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arXiv:2606.00433 · Physical Review Letters

Learning Mid-circuit Measurement Backaction from Three Repeated Measurements

Chia-Tung Chu, Su-un Lee, Han Zheng, Senrui Chen, Bibek Pokharel, Alireza Seif, Liang Jiang

quant-phSubmitted May 29, 2026• Announced Jun 2, 2026• 0 citations
v1 · May 29, 2026v2 · Sep 30, 2026v3 · Oct 16, 2026
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Abstract

Accurate modeling of mid-circuit measurements (MCMs) is essential for dynamic-circuit operations such as syndrome extraction, measurement-based reset, and the separation of state-preparation and measurement (SPAM) 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 non-identifiability into narrow, gauge-aware error intervals. Implemented on IBM superconducting processors, the learned instrument improves Pauli-observable prediction by ${\sim}100\times$ over a conventional confusion-matrix model and reveals a $T_1$-decay dominated backaction. Our protocol provides a compact characterization layer for SPAM error separation, reset optimization, and noise-aware quantum error correction.

DOI
10.1103/y6x3-348l
Comments
5 pages, 2 figures; Supplemental Material included

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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 nnn-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.
Mid-circuit measurements (MCMs) are critical components of the quantum error correction protocols expected to enable utility-scale quantum computing. MCMs can be modeled by quantum instruments (a type of quantum operation or process), which can be characterized self-consistently using gate set tomography. However, experimentally estimated quantum instruments are often hard to interpret or relate to device physics. We address this challenge by adapting the error generator formalism -- previously used to interpret noisy quantum gates by decomposing their error processes into physically meaningful sums of "elementary errors" -- to MCMs. We deploy our new analysis on a transmon qubit device to tease out and quantify error mechanisms including amplitude damping, readout error, and imperfect collapse. We examine in detail how the magnitudes of these errors vary with the readout pulse amplitude, recover the key features of dispersive readout predicted by theory, and show that these features can be modeled parsimoniously using a reduced model with just a few parameters.
Midcircuit measurements (MCMs) are crucial ingredients in the development of fault-tolerant quantum computation. While there have been rapid experimental progresses in realizing MCMs, a systematic method for characterizing noisy MCMs is still under exploration. In this work, we develop a cycle benchmarking (CB)-type algorithm to characterize noisy MCMs. The key idea is to use a joint Fourier transform on the classical and quantum registers and then estimate parameters in the Fourier space, analogous to Pauli fidelities used in CB-type algorithms for characterizing the Pauli-noise channel of Clifford gates. Furthermore, we develop a theory of the noise learnability of MCMs, which determines what information can be learned about the noise model (in the presence of state preparation and terminating measurement noise) and what cannot, which shows that all learnable information can be learned using our algorithm. As an application, we show how to use the learned information to test the independence between measurement noise and state-preparation noise in an MCM. Finally, we conduct numerical simulations to illustrate the practical applicability of the algorithm. Similar to other CB-type algorithms, we expect the algorithm to provide a useful toolkit that is of experimental interest.
Building error-corrected quantum computers relies crucially on measuring and modeling noise on candidate devices.In particular, optimal error correction requires knowing the noise that occurs in the device as it executes the circuits required for error correction.As devices increase in size, we will become more reliant on efficient models of this noise.However, such models must still retain the information required to optimize the algorithms used for error correction.Here, we propose a method of extracting detailed information of the noise in a device running syndrome extraction circuits.We introduce and execute an experiment on a superconducting device using 39 of its qubits in a surface code doing repeated rounds of syndrome extraction but omitting the midcircuit measurement and reset.We show how to extract from the 20 data qubits the information needed to build noise models of various sophistication in the form of graphical models.These models give efficient descriptions of noise in large-scale devices and are designed to illuminate the effectiveness of error correction against correlated noise.Our estimates are furthermore precise: we learn a consistent global distribution where all one-and two-qubit error rates are known to a relative error of 0.1%.By extrapolating our experimentally learned noise models toward lower error rates, we demonstrate that accurate correlated noise models are increasingly important for successfully predicting subthreshold behavior in quantum error-correction experiments.
Mid-circuit measurement (MCM) enables qubit reuse and dynamic control in quantum processors, underpinning resource-efficient algorithms and quantum error correction. However, MCM introduces non-negligible errors, including measurement-induced crosstalk, idling-qubit decoherence, and reset infidelity. Additionally, MCM error rates vary across qubits within the same processor, with some exhibiting substantially higher errors. Existing compilers, including Qiskit-compiler and QR-Map, ignore MCM error variations, leading to fidelity loss in circuits with frequent MCM operations. In this paper, we present MERA, an MCM-error-aware quantum compilation framework that integrates MCM error modeling into the layout, routing, and scheduling stages. We first use the lightweight profiling method to capture a per-qubit MCM error distribution that remains stable for over 24 hours. The distribution guides MERA in applying MCM-error-aware layout and routing, while MERA further incorporates context-aware dynamic decoupling to improve fidelity. In evaluation, MERA delivers 24.94% -- 80.48% average fidelity gains over the Qiskit-compiler (optimization level 3) across different groups in selected benchmarks without additional SWAP overhead. It also boosts the fidelity of QR-Map-generated circuits by 29.26% on average (up to 122.58%), demonstrating its effectiveness for circuits with frequent MCM operations.
Error mitigation has enabled quantum computing applications with more than a hundred qubits and deep circuits. Many error mitigation methods are noise-aware, relying on a faithful characterization of the noise channels of the hardware. However, fundamental limitations lead to unlearnable degrees of freedom of the underlying noise models when considering qubits. Here, we show how to leverage noncomputational states as an additional resource to learn state-preparation errors in superconducting qubits. This allows one to fully constrain the noise models. We can thus independently and accurately mitigate state-preparation errors, gate errors, and measurement errors. Our proposed method is also applicable to dynamic circuits with midcircuit measurements. This work opens the door to improved error mitigation for measurements, both at the end of the circuit and midcircuit.