arxiv: 2604.28037 · v1 · submitted 2026-04-30 · 🪐 quant-ph

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Branch-Resolved Characterization of Feed-Forward Error in Dynamic Teleportation via Classical Choi Shadows

Mason Edwards , Prabhat Mishra

Authors on Pith no claims yet

Pith reviewed 2026-05-07 07:35 UTC · model grok-4.3

classification 🪐 quant-ph

keywords dynamic circuitsquantum teleportationfeed-forward errorChoi operatorsclassical shadowsreadout error mitigationmid-circuit measurementbranch-resolved characterization

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The pith

A framework reconstructs branch-specific feed-forward channels in dynamic quantum teleportation using classical Choi shadows.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a method to characterize errors from measurement-conditioned corrections in teleportation circuits without averaging over measurement outcomes. It reconstructs the effective quantum channel for each branch separately by applying classical shadows to an entangled reference qubit and compares three correction strategies: direct physical application, post-processing, and probabilistic readout error mitigation via bit-flip averaging. Experiments on two qubit layouts with different readout error rates show that the best-performing strategy reverses depending on the layout, with feed-forward penalties ranging from 0.02-0.03 to about 0.07. This branch-level view exposes error structures hidden by standard outcome-averaged metrics.

Core claim

The authors show that classical Choi-shadow estimators, validated against full tomography, can recover the distinct Choi operators for each measurement branch in dynamic teleportation. On hardware layouts differing in mid-circuit readout error, physical-application and post-processing strategies exhibit a reversal in relative branch quality when PROM mitigation is applied, demonstrating that branch-resolved analysis captures mitigation behavior that averaged characterizations miss.

What carries the argument

Branch-resolved classical Choi-shadow estimators that reconstruct the feed-forward channel for each measurement outcome via an entangled reference qubit.

If this is right

In high-readout-error layouts, PROM mitigation yields higher branch qualities than post-processing for every branch.
In low-readout-error layouts, post-processing yields higher branch qualities than PROM for every branch.
The operational penalty of feed-forward ranges from roughly 0.02-0.03 on one layout to 0.07 on the other.
Outcome-averaged analyses cannot detect the layout-dependent reversal in which mitigation strategy performs best.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Branch-resolved characterization could guide the selection of mitigation techniques in larger dynamic circuits where different branches dominate the error budget.
The observed dependence on readout error suggests that hardware improvements in mid-circuit measurement fidelity would reduce the relative advantage of any single mitigation approach.
The framework might extend to other protocols that use mid-circuit measurements and classical feed-forward, such as error-corrected teleportation or adaptive algorithms.

Load-bearing premise

The classical Choi-shadow estimators accurately capture the true branch Choi operators without significant bias from readout errors or layout-specific effects.

What would settle it

Repeating the tomography validation on the reference qubit and finding that the shadow-reconstructed branch Choi operators deviate substantially from the tomographic ones, or failing to observe the reported reversal in branch-quality ordering between the two layouts.

Figures

Figures reproduced from arXiv: 2604.28037 by Mason Edwards, Prabhat Mishra.

**Figure 1.** Figure 1: Branch-Resolved Characterization Framework. view at source ↗

**Figure 3.** Figure 3: Decoding quantum circuit. Decodes Alice’s resource qubits into a view at source ↗

**Figure 2.** Figure 2: State preparation quantum circuit. Prepares either entangled view at source ↗

**Figure 4.** Figure 4: Shadow estimator validation against full tomography of branch Choi view at source ↗

**Figure 7.** Figure 7: summarizes our observed aggregated channel metrics. The left panel shows the total feed-forward penalty ∆FF (Eq. 43), and the right panel shows the mean PROM mitigation of branch qualities (Eq. 45), averaged over all four branches. For layout 1, the total feedforward penalties are relatively modest at 0.0199 for the perfect W4 resource, and 0.0259 for the symmetric W4 resource. For layout 2, the total feed… view at source ↗

