Utilities

Utility functions.

ferrmion.utils.find_pauli_weight(symplectic_hamiltonian: ndarray[tuple[int, ...], dtype[bool]]) → floating

Find the average Pauli weight of a symplectic hamiltonian.

Parameters:

symplectic_hamiltonian (NDArray) – The symplectic Hamiltonian.

Returns:

The average Pauli weight.

Return type:

float

Example

>>> import numpy as np
>>> from ferrmion.utils import find_pauli_weight
>>> arr = np.eye((2, 4), dtype=bool)
>>> find_pauli_weight(arr)
1.0

ferrmion.utils.icount_to_sign(icount: int) → complex64

Convert a power of i to a complex value.

Parameters:

icount (int) – The power of i.

Returns:

The complex value.

Return type:

np.complex64

Example

>>> from ferrmion.utils import icount_to_sign
>>> icount_to_sign(1)
1j
>>> icount_to_sign(2)
-1

ferrmion.utils.pauli_to_symplectic(pauli: str, ipower: int = 0) → tuple[ndarray[tuple[int, ...], dtype[bool]], int]

Convert a Pauli operator to symplectic form.

Parameters:

• pauli (str) – The Pauli operator string.

• ipower (NDArray[np.uint]) – power of i coefficient

Returns:

The imaginary cofactor and symplectic matrix.

Return type:

tuple[int, NDArray[np.uint8, np.uint8]]

Example

>>> from ferrmion.utils import pauli_to_symplectic
>>> symp, ipower = pauli_to_symplectic('XIZY')

ferrmion.utils.setup_logs() → None

Initialise logging.

ferrmion.utils.symplectic_hash(symp: ndarray[tuple[int, ...], dtype[bool]]) → bytes

Convert a symplectic vector into a hashable form.

Parameters:

symp (NDArray[bool]) – The symplectic vector.

Returns:

The hashed form of the symplectic vector.

Return type:

bytes

Example

>>> import numpy as np
>>> from ferrmion.utils import symplectic_hash
>>> symp = np.array([True, False, True, False], dtype=bool)
>>> h = symplectic_hash(symp)
>>> isinstance(h, bytes)
True

ferrmion.utils.symplectic_to_pauli(symplectic: ndarray[tuple[int, ...], dtype[bool]], ipower: int = 0) → tuple[str, int]

Convert a symplectic vector into a Pauli String.

Parameters:

• symplectic (NDArray[np.uint8]) – symplectic vector [X terms, Y terms]

• ipower (NDArray[np.uint]) – power of i coefficient

Returns:

The Pauli string and imaginary cofactor.

Return type:

tuple[str, int]

NOTE: symplectic XZ does represent XZ and not Y

So Y=-iXZ needs an imaginary cofactor

Example

>>> import numpy as np
>>> from ferrmion.utils import symplectic_to_pauli
>>> arr = np.array([1, 0, 0, 1], dtype=bool)
>>> pauli, ipower = symplectic_to_pauli(arr)
>>> isinstance(pauli, str)
True

ferrmion.utils.symplectic_to_sparse(symplectic: ndarray[tuple[int, ...], dtype[bool]], ipower: int = 0) → tuple[str, ndarray[tuple[int, ...], dtype[int]], complex64]

Convert a symplectic vector into a Pauli String (sparse form).

Parameters:

• symplectic (NDArray[np.uint8]) – symplectic vector [X terms, Y terms]

• ipower (NDArray[np.uint]) – power of i coefficient

Returns:

The Pauli string, indices of non-identity terms and imaginary coefficient.

Return type:

tuple[str, NDArray[int]]

NOTE: symplectic XZ does represent XZ and not Y

So Y=-iXZ needs an imaginary cofactor

Example

>>> import numpy as np
>>> from ferrmion.utils import symplectic_to_sparse
>>> arr = np.array([1, 0, 0, 1], dtype=bool)
>>> pauli, idx, coeff = symplectic_to_sparse(arr)
>>> isinstance(pauli, str)
True
>>> isinstance(idx, np.ndarray)
True

ferrmion.utils.symplectic_unhash(symp: bytes, length: int) → ndarray[tuple[int, ...], dtype[bool]]

Convert a hashed symplectic vector back to its original form.

Parameters:

• symp (bytes) – The hashed form of the symplectic vector.

• length (int) – The length of the original symplectic vector.

Returns:

The original symplectic vector.

Return type:

NDArray[bool]

Example

>>> import numpy as np
>>> from ferrmion.utils import symplectic_hash, symplectic_unhash
>>> arr = np.array([True, False, True, False], dtype=bool)
>>> h = symplectic_hash(arr)
>>> arr2 = symplectic_unhash(h, 4)
>>> np.all(arr == arr2)
True

ferrmion.utils.two_operator_product(creation: tuple[bool, bool], left, right) → ndarray[tuple[int, ...], dtype[_ScalarType_co]]

Calculate the product of two operators in symplectic form.

Parameters:

• creation (tuple[bool, bool]) – A tuple of two booleans indicating if the operators are creation operators.

• left (NDArray) – The left operator in symplectic form.

• right (NDArray) – The right operator in symplectic form.

Returns:

The product of the two operators in symplectic form.

Return type:

NDArray

Example

>>> left = np.array([[1, 0], [0, 1]])
>>> right = np.array([[0, 1], [1, 0]])
>>> creation = (True, False)
>>> two_operator_product(creation, left, right)
    array([
        [0, 0],
        [1, 0]
        [0, 1],
        [0, 0]])