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---
title: Z2Symmetries
description: API reference for qiskit.aqua.operators.legacy.Z2Symmetries
in_page_toc_min_heading_level: 1
python_api_type: class
python_api_name: qiskit.aqua.operators.legacy.Z2Symmetries
---
# qiskit.aqua.operators.legacy.Z2Symmetries
<Class id="qiskit.aqua.operators.legacy.Z2Symmetries" isDedicatedPage={true} github="https://github.com/qiskit-community/qiskit-aqua/tree/stable/0.9/qiskit/aqua/operators/legacy/weighted_pauli_operator.py" signature="Z2Symmetries(symmetries, sq_paulis, sq_list, tapering_values=None)" modifiers="class">
Z2 Symmetries
**Parameters**
* **symmetries** (*list\[*[*Pauli*](qiskit.quantum_info.Pauli "qiskit.quantum_info.Pauli")*]*) – the list of Pauli objects representing the Z\_2 symmetries
* **sq\_paulis** (*list\[*[*Pauli*](qiskit.quantum_info.Pauli "qiskit.quantum_info.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**](qiskit.aqua.AquaError "qiskit.aqua.AquaError") – Invalid paulis
### \_\_init\_\_
<Function id="qiskit.aqua.operators.legacy.Z2Symmetries.__init__" signature="__init__(symmetries, sq_paulis, sq_list, tapering_values=None)">
**Parameters**
* **symmetries** (*list\[*[*Pauli*](qiskit.quantum_info.Pauli "qiskit.quantum_info.Pauli")*]*) – the list of Pauli objects representing the Z\_2 symmetries
* **sq\_paulis** (*list\[*[*Pauli*](qiskit.quantum_info.Pauli "qiskit.quantum_info.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**](qiskit.aqua.AquaError "qiskit.aqua.AquaError") – Invalid paulis
</Function>
## Methods
| | |
| --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------- |
| [`__init__`](#qiskit.aqua.operators.legacy.Z2Symmetries.__init__ "qiskit.aqua.operators.legacy.Z2Symmetries.__init__")(symmetries, sq\_paulis, sq\_list\[, …]) | **param symmetries**the list of Pauli objects representing the Z\_2 symmetries |
| [`consistent_tapering`](#qiskit.aqua.operators.legacy.Z2Symmetries.consistent_tapering "qiskit.aqua.operators.legacy.Z2Symmetries.consistent_tapering")(operator) | Tapering the operator with the same manner of how this tapered operator is created. |
| [`copy`](#qiskit.aqua.operators.legacy.Z2Symmetries.copy "qiskit.aqua.operators.legacy.Z2Symmetries.copy")() | Get a copy of self. |
| [`find_Z2_symmetries`](#qiskit.aqua.operators.legacy.Z2Symmetries.find_Z2_symmetries "qiskit.aqua.operators.legacy.Z2Symmetries.find_Z2_symmetries")(operator) | Finds Z2 Pauli-type symmetries of an Operator. |
| [`is_empty`](#qiskit.aqua.operators.legacy.Z2Symmetries.is_empty "qiskit.aqua.operators.legacy.Z2Symmetries.is_empty")() | Check the z2\_symmetries is empty or not. |
| [`taper`](#qiskit.aqua.operators.legacy.Z2Symmetries.taper "qiskit.aqua.operators.legacy.Z2Symmetries.taper")(operator\[, tapering\_values]) | Taper an operator based on the z2\_symmetries info and sector defined by tapering\_values. |
| [`two_qubit_reduction`](#qiskit.aqua.operators.legacy.Z2Symmetries.two_qubit_reduction "qiskit.aqua.operators.legacy.Z2Symmetries.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`](#qiskit.aqua.operators.legacy.Z2Symmetries.cliffords "qiskit.aqua.operators.legacy.Z2Symmetries.cliffords") | Get clifford operators, build based on symmetries and single-qubit X. |
| [`sq_list`](#qiskit.aqua.operators.legacy.Z2Symmetries.sq_list "qiskit.aqua.operators.legacy.Z2Symmetries.sq_list") | returns sq list |
| [`sq_paulis`](#qiskit.aqua.operators.legacy.Z2Symmetries.sq_paulis "qiskit.aqua.operators.legacy.Z2Symmetries.sq_paulis") | returns sq paulis |
