \(\tilde{\gamma_i}\). Then they are related by the equation

\[ \tilde{\gamma_i} = \sum_j O_{ij} \gamma_j. \]

Args
transformation_matrix A real orthogonal matrix representing the basis transformation.

Returns
The rotated operator.

__add__

View source

__add__(
    other
)

__eq__

View source

__eq__(
    other
)

Approximate numerical equality.

__mul__

View source

__mul__(
    other
)

__ne__

View source

__ne__(
    other
)

Return self!=value.

__neg__

View source

__neg__()

__pow__

View source

__pow__(
    other
)

__rmul__

View source

__rmul__(
    other
)

__sub__

View source

__sub__(
    other
)

__truediv__

View source

__truediv__(
    other
)