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arXiv:2511.12227

Scalable quantum error mitigation for dynamical decoupling

Weibin Ni, Zhijie Li, Guanyu Qu, Asif Equbal, Zhecheng Sun, Jiale Dai, Fazhan Shi, Lei Sun

quant-phSubmitted Nov 15, 2025• Announced Nov 18, 2025• 0 citations• Revised Feb 15, 2026 (v2)
v1 · Nov 15, 2025v2 · Feb 15, 2026
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Abstract

Quantum coherence remains a fundamental challenge for advancing quantum technologies. Although dynamical decoupling can suppress decoherence noise, it frequently misestimates decoherence times due to control errors -- a previously underappreciated issue. Here, we present Hadamard phase cycling, a scalable non-Markovian quantum error mitigation method using group-structured phase configurations to filter spurious dynamics. Validated across molecular electron spins, nitrogen-vacancy centers in diamond, nuclear spins, trapped ions, and superconducting qubits, this technique enables accurate decoherence time characterization and enhanced state fidelity with linear complexity. Our results indicate that many reported ultralong decoherence times stem from artifacts like coherence-population mixing rather than genuine noise suppression. By ensuring dynamical authenticity, Hadamard phase cycling establishes a robust framework for reliable quantum control, paving the way for reassessment and advancement of coherence benchmarks in the NISQ era.

