Channel-Adapted Quantum Error Correction for the Amplitude Damping Channel

TL;DR

This paper develops specialized quantum error correction codes tailored for the amplitude damping channel, introducing new stabilizer codes and optimization strategies for improved error correction in quantum systems.

Contribution

It generalizes existing amplitude damping codes, introduces new stabilizer codes, and provides quantum circuits and optimization methods for better error correction.

Findings

Generalized [2(M+1),M] codes for amplitude damping

Presented a [7,3] code based on Hamming code

Optimized recovery operations based on damping probability

Abstract

We consider error correction procedures designed specifically for the amplitude damping channel. We analyze amplitude damping errors in the stabilizer formalism. This analysis allows a generalization of the [4,1] `approximate' amplitude damping code of quant-ph/9704002. We present this generalization as a class of [2(M+1),M] codes and present quantum circuits for encoding and recovery operations. We also present a [7,3] amplitude damping code based on the classical Hamming code. All of these are stabilizer codes whose encoding and recovery operations can be completely described with Clifford group operations. Finally, we describe optimization options in which recovery operations may be further adapted according to the damping probability gamma.