Operator Library

Building on top of the operator representations provided by operators, this module provides various tools to simplify the construction of commonly used operators.

Commutator Generators

Operator classes can implement the SupportsCommutators Protocol, which allows them to be used with the functions listed in the table below, to quickly compute multiple commutator variants.

SupportsCommutators	A runtime-checkable Protocol indicating support for efficient commutator generation.
commutator(op_a, op_b)	Computes the commutator of two operators.
anti_commutator(op_a, op_b)	Computes the anti-commutator of two operators.
double_commutator(op_a, op_b, op_c, sign)	Computes the double-commutator of three operators.

Common Operators

Various common operators can easily be generated from constructor methods. This section provides an overview of these methods for a quick reference, grouped by category.

Electronic Integrals

The constructor methods listed here generally take the coefficients of electronic structure Hamiltonians as an input. Different flavors exist:

• tril: these methods consume 1-dimensional arrays of flattened (generalized) triangular indices

• full: these methods consume high-dimensional arrays

• spin: these methods take separate arrays for the different spin species

• sym: these methods take a single array for one spin species and infer the other spin species

• 1-Body Terms

FermionOperator.from_1body_tril_spin_sym()	Constructs from spin-symmetric triangular 1-body integrals.
FermionOperator.from_1body_tril_spin()	Constructs from separate spin triangular 1-body integrals.

• 2-Body Terms

FermionOperator.from_2body_tril_spin_sym()	Constructs from spin-symmetric triangular 2-body integrals.
FermionOperator.from_2body_tril_spin()	Constructs from separate spin triangular 2-body integrals.

Other Generators

Finally, the following additional operator generator utilities exist in this module:

FCIDump

An electronic structure Hamiltonian in FCIDump format.