Surviving readout errors and incomplete postselection in monitored quantum circuits

arXiv:2610.20712 · quant-ph, cond-mat.stat-mech, cond-mat.str-el · Submitted 2026-10-14 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "Surviving readout errors and incomplete postselection in monitored quantum circuits".

Mira: The gist: Charge sharpening survives readout errors in U(1)-symmetric monitored quantum circuits,

Kai: First, who's behind it and why it matters.

Title and authors: Kai: So we’re looking at this paper called "Surviving readout errors and incomplete postselection in monitored quantum circuits." It deals with how those noisy measurements actually mess with the dynamics of these quantum circuits.

Mira: Yeah, it focuses on a specific kind of circuit called U(one)-symmetric circuits <ref:2610.20712#pg1>. The main thing they find is that even when you have readout errors, like mistakes in recording what happened during a measurement, the charge-sharpening transition still happens at a finite error rate.

Lev: From an engineering standpoint, that’s important because it means the phenomenon we want to use—that sharp transition—isn't completely wiped out by realistic noise levels.

Kai: Exactly, and they show that instead of the fluctuations just vanishing in the sharp phase, you get a finite steady-state plateau instead. It’s not perfect suppression anymore.

Mira: That plateau is what they call residual long-time fluctuation, which means postselecting on noisy data doesn't project you onto a single charge sector anymore because the reported record is compatible with many true histories.

Lev: So, for someone building hardware, that means we can still get some useful information even when the readout isn't perfect. This paper is looking at how errors affect the entire process of conditioning trajectories on imperfect records.

Kai: It’s like trying to see a really sharp feature in a signal where you keep mislabeling some of the data points. That’s what they are doing here with their U(one)-symmetric circuits, which respect that global charge conservation <ref:2610.20712#pg1>.

The paper's summary: Kai: The core idea they are exploring is the competition between two things: measurement-induced purification and noise-induced mixing, especially as you change the measurement rate, p m.

Mira: Right, and they show this competition in a three-regime structure based on p m and the assignment error rate eta. At low measurement rates, fluctuations are still dominated by that initial fuzzy state.

Lev: When you look at the numbers on page three they say at low p m, the fluctuations settle down to a shallow minimum when p m is greater than some critical value, denoted as p* m <ref:2610.20712#pg1>.

Kai: That shallow minimum near that ideal transition point signals exactly where measurement-induced purification and noise-induced mixing are fighting for control over the system's state.

Mira: And they show that this minimum is a fingerprint of the ideal transition surviving inside the noisy signal, which is a key finding for understanding how these transitions behave in practice.

Lev: The decomposition into quantum and classical contributions to charge fluctuation is crucial here; it shows that deep in the charge-sharpening phase, the quantum contribution drops out almost entirely.

Kai: That leaves only the classical part from readout errors as the sole source of fluctuation, which they quantify with delta squared Q cl(eta) = E(eta) delta squared Q maxcl at maximal noise <ref:2610.20712#pg1>.

Mira: So, even when the quantum uncertainty is suppressed, you still have that classical error term causing fluctuations that depend on the error rate eta.

The paper's improvements: Kai: One of the biggest takeaways they present is how this structure helps us understand and potentially mitigate readout errors in real systems.

Lev: Specifically, the authors suggest that decomposing those charge fluctuations into quantum and classical parts gives us a minimal mitigation framework, which is a route to locate the transition directly from experimental data.

Mira: They show that the growth rate of the classical contribution changes across these three regimes depending on how fast you are measuring, reflecting how memory retained through partial postselection suppresses noise-induced mixing relative to an estimate where everything is uncorrelated.

Kai: And they point out a specific failure at intermediate measurement rates, where F becomes less than zero, which singles out the regime where memory from partial postselection makes the effective error channel strongly non-Markovian.

Lev: That non-Markovian behavior is what we need to look for if we want to use this as a diagnostic tool for our hardware noise.

Mira: They also show that the classical contribution grows monotonically with the measurement rate, but its growth rate shifts across those three regimes, which is important because it shows how much better partial postselection can be at intermediate rates than a fully uncorrelated estimate.

Kai: So, they’ve essentially given us a way to use charge fluctuations as a robust probe for measurement-induced criticality even when you have imperfect records.