**Figure 6.** Figure 6: Estimated branch qualities qˆℓ for all four branch labels ℓ obtained using the symmetric W4 resource. Left panel: results from physical qubit layout 1. Right panel: results from physical qubit layout 2. Error bars show the 95% bootstrap confidence intervals. The layout-dependent reversal between PROM mitigation and post-processing is maintained across both resources view at source ↗

read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper introduces branch-resolved Choi-shadow characterization of feed-forward errors in dynamic teleportation and reports a reversal in mitigation performance across hardware layouts, but leaves the key PROM estimator unvalidated against tomography.

read the letter

The core contribution is a practical way to measure feed-forward errors per measurement branch in teleportation circuits instead of averaging them away. They reconstruct branch Choi operators with classical shadows on an entangled reference qubit and compare three correction strategies: direct physical application, post-processing, and a mitigated physical version using bit-flip averaging probabilistic readout error mitigation. Experiments on two superconducting layouts that differ in readout error show a clear reversal: PROM outperforms post-processing on the noisier layout while the reverse holds on the cleaner one, with operational penalties of roughly 0.02-0.03 and 0.07 respectively. That reversal is the most interesting empirical result and is not something outcome-averaged methods would have caught. The validation of the physical-application and post-processing estimators against full tomography is a solid check and gives reasonable confidence in those two channels. The work is experimental and direct, with no heavy theory or free parameters, and the citation pattern looks standard for the subfield. The main limitation is that the PROM estimator receives no equivalent tomography validation. The abstract explicitly checks only the first two methods, and the layouts differ precisely in the readout error that PROM is meant to handle. If the probabilistic model in PROM interacts with mid-circuit measurement noise in a layout-dependent way, the observed reversal could contain a methodological component rather than reflecting pure physical feed-forward error. That gap directly affects how much weight to give the claim that the framework reliably exposes mitigation behavior missed by averages. The paper is aimed at researchers working on error mitigation and dynamic circuits for near-term superconducting processors. A reader who needs concrete diagnostics for branch-dependent errors will find usable numbers and a clear experimental comparison. It is not foundational, but the data are concrete enough that a serious referee should see it. I would send it to peer review with the specific request that the authors either add the missing tomography check for PROM or explain why it was omitted and how they ruled out bias in the reversal.

Referee Report

1 major / 2 minor

Summary. The manuscript presents a framework for branch-resolved characterization of feed-forward errors in dynamic teleportation circuits using classical Choi shadows. It compares three approaches to measurement-conditioned corrections—physical application, post-processing adjustments, and mitigated physical application via Bit-Flip Averaging (BFA)-based Probabilistic Readout Error Mitigation (PROM)—and reconstructs branch Choi operators experimentally via an entangled reference qubit. The physical-application and post-processing Choi-shadow estimators are validated against full tomography of the branch Choi operators. Experiments on two superconducting qubit layouts differing in mid-circuit measurement readout error show a reversal in relative branch-quality ordering between post-processing and PROM, with operational feed-forward penalties of approximately 0.02-0.03 in the higher-readout-error layout (where PROM outperforms post-processing) and roughly 0.07 in the lower-readout-error layout (where post-processing outperforms PROM). The authors conclude that the framework reveals branch-specific error structures and mitigation behaviors missed by state-of-the-art outcome-averaged analyses.

Significance. If the central claims hold after addressing the validation gap, this work is significant for experimental quantum error characterization in dynamic circuits. It demonstrates that branch-resolved analysis can expose mitigation behaviors and error structures not visible in averaged metrics, with direct experimental comparisons on two distinct physical layouts and quantified penalties. This has practical value for superconducting quantum processors where mid-circuit measurements and feed-forward are essential primitives, potentially guiding improved mitigation strategies beyond standard tomography or averaged approaches.

major comments (1)

