Robust GHZ State Preparation via Majority-Voted Boundary Measurements

Christophe Pere; Jean-Baptiste Waring; S\'ebastien Le Beux

arxiv: 2602.19405 · v3 · submitted 2026-02-23 · 🪐 quant-ph

Robust GHZ State Preparation via Majority-Voted Boundary Measurements

Jean-Baptiste Waring , S\'ebastien Le Beux , Christophe Pere This is my paper

Pith reviewed 2026-05-15 21:06 UTC · model grok-4.3

classification 🪐 quant-ph

keywords GHZ statesmajority votingdynamic circuitsmid-circuit measurementsquantum error mitigationnoisy intermediate-scale quantumcoupling graphsfidelity improvement

0 comments

The pith

Group-Majority-Voting prepares high-fidelity GHZ states by fusing parallel local states with majority-voted boundary measurements.

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

The paper presents Group-Majority-Voting (Group-MV) as a way to prepare large GHZ states reliably on noisy quantum devices. It works by splitting the qubit graph into smaller groups for parallel local GHZ preparation and then connecting them through redundant mid-circuit measurements whose results are combined by majority vote. This reduces the impact of measurement errors that would spread via feedforward. On simulated heavy-hex and grid layouts with 30 to 60 qubits, the method reaches 2.4 times the fidelity of the earlier Line Dynamic approach and stays within 3 percent of the ideal unitary case. Readers should care because stable GHZ states support many quantum algorithms and error-correction schemes that currently suffer from noise accumulation.

Core claim

Group-MV partitions arbitrary coupling graphs, prepares local GHZ states in parallel, and fuses them via majority-voted mid-circuit measurements. The majority vote over redundant boundary links mitigates measurement errors that would otherwise propagate through classical feedforward. It generalizes to arbitrary GHZ sizes on arbitrary coupling topologies, achieving 2.4x higher fidelity than the Line Dynamic method while tracking the unitary baseline within 3% on Heavy-hex and Grid topologies for 30-60 qubits.

What carries the argument

Group-Majority-Voting protocol that partitions the coupling graph and uses majority votes on redundant boundary measurements to fuse local GHZ states while suppressing error propagation.

If this is right

Group-MV applies to any GHZ size and any coupling topology.
It delivers 2.4 times higher fidelity than the Line Dynamic method.
Fidelity remains within 3% of the ideal unitary performance.
The protocol has been tested on heavy-hex and grid graphs up to 60 qubits under realistic noise.

Where Pith is reading between the lines

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

Dynamic circuits with mid-circuit measurements can be hardened against readout noise by adding redundant links and voting.
Similar redundancy techniques could improve preparation of other multi-qubit entangled states such as cluster states or W states.
Optimizing the number and placement of boundary measurements might yield further fidelity gains on specific hardware topologies.
The approach suggests a general strategy for scaling entanglement generation on near-term devices without requiring perfect measurements.

Load-bearing premise

The noise model used in the simulations closely matches the error rates and correlations present on actual quantum hardware.

What would settle it

Running the Group-MV protocol on a physical quantum processor and measuring the prepared GHZ state fidelity to check if it exceeds the Line Dynamic method by a factor of approximately 2.4.

Figures

Figures reproduced from arXiv: 2602.19405 by Christophe Pere, Jean-Baptiste Waring, S\'ebastien Le Beux.

**Figure 1.** Figure 1: Overview of the Group-MV method. (a) A square lattice quantum processor (illustrated using a grid topology for reference), with a highlighted region indicating the partitioned area. (b) Two adjacent groups, 𝐺𝐴 (green) and 𝐺𝐵 (blue), each prepared in a local GHZ state. Red edges indicate the boundary links used for majority-vote correction. (c) Dynamic circuit for fusing |GHZ𝐴⟩ and |GHZ𝐵 ⟩ into |GHZ𝐴∪𝐵 ⟩. C… view at source ↗

