pauliarray.mapping package

Submodules

pauliarray.mapping.fermion module

class pauliarray.mapping.fermion.BravyiKitaev(num_qubits: int)

Bases: FermionMapping

__init__(num_qubits: int)

Initialize the Bravyi-Kitaev mapping for a given number of qubits. Maps fermionic operators to qubit operators.

Parameters:

num_qubits (int) – The number of qubits to be used in the mapping.

_build_bravyi_kitaev_mapping_matrix(num_qubits: int) → np.ndarray[np.bool]

Constructs the Bravyi-Kitaev mapping matrix for the given number of qubits.

Parameters:

num_qubits (int) – The number of qubits.

Returns:

The Bravyi-Kitaev mapping matrix.

Return type:

“np.ndarray[np.bool]”

class pauliarray.mapping.fermion.FermionMapping(mapping_matrix: np.ndarray[np.bool], name: str = 'mapping')

Bases: object

Base class to represent a Fermion-to-qubit mapping.

mapping_matrix

A boolean numpy array representing the mapping matrix.

Type:

“np.ndarray[np.bool]”

name

A name identifier for the mapping (default is “mapping”).

Type:

str

_mapping_matrix_inv

The inverse of the mapping matrix, initially None

Type:

“np.ndarray[np.bool]”, optional

and computed on demand.

_heavyside_matrix

The Heavyside matrix, initially None and computed

Type:

“np.ndarray[np.bool]”, optional

on demand.

_parity_matrix

The parity matrix, initially None and computed on demand.

Type:

“np.ndarray[np.bool]”, optional

__init__(mapping_matrix: np.ndarray[np.bool], name: str = 'mapping')

Constructs all the necessary attributes for the FermionMapping object.

Parameters:

• mapping_matrix – “np.ndarray[np.bool]” A boolean numpy array representing the mapping matrix.

• name – str, optional A name identifier for the mapping (default is “mapping”).

static _flip_factors(i_orbitals: np.ndarray[np.int], j_orbitals: np.ndarray[np.int], *args: Tuple[np.ndarray[np.int]]) → ndarray[Any, dtype[float64]]

Computes flip factors of the type

\[f_\mu = (-1)^{\delta_{i_\mu j_\mu} + \delta_{i_\mu k_\mu} + \ldots}.\]

Parameters:

• i_orbitals ("np.ndarray[np.int]") – The indices of the orbital i the operator is acting on.

• j_orbitals ("np.ndarray[np.int]") – The indices of the orbital i the operator is acting on.

• etc...

Returns:

The factors.

Return type:

NDArray[float]

_flip_operators(i_orbitals: np.ndarray[np.int], factors: ndarray[Any, dtype[float64]]) → OperatorArrayType1

Constructs an OperatorArray with the \(\mu^\text{th}\) flip operators acting on the orbitals \(i_\mu\)

\[\hat{F}_\mu = \frac{1}{2}(1 + f_\mu \hat{Z}_q^{[\mathsf{M}^{-1}]_{i_\mu q}]})\]

where \(f_\mu\) is a factor (+1 or -1) associted with the creation and annihilation operators.

Parameters:

• i_orbitals (NDArray[int]) – The indices of the orbital i the operator is acting on

• factors (NDArray[float]) – The factors (+1 or -1) defining if a creation or an annihilation operator is

• applied.

Returns:

The array of flip operators.

Return type:

OperatorArrayType1

_update_factors(i_orbitals: np.ndarray[np.int], j_orbitals: np.ndarray[np.int], *args: Tuple[np.ndarray[np.int]]) → ndarray[Any, dtype[float64]]

Computes update factors of the type

\[f_\mu = (-1)^{\theta_{i_\mu j_\mu} - \theta_{j_\mu i_\mu} + \ldots}.\]

Parameters:

• i_orbitals ("np.ndarray[np.int]") – The indices of the orbital i the operator is acting on.

• j_orbitals ("np.ndarray[np.int]") – The indices of the orbital i the operator is acting on.

• etc...

Returns:

The factors.

Return type:

NDArray[float]

_update_operators(i_orbitals: np.ndarray[np.int], j_orbitals: np.ndarray[np.int], *args: Tuple[np.ndarray[np.int]]) → OperatorArrayType1

Updates the operators based on the given orbitals, using the Heaviside matrix, the inverse mapping matrix, and the transposed mapping matrix. The function processes the input orbitals to generate updated Z and X strings, used to create new Pauli operators.

