# Reliable channel-adapted error correction: Bacon-Shor code recovery from amplitude damping

## TL;DR

This paper presents two efficient, fault-tolerant error correction schemes tailored for amplitude damping noise in Bacon-Shor codes, reducing qubit requirements and enhancing robustness using Clifford operations.

## Contribution

Introduction of two novel, resource-efficient error correction schemes for amplitude damping noise in Bacon-Shor codes, compatible with fault-tolerance methods.

## Key findings

- One scheme uses one-qubit teleportation and requires 25% of the qubits of standard methods.
- The second scheme employs stabilizer measurements, needing only half as many qubits.
- Both schemes are compatible with existing fault-tolerance techniques.

## Abstract

We construct two simple error correction schemes adapted to amplitude damping noise for Bacon-Shor codes and investigate their prospects for fault-tolerant implementation. Both consist solely of Clifford gates and require far fewer qubits, relative to the standard method, to achieve correction to a desired order in the damping rate. The first, employing one-bit teleportation and single-qubit measurements, needs only one fourth as many physical qubits, while the second, using just stabilizer measurements and Pauli corrections, needs only half. We show that existing fault-tolerance methods can be employed for the latter, while the former can be made to avoid potential catastrophic errors and can easily cope with damping faults in ancilla qubits.