Conclusion: Mira: So, to wrap up the paper "Surviving readout errors and incomplete postselection in monitored quantum circuits," they confirm that finite readout error doesn't destroy the charge-sharpening transition.

Kai: They replace the vanishing fluctuations of the sharp phase with a finite plateau that depends on eta, while keeping the timescale separation between phases intact.

Lev: The existence of that shallow minimum near p* m in long-time fluctuations as a function of measurement rate p m is what really tells us something new here.

Kai: It’s that competition between measurement-induced purification and noise-induced mixing we talked about earlier.

Mira: They’ve identified three distinct regimes for the measurement rate: low p m, intermediate rates, and high rates, each with a different dynamic behavior in the fluctuations.

Lev: The decomposition into quantum and classical parts offers a minimal mitigation framework to locate that transition directly from experimental data.

Kai: It shows charge fluctuations are a robust probe for measurement-induced criticality even under realistic readout noise.

Murtaza Ali Mir, Teemu Ojanen, Ali G. Moghaddam

Computational Physics Laboratory, Tampere University · Helsinki Institute of Physics P.O. Box 64, Finland · Department of Applied Physics, Aalto University

quant-ph, cond-mat.stat-mech, cond-mat.str-el

Submitted: 2026-10-14

Updated: 2026-10-14

Comments: 8 pages, 4 figures

License: http://creativecommons.org/licenses/by-nc-nd/4.0/

Importance score: 91/100

The gist: The gist: Charge sharpening survives readout errors in U(1)-symmetric monitored quantum circuits, with the sharp phase's vanishing fluctuations replaced by a finite steady-state plateau and a shallow

Key concepts

Charge Sharpening Transition: This is a phase transition where local gates and measurements confine the quantum system to a single, fixed charge Hilbert subspace. It suppresses fluctuations between different charge sectors, indicating that the system has achieved a state of high coherence within that specific charge sector.
Readout Noise and Incomplete Postselection: Assignment errors mean reported measurement outcomes may differ from true ones. Postselecting on these noisy sequences yields a mixed state, meaning the conditioning is imperfect. This noise causes distinct true histories to be inferred as belonging to the same charge sector, leading to residual long-time fluctuations.
Three-Regime Structure: The system exhibits three distinct behaviors depending on the measurement rate (pm): low rates show initial fuzzy states; intermediate rates show competition between purification and mixing; high rates result in a plateau of residual fluctuations. This structure reveals how noise affects the transition dynamics across different experimental speeds.

Terminology

Quantum Circuits — 1× in this paper · explained in 2 episodes

Summary

The gist: Charge sharpening survives readout errors in U(1)-symmetric monitored quantum circuits, with the sharp phase's vanishing fluctuations replaced by a finite steady-state plateau and a shallow minimum near ideal transition point p

(Page 1).

How it works

The study investigates how readout errors affect the dynamics of monitored quantum circuits, which involves the competition between unitary evolution and non-unitary monitoring by local measurements (Page 1). These errors make postselection effectively incomplete because conditioning trajectories on imperfect rather than true records is performed (Page 1). Focusing on U(1)-symmetric circuits, the researchers found that the charge-sharpening transition survives at a finite error rate, where the sharp phase's vanishing fluctuations are replaced by a finite steady-state plateau (Page 1).

The charge-sharpening transition occurs when local unitary gates and projective measurements in an alternating sequence respect a global U(1) charge, confining the system to a single, fixed charge Hilbert subspace (Page 2). This transition marks the point where the system suppresses mixedness associated with fluctuations between charge sectors, but it does not imply total purification of the state (Page 2). Because different outcome sequences generally sharpen to different charge sectors, this phenomenon is inherently more sensitive to readout errors than entanglement or purification transitions (Page 2). A single misassigned outcome causes the inferred charge sector to diverge from the true one, effectively mixing distinct charge sectors under postselection (Page 2).

Readout noise

The presence of assignment errors means the reported measurement outcome can differ from the true one, with a probability given by Equation (1) (Page 3). The researchers allow for asymmetric assignment errors, where η is the probability of misassigning 0 as 1 and η' is the probability of misassigning 1 as 0 (Page 3). Postselecting on a given noisy outcome sequence m˜ yields a mixed state ρm˜, formed from ideal postmeasurement states weighted by the probability of reporting m˜ given m together with the probability of m itself (Page 3).

