Quantum Error Correction and Dynamical Decoupling: Better Together or Apart?

• URL: http://arxiv.org/abs/2602.19042v1
• Date: Sun, 22 Feb 2026 04:35:26 GMT
• Title: Quantum Error Correction and Dynamical Decoupling: Better Together or Apart?
• Authors: Victor Kasatkin, Mario Morford-Oberst, Arian Vezvaee, Daniel A. Lidar,
• Abstract summary: Quantum error correction (QEC) and dynamical decoupling (DD) are tools for protecting quantum information.<n>We analyze a hybrid memory cycle where DD is implemented logically (LDD) using normalizer elements of an $[n,k,d]]$ stabilizer code.<n>We show how LDD suppresses at least one minimum-weight uncorrectable Pauli error for the chosen recovery map.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: Quantum error correction (QEC) and dynamical decoupling (DD) are tools for protecting quantum information. A natural goal is to combine them to outperform either approach alone. Such a benefit is not automatic: physical DD can conflict with an encoded subspace, and QEC performance is governed by the errors that survive decoding, not necessarily those DD suppresses. We analyze a hybrid memory cycle where DD is implemented logically (LDD) using normalizer elements of an $[[n,k,d]]$ stabilizer code, followed by a round of syndrome measurement and recovery (or, in the detection setting, postselection on a trivial syndrome). In an effective Pauli model with physical error probability $p$, LDD suppression factor $p_{DD}$, and recovery imperfection rate $p_{QEC}$ (or $p_{QED}$), we derive closed-form entanglement-fidelity expressions for QEC-only, LDD-only, physical DD, and the hybrid LDD+QEC protocol. The formulas are expressed via a small set of code-dependent weight enumerator polynomials, making the role of the decoder and the LDD group explicit. For ideal recovery LDD+QEC outperforms QEC-only iff the conditional fraction of uncorrectable Pauli errors is larger in the LDD-suppressed sector than in the unsuppressed sector. In the low-noise regime, a sufficient design rule guaranteeing hybrid advantage is that LDD suppresses at least one minimum-weight uncorrectable Pauli error for the chosen recovery map. We show how stabilizer-equivalent choices of LDD generators can be used to enforce this condition. We supplement our analysis with numerical results for the $[[7,1,3]]$ Steane code and a $[[13,1,3]]$ code, mapping regions of hybrid-protocol advantage in parameter space beyond the small-$p$ regime. Our work illustrates the need for co-design of the code, decoder, and logical decoupling group, and clarifies the conditions under which the hybrid LDD+QEC protocol is advantageous.

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