Operator Representations¶

This module provides various data structures for representing fermionic operators in different bases.

Fermion Operator¶

This operator represents fermionic operators in terms of the second-quantization creation and annihilation operators.

`FermionAction`	A fermionic creation or annihilation action.
`FermionOperator`	A spin-less fermionic operator.
`cre`(mode)	A convenience alias for `FermionAction.creation()`.
`ann`(mode)	A convenience alias for `FermionAction.annihilation()`.

Majorana Operator¶

This operator represents fermionic operators in terms of Majorana fermions.

`MajoranaAction`	The MajoranaAction type.
`MajoranaOperator`	A Majorana fermion operator.
`gamma`(mode, is_prime)	Create a majorana fermion.

Protocol¶

All operator classes provides by this submodule implement at least those methods specified by the protocol below:

class OperatorTrait¶

Bases: Protocol

A protocol indicating all methods implemented by operator classes.

classmethod zero()¶

Constructs the additive identity operator.

Return type:: Self

classmethod one()¶

Constructs the multiplicative identity operator.

Return type:: Self

__iadd__(other)¶

Adds another operator to this one.

Parameters:: other (Self)

__add__(other)¶

Adds two operators.

Parameters:: other (Self)
Return type:: Self

__isub__(other)¶

Subtracts another operator from this one.

Parameters:: other (Self)

__sub__(other)¶

Subtracts two operators.

Parameters:: other (Self)
Return type:: Self

__imul__(other)¶

Multiplies this operator by a scalar.

Parameters:: other (complex)

__mul__(other)¶

Multiplies an operator by a scalar.

Parameters:: other (complex)
Return type:: Self

__idiv__(other)¶

Divides this operator by a scalar.

Parameters:: other (complex)

__div__(other)¶

Divides an operator by a scalar.

Parameters:: other (complex)
Return type:: Self

__neg__()¶

Negates this operator.

Return type:: Self

__iand__(other)¶

Composes (left-multiplies) another operator onto this one.

Parameters:: other (Self)

__and__(other)¶

Composes (left-multiplies) two operators.

Parameters:: other (Self)
Return type:: Self

__imatmul__(other)¶

Takes the dot-product (right-multiplication) of another operator onto this one.

Parameters:: other (Self)

__matmul__(other)¶

Takes the dot-product (right-multiplication) two operators.

Parameters:: other (Self)
Return type:: Self

__pow__(exponent, modulo)¶

Exponentiates this operator by the integer exponent.

Parameters:

exponent (int)
modulo (int | None)

Return type:

Self

__len__()¶

Returns the length of this operator.

Return type:: int

iter_terms()¶

Iterates over the terms of this operator.

Return type:: Iterator

classmethod from_terms(terms)¶

Constructs a new operator from an iterator (see also iter_terms()).

Parameters:: terms (Iterable)
Return type:: Self

equiv(other, atol)¶

Checks this operator with another for equivalence up to the specified absolute tolerance.

Parameters:

other (Self)
atol (float)

Return type:

bool

ichop(atol)¶

Trims coefficients below the absolute tolerance from this operator.

Parameters:: atol (float)

simplify(atol)¶

Simplifies the terms of this operator, discarding those below the absolute tolerance.

Parameters:: atol (float)
Return type:: Self

adjoint()¶

Returns the adjoint of this operator.

Return type:: Self

get_support()¶

Returns the set of mode indices which this operator acts upon.

Return type:: frozenset[int]

relabel_modes(permutation)¶

Relabels the modes of the operator.

Parameters:: permutation (list[int])
Return type:: Self

normal_ordered(*args, **kwargs)¶

Returns the normal-ordered form of this operator.

Note

A specific implementation of this method may take additional arguments.

Return type:: Self

get_coeffs()¶

Returns the term coefficients.

Return type:: list[complex]

property groups: list[int] | None¶: Returns the groups indices.

split_out_groups()¶

Splits this operator into an optional list of new operators based on its groups.

Return type:: list[Self]