Mid-circuit measurements are essential primitives for dynamic circuits and quantum error correction, yet characterizing their induced disturbance on spectator qubits remains a central practical problem. Device-level benchmarking often compresses this disturbance into low-order proxy metrics such as $T_1$, $T_2$, readout assignment error, and pairwise crosstalk. We argue that these proxies can be operationally incomplete for multiscale dynamic circuits. We introduce a higher-order context-conditioned kernel, $Γ_{\mathrm{eff}}[Y,O] = Γ_{\mathrm{loc}}[O] + Γ_{\mathrm{proxy}}[O] + Γ_{\mathrm{rel}}[Y,O]$, where $Y$ is a global context label and $O$ a local observable. The term $Γ_{\mathrm{rel}}[Y,O]$ is a phenomenological compression ansatz isolating residual context dependence unexplained by standard proxies. To avoid impossibility issues of quantum partial-information decompositions on non-commuting algebras, the Möbius weights entering this ansatz are evaluated operationally on classical measurement outcomes. We present evidence in three steps. First, earlier GHZ-versus-clock hardware results motivate an observable-class split. Second, we present dynamical evidence using the A6 synthetic hardware harness. A6 injects a pure higher-order context dependence via a programmed conditional interaction. Because the $(C_0,C_1,C_2)$ parity context is invisible to singles and pairs by construction, standard low-order diagnostics are fundamentally blind to the source of the probe's disturbance. Third, we demonstrate coherent controllability through the A6.2 quantum-eraser experiment. Programmable MARK interactions suppress unconditional fringes while eraser-basis conditioning restores them, consistent with complementarity bounds. These results validate a context-conditioned description of backaction over proxy-only null models.
Comments
11 pages, 4 figures, 2 tables. Includes empirical data, rigorous passive controls, and a hardware-native quantum eraser validation on IBM superconducting processors. Open-source Qiskit artifacts available via Zenodo
Mid-circuit measurements are essential primitives for dynamic circuits and quantum error correction, yet characterizing their induced disturbance on spectator qubits remains a central practical problem. Device-level benchmarking often compresses this disturbance into low-order proxy metrics such as T1, T2, readout assignment error, and pairwise crosstalk. We argue that these proxies can be operationally incomplete for multiscale dynamic circuits. We introduce a higher-order context-conditioned kernel, Γeff[Y,O]=Γloc[O]+Γproxy[O]+Γrel[Y,O], where Y is a global context label and O a local observable. The term Γrel[Y,O] is a phenomenological compression ansatz isolating residual context dependence unexplained by standard proxies. To avoid impossibility issues of quantum partial-information decompositions on non-commuting algebras, the Möbius weights entering this ansatz are evaluated operationally on classical measurement outcomes. We present evidence in three steps. First, earlier GHZ-versus-clock hardware results motivate an observable-class split. Second, we present dynamical evidence using the A6 synthetic hardware harness. A6 injects a pure higher-order context dependence via a programmed conditional interaction. Because the (C0,C1,C2) parity context is invisible to singles and pairs by construction, standard low-order diagnostics are fundamentally blind to the source of the probe's disturbance. Third, we demonstrate coherent controllability through the A6.2 quantum-eraser experiment. Programmable MARK interactions suppress unconditional fringes while eraser-basis conditioning restores them, consistent with complementarity bounds. These results validate a context-conditioned description of backaction over proxy-only null models.
Accurate modeling of midcircuit measurements (MCMs) is essential for dynamic-circuit operations such as syndrome extraction, measurement-based reset, and the separation of state-preparation and measurement error. Unlike terminal measurement, a noisy MCM both produces a classical outcome and alters the incoming quantum state, thereby influencing subsequent circuit operations. This makes conventional confusion-matrix or fidelity-level characterization insufficient. Here, we introduce an efficient, self-consistent protocol for learning a single-qubit Z-twirled MCM instrument, retaining the readout-backaction correlations and excitation-decay asymmetry that are erased in Pauli-error descriptions. Remarkably, readout bit strings from only three repeated MCMs on a maximally mixed input determine all learnable parameters of the reduced instrument, up to a single unidentifiable gauge degree of freedom. Physicality constraints convert this nonidentifiability into narrow, gauge-aware error intervals. Implemented on IBM superconducting processors, the learned instrument improves Pauli-observable prediction by ∼100× over a conventional confusion-matrix model and reveals a T1-decay dominated backaction. Our protocol provides a compact characterization layer for state-preparation and measurement error separation, reset optimization, and noise-aware quantum error correction.