[Abstract] Abstract: The validation of Choi-shadow estimators against full tomography is reported only for the physical-application and post-processing methods, but not for the BFA-based PROM mitigated physical application. Since the headline observation is a reversal in relative branch-quality ordering between post-processing and PROM across the two layouts (which differ in readout error), and the claim is that the framework reliably reveals mitigation behavior missed by outcome-averaged analyses, the absence of this validation for PROM is load-bearing. An uncharacterized bias in the PROM estimator (e.g., from interaction between the probabilistic readout-error model and mid-circuit measurement noise) could render the reversal and branch-specific insights methodological artifacts rather than physical results.

minor comments (2)

[Abstract] Abstract: The feed-forward penalties are described as 'approximately 0.02-0.03' and 'roughly 0.07'; reporting exact values with statistical uncertainties or error bars from the experiments (and referencing the relevant figure or table) would improve precision and reproducibility.
[Methods] The manuscript should clarify the exact assumptions underlying the classical Choi-shadow reconstruction for all three methods, particularly any differences in how readout errors are modeled for PROM versus the other approaches.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting the importance of comprehensive validation for all estimators, especially given the central role of the observed reversal between post-processing and PROM. We address the major comment below and will revise the manuscript accordingly to strengthen the claims.

read point-by-point responses

Referee: [Abstract] Abstract: The validation of Choi-shadow estimators against full tomography is reported only for the physical-application and post-processing methods, but not for the BFA-based PROM mitigated physical application. Since the headline observation is a reversal in relative branch-quality ordering between post-processing and PROM across the two layouts (which differ in readout error), and the claim is that the framework reliably reveals mitigation behavior missed by outcome-averaged analyses, the absence of this validation for PROM is load-bearing. An uncharacterized bias in the PROM estimator (e.g., from interaction between the probabilistic readout-error model and mid-circuit measurement noise) could render the reversal and branch-specific insights methodological artifacts rather than physical results.

Authors: We agree that validating the PROM estimator against full tomography is essential to substantiate the reversal observation and to exclude potential biases arising from the interaction between the probabilistic readout-error model and mid-circuit measurement noise. In the revised manuscript, we will add a direct validation of the BFA-based PROM mitigated physical application Choi-shadow estimator against full tomography of the branch Choi operators, performed on the same data sets used for the physical-application and post-processing validations. This will confirm that the branch-quality ordering and operational penalties (0.02-0.03 and ~0.07) reflect physical behavior rather than methodological artifacts, thereby reinforcing the framework's ability to expose mitigation behaviors missed by averaged analyses. revision: yes

Circularity Check

0 steps flagged

No significant circularity in experimental characterization framework

full rationale

The paper is an experimental characterization study that reconstructs branch Choi operators using an entangled reference qubit and validates physical-application and post-processing Choi-shadow estimators directly against full tomography. Claims about branch-specific error structure, mitigation behavior, and the observed reversal in relative branch qualities across two layouts with differing readout errors rest on these empirical comparisons and direct measurements. No mathematical derivation chain exists that reduces predictions or results to fitted inputs by construction, no self-definitional steps, no load-bearing self-citations, and no ansatzes or uniqueness theorems imported from prior author work. The central assertions are grounded in external benchmarks (tomography) and layout-specific data rather than tautological reductions, rendering the work self-contained with no circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work rests on standard quantum-information assumptions for channel characterization via Choi operators and entangled references. No free parameters, invented entities, or ad-hoc axioms are evident from the abstract.

axioms (2)

domain assumption Quantum operations on each measurement branch can be faithfully represented by Choi operators reconstructed from an entangled reference qubit.
Invoked in the experimental reconstruction of branch Choi operators.
domain assumption The three correction strategies (physical application, post-processing, PROM) produce comparable effective channels that can be ranked by the reconstructed operators.
Central to the comparative analysis across branches and layouts.

pith-pipeline@v0.9.0 · 5565 in / 1360 out tokens · 53959 ms · 2026-05-07T07:35:34.749429+00:00 · methodology

discussion (0)

Reference graph

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