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arXiv:2602.19042

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

Victor Kasatkin, Mario Morford-Oberst, Arian Vezvaee, Daniel A. Lidar

quant-phSubmitted Feb 22, 2026• Announced Feb 24, 2026• 0 citations• Revised Apr 1, 2026 (v2)
v1 · Feb 22, 2026v2 · Apr 1, 2026v3 · Jul 11, 2026
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Abstract

Quantum error correction/detection (QEC/QED) 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 encoded subspace, and QEC performance is governed by the errors that survive decoding, not just 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, QED-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 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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Quantum error correction (QEC) codes are necessary to fault-tolerantly operate quantum computers. However, every such code is inherently limited by its inability to detect logical errors. Here, we propose and implement a method that leverages dynamical decoupling (DD) to drastically suppress logical errors. The key to achieving this is to use the normalizer elements of the QEC code as DD pulses, which we refer to as normalizer dynamical decoupling (NDD). The resulting hybrid QEC-NDD strategy is in principle capable of handling arbitrary weight errors. We test an error detecting version of this strategy using IBM transmon devices and the [[4, 2, 2]] code, demonstrating performance that significantly exceeds the capabilities of using either this code or DD in isolation. We present a method that allows for the detection of logical errors affecting logically encoded Bell states, which, in this case, arise primarily from crosstalk among physical qubits. Building on this, we experimentally demonstrate high-fidelity entangled logical qubits. The fidelities we achieve are beyond-breakeven, i.e., they significantly exceed the corresponding fidelities of unprotected entangled qubits in the same setting. Quantum error correction codes are hindered by the inability to detect logical errors. Here the authors demonstrate a method that integrates quantum error correction with logical level dynamical decoupling to suppress these errors and achieve high fidelity entangled logical qubits.
Quantum error correction (QEC), the lynchpin of fault-tolerant quantum computing (FTQC), is designed and validated against well-behaved Pauli stochastic error models. But in real-world deployment, QEC protocols encounter a vast array of other errors -- coherent and non-Pauli errors -- whose impacts on quantum circuits are vastly different than those of stochastic Pauli errors. The impacts of these errors on QEC and FTQC protocols have been largely unpredictable to date due to exponential classical simulation cost. Here, we show how to accurately and efficiently model the effects of coherent and non-Pauli errors on FTQC, and we study the effects of such errors on syndrome extraction for surface and bivariate bicycle codes, and on magic state cultivation. Our analysis suggests that coherent error can shift fault-tolerance thresholds, increase the space-time cost of magic state cultivation, and can increase logical error rates by an order of magnitude compared to equivalent stochastic errors. These analyses are enabled by a new technique for mapping any Markovian circuit-level error model with sufficiently small error rates onto a detector error model (DEM) for an FTQC circuit. The resulting DEM enables Monte Carlo estimation of logical error rates and noise-adapted decoding, and its parameters can be analytically related to the underlying physical noise parameters to enable approximate strong simulation.
Quantum control and fault-tolerant quantum computing (FTQC) are two of the cornerstones on which the hope of realizing a large-scale quantum computer is pinned, yet only preliminary steps have been taken towards formalizing the interplay between them. Here we explore this interplay using the powerful strategy of dynamical decoupling (DD), and show how it can be seamlessly and optimally integrated with FTQC. To this end we show how to find the optimal decoupling generator set (DGS) for various subspaces relevant to FTQC, and how to simultaneously decouple them. We focus on stabilizer codes, which represent the largest contribution to the size of the DGS, showing that the intuitive choice comprising the stabilizers and logical operators of the code is in fact optimal, i.e., minimizes a natural cost function associated with the length of DD sequences. Our work brings hybrid DD-FTQC schemes, and their potentially considerable advantages, closer to realization.
The promise of quantum computing is closer to reality today than ever before, thanks to rapid progress in the development of quantum hardware. Even as qubit lifetimes and gate fidelities continue to improve, realizing robust, fault-tolerant quantum computers is contingent upon the successful implementation of quantum error correction (QEC). Conventional QEC schemes have rather high resource overheads and low threshold requirements, making them challenging to implement on present day hardware. Here, we use a recently developed noise-adapted 3-qubit QEC scheme to demonstrate break-even performance against native amplitude-damping (AD) noise on IBM quantum hardware. We use variational quantum circuits to construct hardware-efficient encoding and decoding circuits. This scheme is probabilistic due to the non-unitary nature of the recovery operators, which are implemented via the block-encoding technique. We demonstrate logical qubit lifetimes exceeding those of the physical qubits by performing multiple rounds of QEC. To further protect the qubits from dephasing due to crosstalk, we incorporate dynamical decoupling into our noise-adapted QEC scheme in a seamless fashion. To account for the post-selection overhead, we define a measure of gain, that allows for faithful performance benchmarking of the protocol. Our analysis suggests that the performance of our protocol is limited primarily by the measurement readout fidelity, and is bound to improve with successive generations of quantum processors.
What must a quantum error-correction decoder know about temporally correlated noise, and what does it cost to learn? We study this question for fixed stabilizer memory experiments with known system-environment interactions. We formulate calibration in terms of the fidelity differences that select a Pauli recovery and relate missing information to the resulting fidelity loss. Our main example uses weak coherent XXX rotations in a class of CSS codes including Shor, Steane, and odd-distance rotated surface codes. All physical qubits share a sign either fixed throughout a run or independently redrawn each interval. The two models have identical syndrome statistics and the same spatiotemporal Pauli process (SPP), obtained by Pauli-twirling every noise interval. Yet at suitable storage times, they require different logical corrections. In the weak-noise limit, each model is almost perfectly correctable when known. Without model information, even the best final recovery has a worst-case fidelity loss approaching 1/21/21/2 relative to the noise-aware optimum, despite access to the full syndrome record. For this pair of models, at fixed code and fixed positive target loss below 1/21/21/2, we prove matching calibration bounds. With logical preparation and final readout, complete QEC cycles require a number of noise intervals scaling as the inverse rotation angle raised to the code's XXX distance. Allowing two uninterrupted intervals before one extraction reduces the optimal cost to inverse-square scaling. Physical Pauli twirling of every noise interval changes both recovery performance and its information requirements. Discarding the record of applied random Pauli operations makes the SPP sufficient for optimal recovery. Keeping this record can improve the attainable fidelity, but reaching that optimum may require additional noise information.
Dynamical decoupling (DD) is a widely-used quantum control technique that takes advantage of temporal symmetries in order to partially suppress quantum errors without the need resource-intensive error detection and correction protocols. This and other open-loop error mitigation techniques are critical for quantum information processing in the era of Noisy Intermediate-Scale Quantum technology. However, despite its utility, dynamical decoupling does not address errors which occur at unstructured times during a circuit, including certain commonly-encountered noise mechanisms such as cross-talk and imperfectly calibrated control pulses. Here, we introduce and demonstrate an alternative technique - `quantum measurement emulation' (QME) - that effectively emulates the measurement of stabilizer operators via stochastic gate application, leading to a first-order insensitivity to coherent errors. The QME protocol enables error suppression based on the stabilizer code formalism without the need for costly measurements and feedback, and it is particularly well-suited to discrete coherent errors that are challenging for DD to address.