The charge dynamics are quantified through the mean charge fluctuation δ2Q = E[U,M,m˜] h δ2Qρm˜i (Page 3). In Figure 2, the normalized charge fluctuation F(t) shows that while ideal measurements suppress fluctuations efficiently, finite assignment error leaves a residual long-time fluctuation (Page 3). This residual plateau arises because the reported record m˜ is compatible with many distinct true histories m, meaning postselecting on m˜ no longer projects the state onto a single charge sector (Page 3).

Charge dynamics under readout noise

The mean charge fluctuation δ2Q is decomposed into quantum and classical contributions, where the quantum contribution captures intratrajectory fluctuations arising from quantum uncertainty within each pure state (trajectory) in the ensemble, coinciding with ideal noise-free postselected fluctuations Fqu ≡ Fη=0 (Page 8). The classical contribution captures inter-trajectory variance—how much ⟨Q⟩m differs from one record m to another within the noisy ensemble—which is a quantitative measure of noise-induced mixing (Page 8).

The decomposition shows that deep in the charge-sharpening phase, the quantum contribution to fluctuations is essentially fully suppressed, leaving only the classical part from readout errors as the sole remaining source (Page 8). This classical part takes the form δ2Qcl(η) = E(η) δ2Qmaxcl, where δ2Qmaxcl is the maximal classical fluctuations at maximal noise (Page 8).

Three-regime structure

The long-time steady-state fluctuations exhibit a three-regime structure as a function of measurement rate pm and error rate η (Page 4).

At low pm, fluctuations remain dominated by the initial charge-fuzzy state, and partial postselection under noise is still effective enough to reduce them down to a shallow minimum at p∗m ∼ p> (Page 4).
At intermediate rates, p∗m < pm < 0.4, purification and noise-induced mixing compete directly, with mixing increasingly dominant as pm grows, so the fluctuations rise (Page 4).
At high rates, pm > 0.4, the two effects balance, producing a plateau of residual fluctuations independent of pm (Page 4).

The shallow minimum near p> signals a competition between measurement-induced purification and noise-induced mixing (Page 4). This minimum is a fingerprint of the ideal transition surviving inside a noisy signal (Page 5). The classical contribution grows monotonically with measurement rate, but its growth rate changes across these three regimes, reflecting how memory retained through partial postselection suppresses noise-induced mixing relative to the fully uncorrelated estimate at intermediate rates (Page 8).

Conclusion

The results demonstrate that finite readout error does not destroy the charge-sharpening transition, but converts the sharp phase’s vanishing fluctuations into a finite, η-dependent plateau while preserving the timescale separation between the two phases (Page 5). The existence of a minimum near p> in long-time fluctuations as a function of measurement rate pm is attributed to competition between measurement-induced purification and noise-induced mixing (Page 4). This structure identifies three distinct regimes as a function of measurement rate: low pm, intermediate rates, and high rates (Page 4). The study establishes charge fluctuations as a robust probe of measurement-induced criticality under realistic readout noise (Page 5).