Comments
51 pages, 12 figures

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Quantum coherence remains a fundamental challenge for advancing quantum technologies. Although dynamical decoupling can suppress decoherence noise, it frequently misestimates decoherence times due to control errors -- a previously underappreciated issue. Here, we present Hadamard phase cycling, a scalable non-Markovian quantum error mitigation method using group-structured phase configurations to filter spurious dynamics. Validated across molecular electron spins, nitrogen-vacancy centers in diamond, nuclear spins, trapped ions, and superconducting qubits, this technique enables accurate decoherence time characterization and enhanced state fidelity with linear complexity. Our results indicate that many reported ultralong decoherence times stem from artifacts like coherence-population mixing rather than genuine noise suppression. By ensuring dynamical authenticity, Hadamard phase cycling establishes a robust framework for reliable quantum control, paving the way for reassessment and advancement of coherence benchmarks in the NISQ era.
Complex quantum systems and their various applications are susceptible to noise of coherent and incoherent nature. Characterization of noise and its sources is an open, key challenge in quantum technology applications, especially in terms of distinguishing between inherent incoherent noise and systematic coherent errors. In this paper, we study a scheme of repeated sequential measurements that enables the characterization of incoherent errors by reducing the effects of coherent errors. We demonstrate this approach using a coherently controlled nitrogen vacancy in diamond, coupled to both a natural nuclear spin bath (non-Markovian) and to experimentally controlled relaxation through an optical pumping process (nearly Markovian). Our results show mitigation of coherent errors both for Markovian and non-Markovian incoherent noise profiles. We apply this scheme to the estimation of the dephasing time (T2*) due to incoherent noise. We observe an improved robustness against coherent errors in the estimation of dephasing time (T2*) compared to the standard (Ramsey) measurement.
Realistic quantum computing is subject to noise. Therefore, an important frontier in quantum computing is to implement noise-resilient quantum control over qubits. At the same time, dynamical decoupling can protect the coherence of qubits. Here we demonstrate non-trivial quantum evolution steered by dynamical decoupling control, which simultaneously suppresses noise effects. We design and implement a self-protected controlled-NOT gate on the electron spin of a nitrogen-vacancy centre and a nearby carbon-13 nuclear spin in diamond at room temperature, by employing an engineered dynamical decoupling control on the electron spin. Final state fidelity of 0.91(1) is observed in preparation of a Bell state using the gate. At the same time, the qubit coherence time is elongated at least 30 fold. The design scheme does not require the dynamical decoupling control to commute with the qubit interaction and therefore works for general qubit systems. This work marks a step towards implementing realistic quantum computing systems. Realistic quantum computers require a high degree of qubit control and must also be resilient to noise. Using dynamical decoupling control techniques, Liuet al.implement a self-protected controlled-NOT gate for electron and nuclear spins that retains a high final state fidelity.
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The performance of quantum computers is hindered by decoherence and crosstalk, which cause errors and limit the ability to perform long computations. Dynamical decoupling is a technique that alleviates these issues by applying carefully timed pulses to individual qubits, effectively suppressing unwanted interactions. However, as quantum devices grow in size, it becomes increasingly important to minimize the time required to implement dynamical decoupling across the entire system. Here, we present “chromatic Hadamard dynamical decoupling” (CHaDD), an approach that efficiently schedules dynamical decoupling pulses for quantum devices with arbitrary qubit connectivity. By leveraging Hadamard matrices, CHaDD achieves a circuit depth that scales linearly with the chromatic number of the connectivity graph for general two-qubit interactions, assuming instantaneous pulses. This includes Z Z crosstalk, which is prevalent in superconducting quantum processing units (QPUs). The scaling of CHaDD represents an exponential improvement over all previous multiqubit decoupling schemes for devices with connectivity graphs the chromatic number of which grows at most polylogarithmically with the number of qubits. For graphs with a constant chromatic number, the scaling of CHaDD is independent of the number of qubits. We report on experiments we have conducted using IBM QPUs that confirm the advantage conferred by CHaDD. Our results suggest that CHaDD can become a useful tool for enhancing the performance and scalability of quantum computers by efficiently suppressing decoherence and crosstalk across large qubit arrays.
Zero-noise extrapolation (ZNE) is an established quantum error mitigation technique that infers noise-free expectation values by scaling circuit noise and extrapolating to the zero-noise limit. Standard ZNE formulations implicitly assume memoryless Markovian gate noise, where error rates scale linearly with circuit duration. In physical solid-state quantum processors dominated by colored 1/fα1/f^\alpha1/fα environmental dephasing, this fundamental assumption fails: non-Markovian noise induces superlinear coherence decay χ(t)∝t1+α\chi(t) \propto t^{1+\alpha}χ(t)∝t1+α, causing standard polynomial extrapolation to diverge. In this work, we demonstrate how inserting dynamical decoupling (DD) sequences into idle circuit intervals spectrally filters low-frequency noise components, linearizing the effective decay profile into a Markovian regime χeff(t)∝t\chi_{\text{eff}}(t) \propto tχeff​(t)∝t. We benchmark this combined DD–ZNE framework by reconstructing the order parameter across the quantum phase transition of a 1D Transverse-Field Ising Model (TFIM). Our results demonstrate that while standalone ZNE fails under non-Markovian dephasing, the combined DD–ZNE approach eliminates extrapolation divergence and reliably recovers ideal quantum observables. Key Highlights: Theoretical Breakdown: Analytical derivation showing why polynomial ZNE diverges under 1/fα1/f^\alpha1/fα dephasing environments due to superlinear temporal scaling. Filter Function Engineering: Demonstration of spectator-qubit XY-4 pulse insertion as a high-pass spectral filter that suppresses low-frequency noise and restores linear decay dynamics. Phase Transition Benchmark: Validation on a 4-qubit 1D TFIM order parameter (⟨σz(0)σz(1)⟩\langle \sigma_z^{(0)} \sigma_z^{(1)} \rangle⟨σz(0)​σz(1)​⟩) across g∈[0.1,2.0]g \in [0.1, 2.0]g∈[0.1,2.0], demonstrating a >69%>69\%>69% error reduction over unmitigated circuits and preventing non-physical polynomial divergence.
Abstract In the scale-up of quantum computers, the framework underpinning fault-tolerance generally relies on the strong assumption that environmental noise affecting qubit logic is uncorrelated (Markovian). However, as physical devices progress well into the complex multi-qubit regime, attention is turning to understanding the appearance and mitigation of correlated — or non-Markovian — noise, which poses a serious challenge to the progression of quantum technology. This error type has previously remained elusive to characterisation techniques. Here, we develop a framework for characterising non-Markovian dynamics in quantum systems and experimentally test it on multi-qubit superconducting quantum devices. Where noisy processes cannot be accounted for using standard Markovian techniques, our reconstruction predicts the behaviour of the devices with an infidelity of 10 −3 . Our results show this characterisation technique leads to superior quantum control and extension of coherence time by effective decoupling from the non-Markovian environment. This framework, validated by our results, is applicable to any controlled quantum device and offers a significant step towards optimal device operation and noise reduction.