Parameters:

• i_orbitals ("np.ndarray[np.int]") – The first set of orbitals.

• j_orbitals ("np.ndarray[np.int]") – The second set of orbitals.

• *args (Tuple["np.ndarray[np.int]"]) – Additional sets of orbitals.

Returns:

The updated operators as an OperatorArrayType1 object.

Return type:

opa.OperatorArrayType1

_update_operators_2(i_orbitals: np.ndarray[np.int], j_orbitals: np.ndarray[np.int]) → OperatorArrayType1

Constructs an OperatorArray with the \(\mu^\text{th}\) main operators acting on the orbitals \(i_\mu\) and \(j_\mu\) in a one-body fermionic operator

\[\hat{U}^{(2)}_{\mu} = (-1)^{\theta_{i_\mu j_ \mu}} \hat{X}_q^{M_{qi_\mu} + M_{qj_\mu}}.\]

Parameters:

• i_orbitals (NDArray[int]) – The indices of the orbital i the operator is acting on.

• j_orbitals (NDArray[int]) – The indices of the orbital j the operator is acting on.

Returns:

The array of operators.

Return type:

OperatorArrayType1

_update_operators_4(i_orbitals: np.ndarray[np.int], j_orbitals: np.ndarray[np.int], k_orbitals: np.ndarray[np.int], l_orbitals: np.ndarray[np.int]) → OperatorArrayType1

Constructs an OperatorArray with the \(\mu^\text{th}\) main operators acting on the orbitals \(i_\mu\), \(j_\mu\), \(k_\mu\) and \(l_\mu\) in a two-body fermionic operator.

\[(-1)^{\theta_{ij} + \theta_{i_\mu k_\mu} + \theta_{i_\mu l_\mu} + \theta_{j_\mu k_\mu} + \theta_{j_\mu l_\mu} + \theta_{k_\mu l_\mu}} \hat{X}_q^{M_{qi_\mu} + M_{qj_\mu} + M_{qk_\mu} + M_{ql_\mu}} \hat{Z}_q^{(\theta_{i_\mu p} + \theta_{j_\mu p} + \theta_{k_\mu p} + \theta_{l_\mu p})[\mathsf{M}^{-1}]_{pq}}\]

Parameters:

• i_orbitals (NDArray[int]) – The indices of the orbital i the operator is acting on.

• j_orbitals (NDArray[int]) – The indices of the orbital j the operator is acting on.

• k_orbitals (NDArray[int]) – The indices of the orbital k the operator is acting on.

• l_orbitals (NDArray[int]) – The indices of the orbital l the operator is acting on.

Returns:

The array of operators.

Return type:

OperatorArrayType1

assemble_creation_annihilation_operators() → Tuple[OperatorArrayType1, OperatorArrayType1]

Constructs the creation and annihilation operators for all available states and returns them as OperatorArrays.

Returns:

The creation operators OperatorArrayType1: The annihilation operators

Return type:

OperatorArrayType1

assemble_one_body_operator_array() → OperatorArrayType1

Assembles an array of one-body operators.

Returns:

An operator array of one-body operators.

Return type:

opa.OperatorArrayType1

assemble_qubit_hamiltonian_from_arrays(one_body: np.ndarray[np.complex], two_body: np.ndarray[np.complex]) → Operator

Assemble the whole qubit Hamiltonian as an Operator using fermionic integrals given as arrays.

Parameters:

• one_body ("np.ndarray[np.complex]") – The one-body fermionic integrals as a 2d array

• two_body ("np.ndarray[np.complex]") – The two-body fermionic integrals as a 4d array (in physicist order)

Returns:

The qubit Hamiltonia

Return type:

Operator

assemble_qubit_hamiltonian_from_sparses(one_body_tuple: Tuple, two_body_tuple: Tuple) → Operator

Assemble the whole qubit Hamiltonian as an Operator using fermionic integrals given in sparse representations.

Parameters:

• one_body_tuple (Tuple) – Contains the argument for the one_body_operator_from_sparse method.

• two_body_tuple (Tuple) – Contains the argument for the two_body_operator_from_sparse method.

Returns:

The qubit Hamiltonian

Return type:

op.Operator

assemble_two_body_operator_array() → OperatorArrayType1

Assembles an array of two-body operators.

Returns:

An operator array of two-body operators.

