Reference

Below is a summary of the list of functions and methods currently supported by fastfermion. For more details about how to use these functions, use help(<function name>) in the Python console.

Constructing polynomials

Function
poly	Parse string expression
paulis	Get 3N Pauli generators
fermis	Get annihilation operators
majoranas	Get Majorana operators
from_openfermion	Convert from OpenFermion
to_openfermion	Convert to OpenFermion

Operations on polynomials

Function
degree	Degree of polynomial
dagger	Adjoint of a polynomial
coefficient	Get monomial's coefficient
norm	Norm of the coefficient vector
truncate	Remove high degree terms
compress	Remove terms with small weight
extent	Number of variables in a polynomial
permute	Permute variables
sparse	Sparse matrix representation of polynomial
commutes	Check if two polynomials commute
commutator	Commutator of two polynomials

NOTE: All of the functions above can be invoked using the dot notation. For example, if \(A\) is a {Pauli,Fermi,Majorana} polynomial, then degree(A) or A.degree() are equivalent.

Transforms

Function
topauli	Convert to Pauli polynomial
tofermi	Convert to Fermi polynomial
tomajorana	Convert to Majorana polynomial
jw	Jordan-Wigner transform (Fermi -> Pauli)
rjw	Reverse Jordan-Wigner transform (Pauli -> Fermi)

NOTE: If \(A\) is a Fermi polynomial then jw(A) and A.topauli() are equivalent. Similarly if \(A\) is a Pauli polynomial then rjw(A) and A.tofermi() are equivalent.

NOTE: The functions topauli, tofermi, tomajorana can also be invoked with the dot notation. For example, if \(A\) is a Fermi polynomial, then A.tomajorana() and tomajorana(A) are equivalent.

Pauli unitaries and propagation

In fastfermion, a (Pauli) circuit is simply represented as a list of unitaries. Currently fastfermion supports the following types of unitaries H, S, CZ, CNOT, SWAP, ROT.

Function
H	Hadamard gate
S	S gate
CZ	CZ gate
CNOT	CNOT gate
SWAP	SWAP gate
ROT	Pauli rotation \(U=e^{-i \theta/2 P}\) where \(P\) is a Pauli string
from_cirq	Convert Cirq circuit into a list of fastfermion unitaries
propagate	Propagate a Pauli polynomial through a circuit (Heisenberg evolution)

Majorana rotations and propagation

fastfermion can also be used for Majorana propagation.

Function
MROT	Majorana rotation \(U = e^{-i\theta/2 M}\) where \(M\) is a Hermitian Majorana monomial
propagate	Propagate a Majorana polynomial through a sequence of Majorana rotations