| [`symmetries`](#qiskit.aqua.operators.legacy.Z2Symmetries.symmetries "qiskit.aqua.operators.legacy.Z2Symmetries.symmetries") | return symmetries |
| [`tapering_values`](#qiskit.aqua.operators.legacy.Z2Symmetries.tapering_values "qiskit.aqua.operators.legacy.Z2Symmetries.tapering_values") | returns tapering values |
### cliffords
<Attribute id="qiskit.aqua.operators.legacy.Z2Symmetries.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](qiskit.aqua.operators.legacy.WeightedPauliOperator "qiskit.aqua.operators.legacy.WeightedPauliOperator")]
</Attribute>
### consistent\_tapering
<Function id="qiskit.aqua.operators.legacy.Z2Symmetries.consistent_tapering" signature="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*](qiskit.aqua.operators.legacy.WeightedPauliOperator "qiskit.aqua.operators.legacy.WeightedPauliOperator")) – the to-be-tapered operator
**Returns**
the tapered operator
**Return type**
TaperedWeightedPauliOperator
**Raises**
[**AquaError**](qiskit.aqua.AquaError "qiskit.aqua.AquaError") – The given operator does not commute with the symmetry
</Function>
### copy
<Function id="qiskit.aqua.operators.legacy.Z2Symmetries.copy" signature="copy()">
Get a copy of self.
**Return type**
`Z2Symmetries`
**Returns**
copy
</Function>
### find\_Z2\_symmetries
<Function id="qiskit.aqua.operators.legacy.Z2Symmetries.find_Z2_symmetries" signature="find_Z2_symmetries(operator)" modifiers="classmethod">
Finds Z2 Pauli-type symmetries of an Operator.
**Return type**
`Z2Symmetries`
**Returns**
a z2\_symmetries object contains symmetries, single-qubit X, single-qubit list.
</Function>
### is\_empty
<Function id="qiskit.aqua.operators.legacy.Z2Symmetries.is_empty" signature="is_empty()">
Check the z2\_symmetries is empty or not.
**Returns**
empty
**Return type**
bool
</Function>
### sq\_list
<Attribute id="qiskit.aqua.operators.legacy.Z2Symmetries.sq_list">
returns sq list
</Attribute>
### sq\_paulis
<Attribute id="qiskit.aqua.operators.legacy.Z2Symmetries.sq_paulis">
returns sq paulis
</Attribute>
### symmetries
<Attribute id="qiskit.aqua.operators.legacy.Z2Symmetries.symmetries">
return symmetries
</Attribute>
### taper
<Function id="qiskit.aqua.operators.legacy.Z2Symmetries.taper" signature="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*](qiskit.aqua.operators.legacy.WeightedPauliOperator "qiskit.aqua.operators.legacy.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`](qiskit.aqua.operators.legacy.WeightedPauliOperator "qiskit.aqua.operators.legacy.WeightedPauliOperator")
**Return type**
list\[[WeightedPauliOperator](qiskit.aqua.operators.legacy.WeightedPauliOperator "qiskit.aqua.operators.legacy.WeightedPauliOperator")] or [WeightedPauliOperator](qiskit.aqua.operators.legacy.WeightedPauliOperator "qiskit.aqua.operators.legacy.WeightedPauliOperator")
**Raises**
[**AquaError**](qiskit.aqua.AquaError "qiskit.aqua.AquaError") – Z2 symmetries, single qubit pauli and single qubit list cannot be empty
</Function>
### tapering\_values
<Attribute id="qiskit.aqua.operators.legacy.Z2Symmetries.tapering_values">
returns tapering values
</Attribute>
### two\_qubit\_reduction
<Function id="qiskit.aqua.operators.legacy.Z2Symmetries.two_qubit_reduction" signature="two_qubit_reduction(operator, num_particles)" modifiers="static">
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*](qiskit.aqua.operators.legacy.WeightedPauliOperator "qiskit.aqua.operators.legacy.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](qiskit.aqua.operators.legacy.WeightedPauliOperator "qiskit.aqua.operators.legacy.WeightedPauliOperator")
</Function>
</Class>
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