Return type:

opa.OperatorArrayType1

property heavyside_matrix: np.ndarray[np.bool]

Returns the Heavyside matrix. Computes it if not already computed.

Returns:

The Heavyside matrix.

Return type:

“np.ndarray[np.bool]”

majoranas() → Tuple[PauliArray, PauliArray]

In a fermion-to-qubit mapping, each creation/annihilation operator is a sum of two majorana operators,

\[0.5 * (P_\text{real} + P_\text{imag})\]

each being a Pauli string. This methods construct these majorana operators.

Returns:

The Pauli strings for \(P_\text{real}\) PauliArray: The Pauli strings for \(P_\text{imag}\)

Return type:

PauliArray

property mapping_matrix_inv

Returns the inverse of the mapping matrix. Computes it if not already computed.

Returns:

The inverse of the mapping matrix.

Return type:

“np.ndarray[np.bool]”

property num_qubits: int

Returns the number of qubits based on the shape of the mapping matrix.

Returns:

The number of qubits.

Return type:

int

occupation_operators() → OperatorArrayType1

Constructs the occupation operators for all available states and returns them as OperatorArray.

Returns:

An Operator array with all the occupation operators.

Return type:

opa.OperatorArrayType1

one_body_operator_from_array(one_body: np.ndarray[np.complex]) → Operator

Converts a one-body array to an operator object.

Parameters:

one_body ("np.ndarray[np.complex]") – A complex numpy array representing the one-body operator.

Returns:

The corresponding operator object.

Return type:

op.Operator

Raises:

• AssertionError. If the input array is not 2-dimensional or if its dimensions do not match the –

• number of qubits. –

one_body_operator_from_sparse(locations: List[np.ndarray[np.int]], values: np.ndarray[np.complex], signs: List[int] | np.ndarray[np.int] | List[np.ndarray[np.int]] = (1, -1)) → Operator

Assemble a one body fermionic operator as an Operator using fermionic integrals given in sparse representations.

Parameters:

• locations (List["np.ndarray[np.int]"]) – Pairs of orbital indices

• values ("np.ndarray[np.complex]") – Values of the integral for the pairs of orbitals

• signs (the operators are creation or annihilation. Can be a list of two) – Values +1 or -1 determining if

• signs

• sign. (or two arrays of)

• [1 (Defaults to)

• -1].

Returns:

The qubit operator

Return type:

op.Operator

property parity_matrix: np.ndarray[np.bool]

Returns the parity matrix. Computes it if not already computed.

Returns:

The parity matrix.

Return type:

“np.ndarray[np.bool]”

two_body_operator_from_array(two_body: np.ndarray[np.complex]) → Operator

Converts a two-body array to an operator object.

Parameters:

two_body ("np.ndarray[np.complex]") – A complex numpy array representing the two-body operator.

Returns:

The corresponding operator object.

Return type:

op.Operator

Raises:

• AssertionError. If the input array's dimensions do not match the number of qubits or if it does not satisfy –

• the required symmetries. –

two_body_operator_from_sparse(locations: List[np.ndarray[np.int]], values: np.ndarray[np.complex], signs: List[int] | np.ndarray[np.int] | List[np.ndarray[np.int]] = (1, 1, -1, -1)) → Operator

Assemble a two-body fermionic operator as an Operator using fermionic integrals given in sparse representations.

Parameters:

• locations (List["np.ndarray[np.int]"]) – Quartet of orbital indices

• values ("np.ndarray[np.complex]") – Values of the integral for the quartets of orbitals

• signs (the operators are creation or annihilation. Can be a list of two) – Values +1 or -1 determining if

• signs

• sign. (or two arrays of)

• [+1 (Defaults to)

• +1

• -1

• -1].

Returns:

The qubit operator

Return type:

op.Operator

class pauliarray.mapping.fermion.JordanWigner(num_qubits: int)

Bases: FermionMapping

__init__(num_qubits: int)

Initializes the Jordan-Wigner mapping for a given number of qubits. Maps fermionic operators to qubit operators.

Parameters:

num_qubits (int) – The number of qubits to be used in the mapping.

class pauliarray.mapping.fermion.Parity(num_qubits: int)

Bases: FermionMapping

__init__(num_qubits: int)

Initializes the Parity mapping for a given number of qubits. Maps fermionic operators to qubit operators.

Parameters:

num_qubits (int) – The number of qubits to be used in the mapping.

Module contents

Mapping module. Implements mapping of operators into qubit operators.