# Quantum error correction with only two extra qubits

## TL;DR

This paper presents fault-tolerant quantum error correction methods that require only two additional qubits, enabling efficient protection of quantum information with minimal qubit overhead.

## Contribution

Introduction of fault-tolerant error-correction procedures using only two ancilla qubits applicable to various distance-three codes.

## Key findings

- Allows testing of the [[5,1,3]] code with only seven qubits total.
- Techniques extend to [[7,1,3]] and [[15,7,3]] codes.
- Enables protection of seven qubits on a 17-qubit device.

## Abstract

Noise rates in quantum computing experiments have dropped dramatically, but reliable qubits remain precious. Fault-tolerance schemes with minimal qubit overhead are therefore essential. We introduce fault-tolerant error-correction procedures that use only two ancilla qubits. The procedures are based on adding "flags" to catch the faults that can lead to correlated errors on the data. They work for various distance-three codes. In particular, our scheme allows one to test the [[5,1,3]] code, the smallest error-correcting code, using only seven qubits total. Our techniques also apply to the [[7,1,3]] and [[15,7,3]] Hamming codes, thus allowing to protect seven encoded qubits on a device with only 17 physical qubits.