**Figure 2.** Figure 2: Graph partitioning and entanglement scaling across topologies. (a–c) Example partitions for Heavy-hex, Grid, and Ring coupling graphs with 𝑁=40 qubits, group size 𝐾=20, and requested boundary redundancy 𝐿=3. Green and blue nodes indicate alternating groups; red edges mark boundary links used for majority-vote fusion. Circled numbers ( 1 , 2 ) indicate correspondence with the 𝑁=40 results in (e) and (f), re… view at source ↗

read the original abstract

Preparing high-fidelity Greenberger-Horne-Zeilinger (GHZ) states on noisy quantum hardware remains challenging due to cumulative gate errors and decoherence. We introduce Group-Majority-Voting (Group-MV), a dynamic-circuit protocol that partitions arbitrary coupling graphs, prepares local GHZ states in parallel, and fuses them via majority-voted mid-circuit measurements. The majority vote over redundant boundary links mitigates measurement errors that would otherwise propagate through classical feedforward. We evaluate Group-MV on simulated Heavy-hex and Grid topologies for 30 through 60 qubits under a realistic noise regime. Group-MV generalizes to arbitrary GHZ sizes on arbitrary coupling topologies, achieving 2.4x higher fidelity than the Line Dynamic method while tracking the unitary baseline within 3%.

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

Group-MV introduces majority-voted boundary fusion for GHZ states on dynamic circuits and shows clear fidelity gains in the reported simulations, but the arbitrary-topology claim rests on narrow tests.

read the letter

The main takeaway is that this work describes a Group-Majority-Voting protocol that splits an arbitrary graph into patches, prepares small GHZ states locally in parallel, and then fuses them with mid-circuit measurements on redundant boundary links, taking a majority vote to reduce measurement error propagation through feedforward. The simulations on heavy-hex and grid graphs for 30-60 qubits report 2.4 times higher fidelity than the line-dynamic baseline while staying within 3 percent of the ideal unitary case. That combination of partitioning plus voting is not in the prior literature they cite, and the concrete numbers give a practical data point for NISQ state preparation work. The protocol description itself is clear enough that someone could try to reproduce the circuit structure. The soft spot is the generalization statement. The paper asserts the method works for any coupling topology and any GHZ size, yet the evaluations stay inside two specific graphs and a narrow qubit window. No scaling analysis, no additional graph families, and no inductive argument are given, so it is unclear how the majority-vote suppression behaves when boundary redundancy drops or when measurement-error paths change. The noise model is described only as realistic without parameters or error bars, and there are no hardware runs. This is for people building larger entangled states on current hardware who need a dynamic-circuit recipe. A reader working on error mitigation or mid-circuit measurements would get usable ideas from the protocol even if they have to re-derive the noise numbers themselves. I would send it to peer review. The core technique is new and the simulation results are worth checking in detail, even though the breadth of the claims needs more support.

Referee Report

3 major / 2 minor

Summary. The paper introduces Group-Majority-Voting (Group-MV), a dynamic-circuit protocol that partitions arbitrary coupling graphs into subgraphs, prepares local GHZ states in parallel, and fuses them via majority-voted mid-circuit measurements on redundant boundary links to suppress measurement-error propagation. Simulations on Heavy-hex and Grid topologies for 30–60 qubits under a realistic noise regime report that Group-MV achieves 2.4× higher fidelity than the Line Dynamic method while remaining within 3% of the unitary baseline, with the abstract asserting generalization to arbitrary GHZ sizes and coupling topologies.

Significance. If the fidelity gains and generalization hold, the protocol would provide a practical route to higher-fidelity GHZ states on noisy hardware with diverse connectivities, reducing the impact of measurement errors in feedforward circuits and potentially enabling larger-scale entanglement generation without requiring perfect two-qubit gates.

major comments (3)

[Abstract] Abstract: the central claim that Group-MV 'generalizes to arbitrary GHZ sizes on arbitrary coupling topologies' is not supported by the reported evidence, which is restricted to simulations on only two topologies (Heavy-hex and Grid) and a narrow qubit range (30–60); no scaling analysis, inductive argument, or additional graph families are presented to justify extrapolation beyond the tested cases.
[Simulation results] Simulation results (implied Results section): fidelity numbers are given without error bars, without explicit values for the noise-model parameters (e.g., gate-error rates, measurement-error probabilities, decoherence times), and without any hardware-validation data, so the reported 2.4× improvement and 3% unitary tracking cannot be assessed for statistical significance or transferability to real devices.
[Protocol description] Protocol description: the error-suppression mechanism of the majority-vote fusion step relies on boundary-link redundancy whose effectiveness can change on low-connectivity or irregular graphs; the manuscript provides no quantitative analysis of how the vote threshold or feedforward structure behaves when the tested Heavy-hex/Grid connectivity assumptions are relaxed.

