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arXiv:2506.11270

Drift-resilient mid-circuit measurement and state preparation error mitigation for dynamic circuits

Jader P. Santos, Raam Uzdin

Published Jun 12, 2025• 0 citations
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Abstract

Quantum error mitigation (QEM) for dynamic circuits, i.e., those incorporating mid-circuit measurements and feedforward, is important for two key reasons. First, quantum error correction (QEC) circuits are instances of dynamic circuits, and therefore a dynamic circuit-compatible QEM can extend circuit depth and address errors that QEC struggles with. Second, recent studies show that dynamic circuits can significantly outperform purely unitary ones. However, mid-circuit measurement errors remain a major bottleneck. Current solutions rely on readout noise characterization that is vulnerable to temporal noise drifts. To the best of our knowledge, no readout mitigation schemes are resilient to temporal noise drifts. By introducing parity-based noise amplification in repeated measurements, we derive and experimentally demonstrate a drift-resilient protocol for addressing preparation, mid-circuit, and terminating measurement errors without requiring calibration or characterization. Drift resilience increases the longest possible execution time (in terms of shots) and enables flexibility by combining data from non-consecutive times. For platforms such as trapped ions, where the measurements are highly disruptive, we provide an alternative reset-based mitigation scheme. We demonstrate our methods experimentally on IBMQ and Quantinuum hardware. Combined with the Layered-KIK gate error mitigation protocol, the presented readout mitigation approach enables "End-to-end" mitigation for dynamic circuits, that can improve the outcomes of QEC experiments, and that covers the widest range of errors to the best of our knowledge. Other applications of the presented methods include a faster alternative to gate-set tomography and diagnostics of defective qubits during the execution of the target algorithm.

