# Z2Symmetries

`qiskit.opflow.primitive_ops.Z2Symmetries(symmetries, sq_paulis, sq_list, tapering_values=None, tol=1e-14)`

Bases: `object`

(opens in a new tab)

Deprecated: Z2 Symmetries

The class `qiskit.opflow.primitive_ops.tapered_pauli_sum_op.Z2Symmetries`

is deprecated as of qiskit-terra 0.24.0. It will be removed no earlier than 3 months after the release date. For code migration guidelines, visit https://qisk.it/opflow_migration (opens in a new tab).

**Parameters**

**symmetries**(*List*(opens in a new tab)*[**Pauli**]*) – the list of Pauli objects representing the Z_2 symmetries**sq_paulis**(*List*(opens in a new tab)*[**Pauli**]*) – the list of single - qubit Pauli objects to construct the Clifford operators**sq_list**(*List*(opens in a new tab)*[**int*(opens in a new tab)*]*) – the list of support of the single-qubit Pauli objects used to build the Clifford operators**tapering_values**(*List*(opens in a new tab)*[**int*(opens in a new tab)*] | None*) – values determines the sector.**tol**(*float*(opens in a new tab)) – Tolerance threshold for ignoring real and complex parts of a coefficient.

**Raises**

**OpflowError** – Invalid paulis

## Attributes

### cliffords

Get clifford operators, build based on symmetries and single-qubit X. :returns: a list of unitaries used to diagonalize the Hamiltonian.

### settings

Return operator settings.

### sq_list

returns sq list

### sq_paulis

returns sq paulis

### symmetries

return symmetries

### tapering_values

returns tapering values

### tol

Tolerance threshold for ignoring real and complex parts of a coefficient.

## Methods

### consistent_tapering

`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** (*PauliSumOp*) – the to-be-tapered operator

**Returns**

The tapered operator

**Raises**

**OpflowError** – The given operator does not commute with the symmetry

**Return type**

### convert_clifford

`convert_clifford(operator)`

This method operates the first part of the tapering. It converts the operator by composing it with the clifford unitaries defined in the current symmetry.

**Parameters**

**operator** (*PauliSumOp*) – to-be-tapered operator

**Returns**

`PauliSumOp`

corresponding to the converted operator.

**Raises**

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

**Return type**

### copy

`copy()`

Get a copy of self. :returns: copy

**Return type**

### find_Z2_symmetries

`classmethod find_Z2_symmetries(operator)`

Finds Z2 Pauli-type symmetries of an Operator.

**Returns**

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

**Return type**

### is_empty

`is_empty()`

Check the z2_symmetries is empty or not. :returns: Empty or not

**Return type**

### taper

`taper(operator)`

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.

The tapering is a two-step algorithm which first converts the operator into a `PauliSumOp`

with same eigenvalues but where some qubits are only acted upon with the Pauli operators I or X. The number M of these redundant qubits is equal to the number M of identified symmetries.

The second step of the reduction consists in replacing these qubits with the possible eigenvalues of the corresponding Pauli X, giving 2^M new operators with M less qubits. If an eigenvalue sector was previously identified for the solution, then this reduces to 1 new operator with M less qubits.

**Parameters**

**operator** (*PauliSumOp*) – the to-be-tapered operator

**Returns**

[`PauliSumOp`

]; otherwise, `PauliSumOp`

**Return type**

If tapering_values is None

**Raises**

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

### taper_clifford

`taper_clifford(operator)`

This method operates the second part of the tapering. This function assumes that the input operators have already been transformed using `convert_clifford()`

. The redundant qubits due to the symmetries are dropped and replaced by their two possible eigenvalues. The tapering_values will be stored into the resulted operator for a record.

**Parameters**

**operator** (*PauliSumOp*) – Partially tapered operator resulting from a call to `convert_clifford()`

**Returns**

[`PauliSumOp`

]; otherwise, `PauliSumOp`

**Return type**

If tapering_values is None

**Raises**

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