On Error Thresholds for Pauli Channels: Some answers with many more questions
2026-03-04 • Information Theory
Information Theory
AI summaryⓘ
The authors study how much error certain quantum codes can tolerate before failing, focusing on a type of error called Pauli channels. They use a mathematical tool called coset weight enumerators to explore how combining small codes in new ways can improve error correction beyond expected limits. They find new examples where these combined codes behave better than predicted, provide exact formulas for some code combinations, and estimate performance for larger codes. Their work highlights both successes and surprising challenges in understanding the limits of quantum error correction.
Pauli channelsquantum error correctionstabilizer codescoset weight enumeratorsconcatenated codesnon-additivityerror thresholdhashing pointrepetition codes
Authors
Avantika Agarwal, Alan Bu, Amolak Ratan Kalra, Debbie Leung, Luke Schaeffer, Graeme Smith
Abstract
This paper focuses on error thresholds for Pauli channels. We numerically compute lower bounds for the thresholds using the analytic framework of coset weight enumerators pioneered by DiVincenzo, Shor and Smolin in 1998. In particular, we study potential non-additivity of a variety of small stabilizer codes and their concatenations, and report several new concatenated stabilizer codes of small length that show significant non-additivity. We also give a closed form expression of coset weight enumerators of concatenated phase and bit flip repetition codes. Using insights from this formalism, we estimate the threshold for concatenated repetition codes of large lengths. Finally, for several concatenations of small stabilizer codes we optimize for channels which lead to maximal non-additivity at the hashing point of the corresponding channel. We supplement these results with a discussion on the performance of various stabilizer codes from the perspective of the non-additivity and threshold problem. We report both positive and negative results, and highlight some counterintuitive observations, to support subsequent work on lower bounds for error thresholds.