Validating quantum processors at scale increasingly relies on approximate classical simulation, which adds truncation error to the comparison between ideal and observed behavior. We describe a 15-qubit dynamic-circuit benchmark that stays within exact state-vector simulation, so the ideal reference value is computed without approximation. The circuit scrambles a 6-qubit system, couples it to a 5-qubit engineered environment, reads out four weakly coupled probe qubits mid-circuit, and then applies the inverse of the scrambling and system–environment coupling to restore the system's coherence. Exact summation over the 16 probe outcomes gives an ideal recovery fidelity F_max = 0.9889 on the 11-qubit system–environment register; the shortfall from unity reflects information carried away by the probes, whose coupling is not inverted and which are discarded after readout. We demonstrate the pipeline with a single 400-shot run on the Quantinuum H2-1 emulator (quantinuum.sim.h2-1e) via Azure Quantum. A local surrogate built from three published H2-1 headline error rates predicted F_exp = 0.8353 ± 0.0054; the emulator returned a readout-mitigated F_rec = 0.7836 ± 0.0212, 2.36 nominal standard errors lower. Because the surrogate's quoted uncertainty reflects sampling error only, we interpret the shortfall as evidence of surrogate-model mismatch—expected, given the emulator's richer noise model—rather than as a statistically calibrated anomaly. No physical-hardware data are reported. Changes in v50: Retitled (formerly "A 15-Qubit Decoherence-Reversal Protocol for Benchmarking Mid-Circuit Measurements and Environmental Imprinting"). Corrected the echo formulation (v49 Eq. 4 was identically 1) and the reported raw frequency (77.5%, not 76.0%). Result reframed as a nominal surrogate-model mismatch on the H2-1 emulator rather than anomalous decoherence; SWAP-routing explanation withdrawn. References corrected; limitations and data/code availability added. Analysis code unchanged from v48. Code and data: https://github.com/dkahng/15-qubit-mcm-protocol
Validating quantum processors at scale increasingly relies on approximate classical simulation, which adds truncation error to the comparison between ideal and observed behavior. We describe a 15-qubit dynamic-circuit benchmark that stays within exact state-vector simulation, so the ideal reference value is computed without approximation. The circuit scrambles a 6-qubit system, couples it to a 5-qubit engineered environment, reads out four weakly coupled probe qubits mid-circuit, and then applies the inverse of the scrambling and system–environment coupling to restore the system's coherence. Exact summation over the 16 probe outcomes gives an ideal recovery fidelity F_max = 0.9889 on the 11-qubit system–environment register; the shortfall from unity reflects information carried away by the probes, whose coupling is not inverted and which are discarded after readout. We demonstrate the pipeline with a single 400-shot run on the Quantinuum H2-1 emulator (quantinuum.sim.h2-1e) via Azure Quantum. A local surrogate built from three published H2-1 headline error rates predicted F_exp = 0.8353 ± 0.0054; the emulator returned a readout-mitigated F_rec = 0.7836 ± 0.0212, 2.36 nominal standard errors lower. Because the surrogate's quoted uncertainty reflects sampling error only, we interpret the shortfall as evidence of surrogate-model mismatch—expected, given the emulator's richer noise model—rather than as a statistically calibrated anomaly. No physical-hardware data are reported. Changes in v50: Retitled (formerly "A 15-Qubit Decoherence-Reversal Protocol for Benchmarking Mid-Circuit Measurements and Environmental Imprinting"). Corrected the echo formulation (v49 Eq. 4 was identically 1) and the reported raw frequency (77.5%, not 76.0%). Result reframed as a nominal surrogate-model mismatch on the H2-1 emulator rather than anomalous decoherence; SWAP-routing explanation withdrawn. References corrected; limitations and data/code availability added. Analysis code unchanged from v48. Code and data: https://github.com/dkahng/15-qubit-mcm-protocol
H. Billah and M.M.H. Sarker contributed equally to this work. Interpreting a fixed quantum circuit's output as evidence of a hardware effect requires ruling out two things usually conflated with it: finite-sample fluctuation, and structure already present in the circuit's own noiseless output. Less commonly checked is a third: whether the reference circuit compared against is the one actually executed, once compiler-level qubit routing is accounted for. We execute a fixed 35-qubit, 243-gate diagnostic circuit on IBM Heron-family hardware (three runs, two backends) and show this third check is essential: the routed circuit submitted to hardware has different noiseless predictions than the logical circuit intended, for several qubits. Against the correct, routed-circuit reference, the aggregate deviation is significant in two of three runs, and four registers (0, 9, 14, 27) show a significant output-probability deviation in every run — though we distinguish a high-confidence subset, {0, 9, 27}, with tightly time-matched calibration, from qubit 14, included only on an exploratory basis given its calibration was retrieved roughly two weeks post-execution. Same-backend replicates correlate more strongly by the Pearson measure, though a rank-based (Spearman) test shows this gap does not survive at the level of register ordering, indicating substantial leverage from a small number of registers rather than a broadly robust pattern; these three executions also share a byte-identical payload and are not independent replications in the strictest sense. The mechanism is only partially resolved: independent single-qubit readout error and raw gate count are ruled out as complete explanations for most of these registers, but the simplest version of the leading hypothesis for the single most-affected register does not reproduce the observed cross-backend pattern even with live, backend-specific timing data. A second, structurally different circuit validated only in simulation calibrates the statistical procedure's behavior under one synthetic noise model; it does not itself establish generality to real hardware, and the specific register set found here should not be expected to generalize beyond this study. Note on scope: this is a methodology and case-study contribution centered on executed-circuit references for fixed-circuit diagnostics, not a characterization of IBM Heron hardware in general or a randomized-benchmarking experiment in the formal sense. Supporting data, the routed OpenQASM circuits, raw measurement counts, and analysis code for this study are available on request from the corresponding author. Affiliation: Sonicium Quantum Lab Ltd., Dhaka, Bangladesh.