Acknowledgments

M.A.M. acknowledges the financial support of the Finnish Ministry of Education and Culture through the Quantum Doctoral Education Pilot Program (QDOC VN/3137/2024-OKM-4) and the Research Council of Finland through the Finnish Quantum Flagship project (TAU 359020) (Page 6). T.O. acknowledges support from the Finnish Research Council project 362573 and the Finnish quantum flagship program (Page 6). A.G.M. acknowledges the financial support from the Finnish Center of Excellence in Quantum Materials QMAT (No. 374166), and the ERC Consolidator Grant ULTRATWISTROICS (No. 101170477) (Page 6). [1] Y. Li, X. Chen, and M. P. A. Fisher, Quantum Zeno effect and the many-body entanglement transition, Phys. Rev. B 98, 205136 (2018) (Page 7). [40] A. Chakraborty, K. Chen, A. Zabalo, J. H. Wilson, and J. H. Pixley, Charge and entanglement criticality in a U(1)-symmetric hybrid circuit of qubits, Phys. Rev. B 110, 045135 (2024) (Page 7). [41] M. A. Mir and A. G. Moghaddam, Readout errors and incomplete postselection in monitored quantum circuits, Zenodo: 10.5281/zenodo.23372650 (Page 7). [44] M. Ippoliti and V. Khemani, Learnability transitions in monitored quantum dynamics via eavesdropper’s classical shadows, PRX Quantum 5, 020304 (Page 7). [12] D. Sticlet, B. D´ora, D. Szombathy, G. Zar´and, and C. P. Moca, Nonstabilizerness in open XXZ spin chains: Universal scaling and dynamics, Phys. Rev. Res. 7, 043130 (Page 7). [28] K. P¨oyh¨onen, A. G. Moghaddam, M. N. Ivaki, and T. Ojanen, Scalable approach to monitored quantum dynamics and entanglement phase transitions, arXiv:2406.19052 (Page 7). [34] Z. Cai, R. Babbush, S. C. Benjamin, S. Endo, W. J. Huggins, Y. Li, J. R. McClean, and T.-E O’Brien, Quantum error mitigation, Rev Mod Phys 95 045005 (2023) (Page 7). [36] B Nachman, M Urb´anek, W A de Jong, and C W Bauer, Unfolding quantum computer readout noise, npj Quantum Information 6 84 (2020) arXiv:1910.01969 (Page 7). [38] F B Maciejewski, F Baccari, Z Zimbor´as, and M Oszmaniec, Modeling and mitigation of cross-talk effects in readout noise with applications to the Quantum Approximate Optimization Algorithm, Quantum 5 464 (2021) (Page 7). [39] R Hicks, B Kobrin, C W Bauer, and B Nachman, Active readout-error mitigation, Phys. Rev. A 105 012419 (2022) (Page 7). [43] U Agrawal, J Lopez-Piqueres, R Vasseur, S Gopalakrishnan, and A C Potter, Observing quantum measurement collapse as a learnability phase transition, Phys. Rev. X 14 041012 (2024) (Page 7).

Improvements for AI systems

This AI system can perform robust parameter estimation for quantum circuits by utilizing charge fluctuations as a probe of measurement-induced criticality, specifically by exploiting the shallow minimum that appears near p in the long-time fluctuations as a function of measurement rate pm.
The improved system can distinguish between the ideal transition point p= and the actual transition observed in noisy data, as this is signaled by a competition between measurement-induced purification and noise-induced mixing, which manifests as a specific scaling behavior in the charge fluctuations.
The system can implement an effective noise mitigation framework by leveraging the decomposition of charge fluctuations into quantum and classical contributions to locate the transition directly from experimental data, as suggested by the decomposition therefore offers a minimal mitigation framework and a route to locate the transition directly from experimental data.
The AI can quantify the non-Markovian memory effects in mid-circuit measurements by detecting deviations in the noise profile, specifically noting that "the failure at intermediate pm, where ∆F < 0, singles out the regime in which memory retained through partial postselection makes the effective error channel strongly non-Markovian."
The system can develop a hybrid theory-experiment probe to distinguish between fuzzy and sharp behavior in noisy settings by calculating ∆F = F − Fapprox cl, which uses an idealized theoretical input to isolate the effects of memory retained through partial postselection.

Abstract

We study how readout errors affect dynamics in monitored quantum circuits. Such errors make postselection effectively incomplete, conditioning trajectories on imperfect rather than true records. Focusing on U(1)-symmetric circuits, we find that the charge-sharpening transition survives at a finite error rate, with the sharp phase's vanishing fluctuations replaced by a finite steady-state plateau. The charge fluctuations show a shallow minimum near the ideal transition point as a function of measurement rate, signaling the competition between measurement-induced purification and noise-induced mixing. By decomposing the fluctuations into quantum and classical contributions, we show the minimum marks where incomplete postselection still retains enough trajectory memory to attenuate noise-induced mixing, leaving a detectable signature of the transition even in a noisy setting. Mid-circuit measurements are far harder to mitigate against readout errors than standard end-of-circuit ones, because the errors corrupt the postselection itself; the decomposition therefore offers a minimal mitigation framework and a route to locate the transition directly from experimental data. Our results show that charge sharpening survives readout errors in a quantitative and experimentally accessible way.