qiskit.aqua.operators.legacy.Z2Symmetries

class Z2Symmetries(symmetries, sq_paulis, sq_list, tapering_values=None)

Z2 Symmetries

Parameters

• symmetries (list[Pauli]) – the list of Pauli objects representing the Z_2 symmetries

• sq_paulis (list[Pauli]) – the list of single - qubit Pauli objects to construct the Clifford operators

• sq_list (list[int]) – the list of support of the single-qubit Pauli objects used to build the Clifford operators

• tapering_values (list[int], optional) – values determines the sector.

Raises

AquaError – Invalid paulis

__init__(symmetries, sq_paulis, sq_list, tapering_values=None)

Parameters

• symmetries (list[Pauli]) – the list of Pauli objects representing the Z_2 symmetries

• sq_paulis (list[Pauli]) – the list of single - qubit Pauli objects to construct the Clifford operators

• sq_list (list[int]) – the list of support of the single-qubit Pauli objects used to build the Clifford operators

• tapering_values (list[int], optional) – values determines the sector.

Raises

AquaError – Invalid paulis

Methods

__init__(symmetries, sq_paulis, sq_list[, …])	param symmetries the list of Pauli objects representing the Z_2 symmetries
consistent_tapering(operator)	Tapering the operator with the same manner of how this tapered operator is created.
copy()	Get a copy of self.
find_Z2_symmetries(operator)	Finds Z2 Pauli-type symmetries of an Operator.
is_empty()	Check the z2_symmetries is empty or not.
taper(operator[, tapering_values])	Taper an operator based on the z2_symmetries info and sector defined by tapering_values.
two_qubit_reduction(operator, num_particles)	Eliminates the central and last qubit in a list of Pauli that has diagonal operators (Z,I) at those positions

Attributes

cliffords	Get clifford operators, build based on symmetries and single-qubit X.
sq_list	returns sq list
sq_paulis	returns sq paulis
symmetries	return symmetries
tapering_values	returns tapering values

property cliffords

Get clifford operators, build based on symmetries and single-qubit X.

Returns

a list of unitaries used to diagonalize the Hamiltonian.

Return type

list[WeightedPauliOperator]

consistent_tapering(operator)

Tapering the operator with the same manner of how this tapered operator is created. i.e., using the same Cliffords and tapering values.

Parameters

operator (WeightedPauliOperator) – the to-be-tapered operator

Returns

the tapered operator

Return type

TaperedWeightedPauliOperator

Raises

AquaError – The given operator does not commute with the symmetry

copy()

Get a copy of self.

Return type

Z2Symmetries

Returns

copy

classmethod find_Z2_symmetries(operator)

Finds Z2 Pauli-type symmetries of an Operator.

Return type

Z2Symmetries

Returns

a z2_symmetries object contains symmetries, single-qubit X, single-qubit list.

is_empty()

Check the z2_symmetries is empty or not.

Returns

empty

Return type

bool

property sq_list

returns sq list

property sq_paulis

returns sq paulis

property symmetries

return symmetries

taper(operator, tapering_values=None)

Taper an operator based on the z2_symmetries info and sector defined by tapering_values. The tapering_values will be stored into the resulted operator for a record.

Parameters

• operator (WeightedPauliOperator) – the to-be-tapered operator.

• tapering_values (list[int], optional) – if None, returns operators at each sector; otherwise, returns the operator located in that sector.

Returns

If

tapering_values is None: [:class`WeightedPauliOperator`]; otherwise, WeightedPauliOperator

Return type

list[WeightedPauliOperator] or WeightedPauliOperator

Raises

AquaError – Z2 symmetries, single qubit pauli and single qubit list cannot be empty

property tapering_values

returns tapering values

static two_qubit_reduction(operator, num_particles)

Eliminates the central and last qubit in a list of Pauli that has diagonal operators (Z,I) at those positions

Chemistry specific method: It can be used to taper two qubits in parity and binary-tree mapped fermionic Hamiltonians when the spin orbitals are ordered in two spin sectors, (block spin order) according to the number of particles in the system.

Parameters

• operator (WeightedPauliOperator) – the operator

• num_particles (Union(list, int)) – number of particles, if it is a list, the first number is alpha and the second number if beta.

Returns

a new operator whose qubit number is reduced by 2.

Return type

WeightedPauliOperator