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.
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.
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.
Abstract Quantum teleportation transfers an unknown qubit state from a sender to a receiver using a shared entangled pair and a classically conditioned correction without moving the physical carrier. On the dynamic-circuit hardware, the complete protocol (which includes mid-circuit measurement and conditional feedforward) now runs on a single circuit. We use this to benchmark three-qubit teleportation on a 156-qubit IBM Heron r2 processor (ibm_fez). A single-qubit RY(θ) input was teleported at six angles along a meridian of the Bloch sphere and reconstructed by state tomography alongside two ablation controls; one without entanglement and the other without feedforward. The full protocol returns a mean fidelity of about 0.945, nearly constant across the angles and above the 2/3 full-Bloch-sphere reference at all six sampled angles. Removing feedforward lowered the fidelity to about 0.51, close to a maximally mixed state. On the other hand, removing entanglement yields (1 + cos²θ)/2 with a mean near 0.75, transferring the population but losing the coherence. Together, these results establish that entanglement and feedforward are both necessary. The calibration-limited fidelity serves as a reference for this class of hardware. A separate run returned a Bell-state fidelity value of 0.957. A branch-resolved analysis confirmed that the four measurement branches are Pauli rotations of the target realigned by feedforward. The reported fidelity depends only on the rotation angle and the device noise.
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.
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.
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× over Qubic. Our CNN discriminator achieves up to 62\% higher accuracy for short measurement durations than the baselines, driving 1.2−9.4× lower logical error rates in QEC. Last, our software mitigation improves fidelity by 18--30\% over baseline methods in DQC workloads.