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.
High-fidelity mid-circuit measurements, which read out the state of specific qubits in a multiqubit processor without destroying them or disrupting their neighbors, are a critical component for useful quantum computing. They enable fault-tolerant quantum error correction, dynamic circuits, and other paths to solving classically intractable problems. But there are few methods to assess their performance comprehensively. In this work, we address this gap by introducing the first randomized benchmarking protocol that measures the rate at which mid-circuit measurements induce errors in many-qubit circuits. Using this protocol, we detect and eliminate previously undetected measurement-induced crosstalk in a 20-qubit trapped-ion quantum computer. Then, we use the same protocol to measure the rate of measurement-induced crosstalk error on a 27-qubit IBM Q processor, and quantify how much of that error is eliminated by dynamical decoupling. Characterisation of quantum operations is fundamental in quantum technologies - quantum computing in particular - but there’s currently no reliably efficient method to assess mid-circuit measurements, which are a key component for subfields like quantum error correction. Here, the authors fill this gap, integrating MCMs into the framework of randomized benchmarking.
Noise characterization of multi-qubit entangling Clifford operations is a key practical bottleneck for quantum error mitigation and for the calibration, validation, and optimization of quantum error-correction protocols, especially in the presence of state preparation and measurement (SPAM) errors. Although cycle benchmarking can isolate some Pauli error components, it cannot resolve the problem of coupled error parameters, which leads to unlearnable degrees of freedom even in simple noisy gates, not to mention general n-qubit Clifford gates. Here we introduce mid-circuit-measurement-based generalized cycle benchmarking, a framework that makes otherwise unidentifiable Pauli fidelities and non-Markovian noise learnable via repeated measurements and classical post-processing. Applying the deferred feed-forward principle to generalized cycle benchmarking, we show that an insertion of mid-circuit measurements can reverse Pauli cycles induced by a general Clifford gate. This fact enables us to reveal a Pauli-noise learnability condition for Clifford gates. Assuming sufficient state preparation quality, we numerically demonstrate the feasibility of characterizing the previously unlearnable noise components. We implement the protocol on superconducting quantum processing units and validate its effectiveness in disambiguating the coupled noise components, benchmarked against conventional tomography. Finally, we observe consistent measurement-induced bit-flip bias and non-Markovian correlations, which define a range of applicability for the Pauli noise model and the proposed noise-characterization protocol.
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.
Near-term quantum computers have been built as intermediate-scale quantum devices and are fragile against quantum noise effects, namely, NISQ devices. Traditional quantum-error-correcting codes are not implemented on such devices and to perform quantum computation in good accuracy with these machines we need to develop alternative approaches for mitigating quantum computational errors. In this work, we propose quantum error mitigation (QEM) scheme for quantum computational errors which occur due to couplings with environments during gate operations, i.e., decoherence. To establish our QEM scheme, first we estimate the quantum noise effects on single-qubit states and represent them as groups of quantum circuits, namely, quantum-noise-effect circuit groups. Then our QEM scheme is conducted by subtracting expectation values generated by the quantum-noise-effect circuit groups from those obtained by the quantum circuits for the quantum algorithms under consideration. As a result, the quantum noise effects are reduced, and we obtain approximately the ideal expectation values via the quantum-noise-effect circuit groups and the numbers of elementary quantum circuits composing them scale polynomial with respect to the products of the depths of quantum algorithms and the numbers of register bits. To numerically demonstrate the validity of our QEM scheme, we run noisy quantum simulations of qubits under amplitude damping effects for four types of quantum algorithms. Furthermore, we implement our QEM scheme on IBM Q Experience processors and examine its efficacy. Consequently, the validity of our scheme is verified via both the quantum simulations and the quantum computations on the real quantum devices. Our QEM scheme is solely composed of quantum-computational operations (quantum gates and measurements), and thus, it can be conducted by any type of quantum device. In addition, it can be applied to error mitigation for many other types of quantum noise effects as well as noisy quantum computing of long-depth quantum algorithms.