---
title: PauliLindbladError (latest version)
description: API reference for qiskit_ibm_runtime.results.PauliLindbladError in the latest version of qiskit-ibm-runtime
source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/qiskit-ibm-runtime/results-pauli-lindblad-error
---

# PauliLindbladError

*class* `PauliLindbladError(generators, rates)`

[GitHub](https://github.com/Qiskit/qiskit-ibm-runtime/tree/stable/0.49/qiskit_ibm_runtime/results/noise_learner.py#L33-L119)

Bases: `object`

A Pauli error channel generated by a Pauli Lindblad dissipators.

This operator represents an N-qubit quantum error channel $E(\rho) = e^{\sum_j r_j D_{P_j}}(\rho)$ generated by Pauli Lindblad dissipators $D_P(\rho) = P \rho P - \rho$, where $P_j$ are N-qubit `Pauli` operators.

The list of Pauli generator terms are stored as a `PauliList` and can be accessed via the [`generators`](#qiskit_ibm_runtime.results.PauliLindbladError.generators "qiskit_ibm_runtime.results.PauliLindbladError.generators") attribute. The array of dissipator rates $r_j$ can be accessed via the [`rates`](#qiskit_ibm_runtime.results.PauliLindbladError.rates "qiskit_ibm_runtime.results.PauliLindbladError.rates") attribute.

The equivalent Pauli error channel can be constructed as a composition of single-Pauli channel terms

$$
E = e^{\sum_j r_j D_{P_j}} = \prod_j e^{r_j D_{P_j}}
= prod_j \left( (1 - p_j) S_I + p_j S_{P_j} \right)
$$

where $p_j = \frac12 - \frac12 e^{-2 r_j}$ \[1].

**Parameters**

- **generators** (*PauliList*) – A list of the Pauli Lindblad generators for the error channel.
- **rates** (*Sequence\[float]*) – A list of the rates for the Pauli-Lindblad `generators`.

**Raises**

**ValueError** – If `generators` and `rates` have different lengths.

**References**

1. E. van den Berg, Z. Minev, A. Kandala, K. Temme, *Probabilistic error cancellation with sparse Pauli–Lindblad models on noisy quantum processors*, Nature Physics volume 19, pages1116–1121 (2023). [arXiv:2201.09866 \[quant-ph\]](https://arxiv.org/abs/2201.09866)

## Attributes

### generators

The Pauli Lindblad generators of this [`PauliLindbladError`](#qiskit_ibm_runtime.results.PauliLindbladError "qiskit_ibm_runtime.results.PauliLindbladError").

### num\_qubits

The number of qubits in this [`PauliLindbladError`](#qiskit_ibm_runtime.results.PauliLindbladError "qiskit_ibm_runtime.results.PauliLindbladError").

### rates

The Lindblad generator rates of this quantum error.

## Methods

### restrict\_num\_bodies

`restrict_num_bodies(num_qubits)`

[GitHub](https://github.com/Qiskit/qiskit-ibm-runtime/tree/stable/0.49/qiskit_ibm_runtime/results/noise_learner.py#L94-L112)

Pauli-Lindblad error containing only those terms acting on exactly `num_qubits` qubits.

The [`PauliLindbladError`](#qiskit_ibm_runtime.results.PauliLindbladError "qiskit_ibm_runtime.results.PauliLindbladError") containing only those terms acting on exactly `num_qubits` qubits.

**Parameters**

**num\_qubits** (*int*) – The number of qubits that the returned error acts on.

**Returns**

The error containing only those terms acting on exactly `num_qubits` qubits.

**Raises**

**ValueError** – If `num_qubits` is smaller than `0`.

**Return type**

[*PauliLindbladError*](#qiskit_ibm_runtime.results.PauliLindbladError "qiskit_ibm_runtime.results.noise_learner.PauliLindbladError")