# Linear-Time Maximum Likelihood Decoding of Surface Codes over the Quantum Erasure Channel

## TL;DR

This paper introduces a linear-time maximum likelihood decoder for surface codes over the quantum erasure channel, enabling fast and optimal error correction crucial for fault-tolerant quantum computing.

## Contribution

It presents the first linear-time decoding algorithm for surface codes over the quantum erasure channel, achieving optimal performance and speed.

## Key findings

- Decoding algorithm operates in linear time.
- Achieves maximum likelihood decoding performance.
- Suitable for real-time error correction in quantum computers.

## Abstract

Surface codes are among the best candidates to ensure the fault-tolerance of a quantum computer. In order to avoid the accumulation of errors during a computation, it is crucial to have at our disposal a fast decoding algorithm to quickly identify and correct errors as soon as they occur. We propose a linear-time maximum likelihood decoder for surface codes over the quantum erasure channel. This decoding algorithm for dealing with qubit loss is optimal both in terms of performance and speed.