DOI
10.48550/arxiv.2506.11270

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Quantum error mitigation (QEM) for dynamic circuits, i.e., those incorporating mid-circuit measurements and feedforward, is important for two key reasons. First, quantum error correction (QEC) circuits are instances of dynamic circuits, and therefore a dynamic circuit-compatible QEM can extend circuit depth and address errors that QEC struggles with. Second, recent studies show that dynamic circuits can significantly outperform purely unitary ones. However, mid-circuit measurement errors remain a major bottleneck. Current solutions rely on readout noise characterization that is vulnerable to temporal noise drifts. To the best of our knowledge, no readout mitigation schemes are resilient to temporal noise drifts. By introducing parity-based noise amplification in repeated measurements, we derive and experimentally demonstrate a drift-resilient protocol for addressing preparation, mid-circuit, and terminating measurement errors without requiring calibration or characterization. Drift resilience increases the longest possible execution time (in terms of shots) and enables flexibility by combining data from non-consecutive times. For platforms such as trapped ions, where the measurements are highly disruptive, we provide an alternative reset-based mitigation scheme. We demonstrate our methods experimentally on IBMQ and Quantinuum hardware. Combined with the Layered-KIK gate error mitigation protocol, the presented readout mitigation approach enables "End-to-end" mitigation for dynamic circuits, that can improve the outcomes of QEC experiments, and that covers the widest range of errors to the best of our knowledge. Other applications of the presented methods include a faster alternative to gate-set tomography and diagnostics of defective qubits during the execution of the target algorithm.
Quantum Error Mitigation is essential for enhancing the reliability of quantum computing experiments. The adaptive KIK error mitigation method has demonstrated significant advantages, including resilience to temporal noise drifts, applicability to non-Clifford gates, and guaranteed performance bounds. However, its reliance on global noise amplification introduces limitations, such as incompatibility with mid-circuit measurements and dynamic circuits, as well as small residual errors due to unaccounted high-order Magnus noise terms. In this work, we propose a layer-based noise amplification approach that overcomes these challenges without incurring additional overhead or experimental complexity. Since the Layered KIK method is inherently compatible with mid-circuit measurements, it enables seamless integration with quantum error correction codes. This synergy allows error correction to address dominant noise mechanisms, while the Layered KIK suppresses residual errors arising from leakage and correlated noise sources. Similarly, for reducing sampling costs, Layered KIK can be combined with complementary mitigation methods for providing drift resilience and broadening the range of addressable errors.
Dynamic quantum circuits integrate mid-circuit measurements and feed-forward operations to enable real-time classical processing and conditional quantum logic. These capabilities are central to key quantum protocols such as quantum error correction, and have recently demonstrated significant potential for reducing quantum resources, including circuit depth and gate count, across a range of applications. However, executing dynamic circuits on real quantum hardware introduces a critical trade-off: while resource requirements decrease, circuit fidelity degrades due to high error rates of mid-circuit measurements, as well as the decoherence errors accumulated during the extended idle periods introduced by both mid-circuit measurements and feed-forward operations. In this paper, we systematically investigate the impact of standard error mitigation techniques on dynamic circuit applications pertaining to Hamiltonian simulation and ground state estimation of physically relevant systems like the Heisenberg model. We explore dynamical decoupling (DD) as a strategy to suppress decoherence and crosstalk errors during idle windows introduced by mid-circuit measurements and feed-forward delays, and also examine error mitigation via zero-noise extrapolation (ZNE). Through experiments conducted on IBM quantum hardware, we benchmark effective combinations of these strategies that maximize the practical benefits of dynamic quantum circuits in these applications. We demonstrate that a combination of DD and ZNE is effective in mitigating the errors introduced during mid-circuit measurements and feed-forward operations, as well as the errors arising from faulty measurements. This approach yields a energy gap improvement of at least 60% in ground state estimation and reduces observed error of time-evolved states by up to 99% for the Ising model and up to 20% for the Heisenberg model.
Current quantum computing platforms suffer from readout errors, where faulty measurement outcomes are reported by the device. These errors are particularly harmful in quantum programs that rely on branch statements, where operations in later parts of the program are dynamically determined by mid-circuit measurements. We propose a general protocol for mitigating mid-circuit measurement errors. Our solution works for any number of mid-circuit measurement and feedforward layers without increasing circuit depth or two-qubit gate counts, is efficient under structural assumptions on error channels, and is suitable for immediate application on noisy intermediate-scale quantum devices. We experimentally demonstrate up to a ∼ 60 % reduction in error on superconducting quantum processors across several practically relevant feedforward circuits, including dynamic qubit resets, shallow-depth Greenberger–Horne–Zeilinger state preparation, and multistage quantum teleportation. This work paves the way for more error-resilient adaptive quantum circuits, crucial for current and future quantum computing applications.
Quantum Error Mitigation is essential for enhancing the reliability of quantum computing experiments. The adaptive KIK error mitigation method has demonstrated significant advantages, including resilience to temporal noise drifts, applicability to non-Clifford gates, and guaranteed performance bounds. However, its reliance on global noise amplification introduces limitations, such as incompatibility with mid-circuit measurements and dynamic circuits, as well as small residual errors due to unaccounted high-order Magnus noise terms. In this work, we propose a layer-based noise amplification approach that overcomes these challenges without incurring additional overhead or experimental complexity. Since the Layered KIK method is inherently compatible with mid-circuit measurements, it enables seamless integration with quantum error correction codes. This synergy allows error correction to address dominant noise mechanisms, while the Layered KIK suppresses residual errors arising from leakage and correlated noise sources. Similarly, for reducing sampling costs, Layered KIK can be combined with complementary mitigation methods for providing drift resilience and broadening the range of addressable errors.
Distributed Quantum Computing (DQC) and Quantum Error Correction (QEC) rely on dynamic circuits that include Mid-Circuit Measurements (MCMs) and classical feedback. These operations present a major bottleneck: MCMs suffer from high error rates that lead to real-time branching errors, while MCM and classical feedback latencies amplify decoherence errors. Current hardware controllers, qubit-state discriminators, and software error mitigation techniques fail to address these challenges holistically. We propose MCMit, a hardware-software co-design to mitigate branching and latency-induced errors. MCMit introduces a scalable, constant-latency multi-control branch instruction for faster classical feedback and two qubit-state discriminators, a transformer, and a CNN, with high accuracy even under short measurement durations. On the software side, static MCM elimination and stochastic branching complement the hardware by mitigating residual branching errors that persist despite hardware improvements. We implement MCMit on Qubic and evaluate it using experimentally extracted QPU readout traces. Our branch instruction reduces feedback latency by up to 70\%, improving circuit depths by up to 7×7\times7× over Qubic. Our CNN discriminator achieves up to 62\% higher accuracy for short measurement durations than the baselines, driving 1.2−9.4×1.2-9.4\times1.2−9.4× lower logical error rates in QEC. Last, our software mitigation improves fidelity by 18--30\% over baseline methods in DQC workloads.
Quantum error mitigation (QEM) infers noiseless expectation values from noisy variants of a target quantum circuit. Unlike quantum error correction, QEM requires no additional hardware resources and is therefore routinely employed in experiments on contemporary quantum processors. QEM strategies based on agnostic noise amplification (ANA) are intrinsically resilient to temporal noise drift during the execution of the experiment, but their sampling cost (runtime overhead) remains a major practical bottleneck. In this work, we introduce the virtual noise scaling framework and combine it with layered mitigation to further enhance performance. While virtual noise scaling consistently reduces sampling overhead, we identify a specific noise threshold for the layered mitigation approach. When the noise level is above this threshold, layered mitigation decreases the sampling overhead; conversely, when below it, the overhead increases. Notably, this threshold is circuit-independent and depends solely on the number of layers. For strong noise, the combination of virtual noise scaling and layered mitigation yields several orders of magnitude reduction in sampling overhead compared with conventional zero-noise extrapolation post-processing. As a result, mitigation tasks that once seemed unrealistic are now challenging but achievable. The proposed approach is compatible with dynamic circuits and can be seamlessly integrated with error detection and quantum error correction schemes. In addition, it is also applicable to ANA-based mitigation of mid-circuit measurements and preparation errors. Our findings extend to any constant-step amplification factors and therefore also apply to probabilistic error amplification (PEA) QEM. We validate our post-processing approach by applying it to previously reported experimental data, where we observe a substantial improvement in mitigation efficiency and accuracy.