minor comments (2)

[Abstract] The abstract should state the precise noise-model parameters and the exact definition of 'realistic noise regime' used in the simulations.
[Figures and tables] Figure captions and simulation tables would benefit from explicit labels for the number of shots, the precise fidelity metric (state fidelity vs. process fidelity), and the baseline unitary circuit depth.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment below, indicating where revisions will be incorporated to improve clarity and support for the claims.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim that Group-MV 'generalizes to arbitrary GHZ sizes on arbitrary coupling topologies' is not supported by the reported evidence, which is restricted to simulations on only two topologies (Heavy-hex and Grid) and a narrow qubit range (30–60); no scaling analysis, inductive argument, or additional graph families are presented to justify extrapolation beyond the tested cases.

Authors: We agree that the reported simulations are limited to Heavy-hex and Grid topologies for 30-60 qubits. The protocol is constructed to apply to arbitrary graphs via subgraph partitioning and boundary majority voting, but we acknowledge the lack of explicit scaling analysis or additional families in the current version. We will revise the abstract to qualify the generalization claim, add an inductive argument in the methods section demonstrating how fidelity scales with group count, and include results from one additional topology (a random 4-regular graph) to better support broader applicability. revision: yes
Referee: [Simulation results] Simulation results (implied Results section): fidelity numbers are given without error bars, without explicit values for the noise-model parameters (e.g., gate-error rates, measurement-error probabilities, decoherence times), and without any hardware-validation data, so the reported 2.4× improvement and 3% unitary tracking cannot be assessed for statistical significance or transferability to real devices.

Authors: We will add error bars derived from 100 independent simulation runs with varied random seeds to all reported fidelities. A new table will explicitly list all noise parameters used (gate error rates, measurement error probabilities, T1/T2 times). The study is simulation-based under a realistic noise model calibrated to current hardware; we will clarify the absence of experimental validation data while emphasizing the model's relevance to superconducting devices. revision: partial
Referee: [Protocol description] Protocol description: the error-suppression mechanism of the majority-vote fusion step relies on boundary-link redundancy whose effectiveness can change on low-connectivity or irregular graphs; the manuscript provides no quantitative analysis of how the vote threshold or feedforward structure behaves when the tested Heavy-hex/Grid connectivity assumptions are relaxed.

Authors: We will add a quantitative analysis subsection examining the majority-vote mechanism on lower-connectivity graphs, including a linear chain and an irregular tree topology. This will report fidelity as a function of vote threshold and number of redundant boundary links, showing how error suppression degrades gracefully when connectivity assumptions are relaxed. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper defines the Group-MV protocol explicitly via graph partitioning, local GHZ preparation, and majority-voted boundary measurements. Reported fidelities are presented as direct simulation outputs on Heavy-hex and Grid topologies for 30-60 qubits; no parameters are fitted to the target performance metrics, no equations reduce the claimed generalization to the simulation inputs by construction, and no self-citations are invoked as load-bearing uniqueness theorems. The generalization assertion is an extrapolation from the evaluated cases rather than a self-referential derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The protocol rests on standard assumptions of quantum circuit execution and noise models; no new free parameters, axioms, or invented entities are introduced beyond conventional quantum computing simulation practices.

axioms (1)

domain assumption Standard quantum mechanics and device noise models govern the simulated Heavy-hex and Grid topologies.
The evaluation assumes a realistic noise regime without providing explicit parameters or validation against hardware.

pith-pipeline@v0.9.0 · 5431 in / 1218 out tokens · 21564 ms · 2026-05-15T21:06:53.914777+00:00 · methodology

discussion (0)

Forward citations

Cited by 1 Pith paper

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MCMit mitigates mid-circuit measurement errors via a new multi-control branch instruction, CNN and transformer discriminators, and software techniques, reporting up to 70% latency reduction and 80% lower logical error...

Reference graph

Works this paper leans on

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