# Noisy Stabilizer Formalism

**Authors:** Maria Flors Mor-Ruiz, Wolfgang Dür  
**arXiv:** [2212.08677](https://arxiv.org/abs/2212.08677)  
**Date:** 2022-12-16  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2212.08677v2/

## Key points

- Stabilizer formalism leverages Gottesman-Knill theorem for manipulating pure stabilizer or graph states using Clifford operations and Pauli measurements
- Noisy stabilizer formalism extends the stabilizer formalism to account for Pauli noise processes affecting stabilizer states
- Noisy stabilizer formalism scales linearly with the number of qubits in the initial state but exponentially with the size of the target state
- It enables efficient description and tracking of noisy stabilizer states under local Pauli measurements to generate multipartite entangled states efficiently
- Mor-Ruiz and Dür's work in Phys. Rev. A 107, 032424 (2023) introduces a novel framework for handling noisy quantum systems efficiently, paving the way for advancements in quantum information processing

## Summary

In the realm of quantum computing, efficient methods for describing and manipulating multi-qubit quantum states and processes have been a subject of intense research. One notable approach is the stabilizer formalism, which leverages the Gottesman-Knill theorem to manipulate pure stabilizer or graph states using Clifford operations and Pauli measurements. These states are crucial in various applications within quantum technologies. Building upon this foundation, Maria Flors Mor-Ruiz and Wolfgang Dür have developed a groundbreaking extension known as the noisy stabilizer formalism. This innovative method not only enables the efficient description and tracking of pure states under Clifford operations and Pauli measurements but also accounts for Pauli noise processes affecting stabilizer states. This includes various types of noise such as uncorrelated and correlated dephasing, as well as single- or multi-qubit depolarizing noise. One key advantage of the noisy stabilizer formalism is its scalability. While it scales linearly with the number of qubits in the initial state, it exhibits exponential scaling in relation to the size of the target state. This feature becomes particularly relevant when manipulating noisy stabilizer states through local Pauli measurements to generate multipartite entangled states involving a few qubits. In such scenarios, this method allows for an efficient description of the resulting state despite its complexity. The work by Mor-Ruiz and Dür, published in Phys. Rev. A 107, 032424 (2023), sheds light on a novel framework that expands our capabilities in handling noisy quantum systems efficiently. By bridging theory with practical applications, their research paves the way for advancements in quantum information processing and lays a solid foundation for future developments in quantum technologies.