Mid-circuit measurement and classical feed-forward are essential primitives for dynamic-circuit teleportation on superconducting quantum processors. However, the error associated with measurement-conditioned corrective operations remains poorly understood when evaluated with respect to individual measurement branches. In this paper, we present a framework for characterizing feed-forward error in dynamic circuit teleportation without losing valuable information related to its behavior across separate branches. We analyze three approaches to applying measurement-conditioned corrections: (i) physical application, (ii) post-processing adjustments, and (iii) a mitigated physical application which utilizes Bit-Flip Averaging (BFA)-based Probabilistic Readout Error Mitigation (PROM). We experimentally reconstruct branch Choi operators via an entangled reference qubit, and validate our physical-application and post-processing Choi-shadow estimators against full tomography of the branch Choi operators. We perform experiments on two physical qubit layouts which differ greatly in mid-circuit measurement readout error, and observe a reversal in the relative order in branch qualities obtained from the post-processing and PROM mitigation strategies. In one physical layout with higher measurement readout error, the operational feed-forward penalty is relatively modest (approximately 0.02-0.03) and PROM produces higher branch qualities than post-processing for every branch. In a separate layout with lower readout error, the operational feed-forward penalty increases to roughly 0.07, and post-processing exceeds PROM for all branch qualities. Our characterization framework can reveal branch-specific error structure and mitigation behavior that state-of-the-art outcome-averaged analyses fail to expose.
Abstract Dynamic circuits with mid-circuit measurement (MCM) and classical feed-forward are essential building blocks for quantum error correction and adaptive quantum protocols. However, in superconducting quantum processors the readout process can induce coherent crosstalk on non-measured (spectator) qubits through the readout resonator, residual photons, and other hardware pathways, leading to deterministic phase kicks (effective Z rotations) that accumulate with the number of MCM events. In this work we present a minimal, reproducible two-qubit Ramsey diagnostic to quantify the spectator-induced phase shift as a function of the number of inserted mid-circuit measurements M, and we demonstrate that a simple virtual-Z (frame) compensation proportional to M can mitigate the resulting phase error on real hardware. In a high-SNR dataset archived on Zenodo (T = 40 μs, 4096 shots per circuit), the effective phase difference Δθeff(M) = θMEAS(M) - θDELAY(M) shifts monotonically in the negative direction as M increases, reaching Δθeff (M=8) = -1.944 ± 0.033 rad. While the contrast r decreases mildly with M, it remains relatively high (r ≈ 0.84 at M = 8), consistent with the effect appearing predominantly as a coherent phase rotation. To mitigate the error, we insert a virtual-Z rotation on the target qubit of the form Rz (comp × M) in the MEAS condition and scan the compensation coefficient comp (rad per measurement). In a MAP dataset (ibm_marrakesh, shots = 512, repeats = 1, M ∈ {0,1,2,4,8}, comp ∈ {-0.02,-0.01,0,+0.01,+0.02}), the RMS of the baseline-referenced phase error Δθeff(M) for M>0 is minimized at comp = -0.01, decreasing from 0.1393 rad (baseline) to 0.0601 rad. Finally, we implement a low-cost calibration probe (M = {0,8}) scanning five compensation settings comp ∈ {-0.02,-0.01,0,+0.01,+0.02} (1024 shots per circuit, repeats = 2) and estimate a session-dependent coefficient compopt ≈ -0.013 rad/measurement from a linear fit of Δθeff(M=8) versus comp. A same-session production sweep using comp = -0.01453 rad/measurement (close to compopt) shows a reduced residual phase error, supporting a practical probe → production workflow for dynamic-circuit execution. All analysis scripts and summary data are made publicly available to support independent reproduction of the reported phase metrics and figures.
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.
Dynamic circuits with mid-circuit measurement (MCM) and classical feed-forward are essential building blocks for quantum error correction and adaptive quantum protocols. However, in superconducting quantum processors the readout process can induce coherent crosstalk on non-measured (spectator) qubits through the readout resonator, residual photons, and other hardware pathways, leading to deterministic phase kicks (effective Z rotations) that accumulate with the number of MCM events. In this work we present a minimal, reproducible two-qubit Ramsey diagnostic to quantify the spectator-induced phase shift as a function of the number of inserted mid-circuit measurements M, and we demonstrate that a simple virtual-Z (frame) compensation proportional to M can mitigate the resulting phase error on real hardware. In a high-SNR dataset archived on Zenodo (T = 40 μs, 4096 shots per circuit), the effective phase difference Δθeff(M) = θMEAS(M) - θDELAY(M) shifts monotonically in the negative direction as M increases, reaching Δθeff (M=8) = -1.944 ± 0.033 rad. While the contrast r decreases mildly with M, it remains relatively high (r ≈ 0.84 at M = 8), consistent with the effect appearing predominantly as a coherent phase rotation. To mitigate the error, we insert a virtual-Z rotation on the target qubit of the form Rz (comp × M) in the MEAS condition and scan the compensation coefficient comp (rad per measurement). In a MAP dataset (ibm_marrakesh, shots = 512, repeats = 1, M ∈ {0,1,2,4,8}, comp ∈ {-0.02,-0.01,0,+0.01,+0.02}), the RMS of the baseline-referenced phase error DθCT(M) for M>0 is reduced from 0.1393 rad (baseline) to 0.0601 rad at comp = -0.01, demonstrating effective error reduction with a single-parameter circuit-level correction. Finally, using a pay-as-you-go execution environment we run a low-cost “calibration probe” (M = {0,8}, three comp points, 32 circuits total) and obtain compopt ≈ +0.0088 rad/measurement from a three-point linear fit. This supports a practical two-stage workflow in which a short probe estimates the session-dependent compensation coefficient, followed by same-session production runs with the calibrated virtual-Z correction.
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