openfermion.ops.MajoranaOperator

A linear combination of products of Majorana operators.

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

.. math:: {\gamma_i, \gamma_j} = \gamma_i \gamma_j + \gamma_j \gammai = 2 \delta{ij}

Note that this implies :math:\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 :math:-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

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Test commutation with another MajoranaOperator

from_dict

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Initialize a MajoranaOperator from a terms dictionary.

Args
terms A dictionary from Majorana term to coefficient

with_basis_rotated_by

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Change to a basis of new Majorana operators.

The input to this method is a real orthogonal matrix :math: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 :math:\gamma_i and the new operators be denoted by :math:\tilde{\gamma_i}. Then they are related by the equation

.. math::

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


Args
transformation_matrix A real orthogonal matrix representing the basis transformation.

Returns
The rotated operator.

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__eq__

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Approximate numerical equality.

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__ne__

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Return self!=value.

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