Avoiding coherent errors with rotated concatenated stabilizer codes

TL;DR

This paper introduces a novel concatenated stabilizer code design that effectively mitigates coherent errors in quantum systems, enhancing fault tolerance and error correction capabilities, especially against amplitude damping errors.

Contribution

It proposes integrating stabilizer codes with constant-excitation codes via concatenation, creating codes immune to coherent phase errors and capable of correcting amplitude damping errors.

Findings

The concatenated codes are immune to coherent phase errors.

Fault-tolerant thresholds are established for the new codes.

An eight-qubit code corrects a single amplitude damping error.

Abstract

Coherent errors, which arise from collective couplings, are a dominant form of noise in many realistic quantum systems, and are more damaging than oft considered stochastic errors. Here, we propose integrating stabilizer codes with constant-excitation codes by code concatenation. Namely, by concatenating an $[[n,k,d]]$ stabilizer outer code with dual-rail inner codes, we obtain a $[[2n,k,d]]$ constant-excitation code immune from coherent phase errors and also equivalent to a Pauli-rotated stabilizer code. When the stabilizer outer code is fault-tolerant, the constant-excitation code has a positive fault-tolerant threshold against stochastic errors. Setting the outer code as a four-qubit amplitude damping code yields an eight-qubit constant-excitation code that corrects a single amplitude damping error, and we analyze this code's potential as a quantum memory.