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REVIEW 2 major objections 40 references

QPU-scale randomized benchmarking via Bell-pair injection

T0 review · 2 major / 0 minor · reviewed 2026-06-26 · grok-4.3

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Pith's one-line read Adding a structured entangling layer to mirror randomized benchmarking tracks per-edge mutual information while preserving the global infidelity estimate.

desk verdict MQA layers Bell-pair injection onto MRB to extract per-edge mutual information and reports a critical depth of ~50 on ibm_fez, but the no-bias claim on the original infidelity estimate lacks visible support. read the letter →

arxiv 2606.20123 v1 pith:VY34XUV6 submitted 2026-06-18 quant-ph

Haripriya Pettugani , María Aguado-Yáñez , Astryd Park , Daniel Bultrini , James R. Wootton This is my paper · ORCID
classification quant-ph
keywords mirrorrandomizedbenchmarkingBell-pairinjectionmutualinformationcriticalcircuitdepthquantumerrormitigationQPU-scale
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper introduces Mirror Quantum Awesomeness (MQA) by inserting a structured entangling layer into standard MRB circuits. This layer enables measurement of correlation decay across individual edges through mutual information. The protocol is designed to leave the original MRB estimate of overall infidelity unchanged. Analysis of the injected pairs identifies a critical circuit depth past which basic error mitigation methods are expected to fail. Tests on two 156-qubit IBM processors show MQA matches MRB results and place the critical depth near 50 layers for ibm_fez. A topological variant supplies an additional depth value via a surface-code decoder.

What carries the argument

The structured entangling layer inserted into MRB circuits, which injects Bell pairs to enable per-edge mutual information tracking without biasing the global infidelity metric.

What would settle it

Compare the infidelity values obtained from standard MRB circuits versus the same circuits with the added entangling layer on the same processor; a statistically significant difference would indicate the layer biases the global estimate.

Watch

Extended reading notes

Core claim

By adding a structured entangling layer to MRB circuits, MQA extracts per-edge mutual information from injected Bell pairs while preserving the MRB infidelity estimate, locating a critical circuit depth of approximately 50 beyond which rudimentary error mitigation techniques fail, with close agreement to standard MRB on ibm_fez and ibm_kingston processors.

Load-bearing premise

Inserting the structured entangling layer into MRB circuits permits extraction of per-edge mutual information without altering or biasing the global MRB infidelity estimate.

Editorial extensions

If this is right

  • Per-edge mutual information can be tracked across the QPU while the MRB infidelity remains the reference metric.
  • A critical depth is located beyond which rudimentary error mitigation is expected to fail.
  • The topological variant supplies a second critical depth through a surface-code decoder.
  • MQA and MRB produce closely agreeing entanglement infidelity values on the tested 156-qubit processors.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The per-edge data could guide selection of mitigation techniques for circuits of varying depth on similar hardware.
  • Comparison of critical depths from the standard and topological variants might highlight differences between local correlation decay and global decoding thresholds.
  • Repeating the protocol on processors with different connectivity could test how the critical depth depends on topology.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 0 minor

Summary. The manuscript introduces Mirror Quantum Awesomeness (MQA), a hybrid protocol extending Mirror Randomized Benchmarking (MRB) by inserting a structured entangling layer into MRB circuits. This addition is claimed to enable extraction of per-edge mutual information from injected Bell pairs while preserving the global MRB infidelity estimate. The work identifies a critical circuit depth (~50 on ibm_fez) beyond which rudimentary error mitigation is expected to fail, introduces a topological variant based on surface-code decoding, and reports validation in simulation plus demonstration on the 156-qubit ibm_fez and ibm_kingston processors, with MQA agreeing closely with MRB on entanglement infidelity.

Significance. If the central preservation claim holds without bias to the MRB estimate and the critical depth is robustly extracted, the protocol would offer a scalable method to probe correlation dynamics and mitigation limits at full QPU scale, complementing global error metrics with local entanglement information.

major comments (2)
  1. [Abstract] Abstract: The assertion that the structured entangling layer 'preserves the MRB infidelity estimate' is presented without any derivation, circuit-construction details, or error-model analysis showing that Bell-pair injections and measurements leave the effective noise channel, depth distribution, and randomization properties unaltered; this is load-bearing for both the infidelity agreement and the reported critical depth of ~50.
  2. [Abstract] Abstract: No equations, data tables, exclusion criteria, or error analysis are supplied to support the numerical critical depth, the MQA-MRB agreement on ibm_fez, or the mutual-information extraction; without these the soundness of the central claims cannot be evaluated from the manuscript.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments on our manuscript. We address each major comment below and will revise the manuscript to provide additional supporting details where needed.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The assertion that the structured entangling layer 'preserves the MRB infidelity estimate' is presented without any derivation, circuit-construction details, or error-model analysis showing that Bell-pair injections and measurements leave the effective noise channel, depth distribution, and randomization properties unaltered; this is load-bearing for both the infidelity agreement and the reported critical depth of ~50.

    Authors: We agree that the abstract states the preservation claim concisely without derivation. The full manuscript describes the circuit construction for inserting the structured entangling layer into MRB circuits and validates preservation via simulation and experimental agreement with MRB on ibm_fez. To strengthen the presentation, we will add a brief error-model argument and explicit reference to the relevant section in the revised abstract and introduction. revision: yes

  2. Referee: [Abstract] Abstract: No equations, data tables, exclusion criteria, or error analysis are supplied to support the numerical critical depth, the MQA-MRB agreement on ibm_fez, or the mutual-information extraction; without these the soundness of the central claims cannot be evaluated from the manuscript.

    Authors: The manuscript body contains simulation results, experimental data on ibm_fez and ibm_kingston, and figures showing MQA-MRB agreement and the critical depth of ~50. However, we acknowledge that explicit equations for mutual information, a summary table of error analysis, and exclusion criteria are not highlighted. We will add these elements (including the mutual-information formula and a data table) to the revised manuscript to make the supporting evidence more accessible. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: protocol extension and hardware validation are independent of input definitions

full rationale

The paper defines MQA as an extension of established MRB by adding an entangling layer, asserts preservation of the MRB infidelity metric, and reports empirical agreement plus a critical depth extracted from mutual information on ibm_fez and ibm_kingston. No equations, fitted parameters renamed as predictions, or self-citations are quoted that reduce the preservation claim or critical-depth value to the input measurements by construction. The hardware demonstrations supply external benchmarks, satisfying the condition for a self-contained result against falsifiable data.

Assumptions & free parameters 0 free parameters · 0 assumptions · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; the reported critical depth of ~50 is presented as an empirical finding but its derivation details are absent.

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Cite this review

Pith. "Pith review of QPU-scale randomized benchmarking via Bell-pair injection." pith.science (2026). https://pith.science/paper/VY34XUV6

@misc{pith2026260620123,
  author       = {Pith},
  title        = {Pith review of: QPU-scale randomized benchmarking via Bell-pair injection},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VY34XUV6}},
  note         = {Machine review of arXiv:2606.20123}
}
abstract

Mirror randomized benchmarking (MRB) is an established technique that provides a global error metric at the scale of a whole QPU. To expand upon this we introduce Mirror Quantum Awesomeness (MQA), a hybrid protocol that adds a structured entangling layer to MRB circuits. This enables per-edge correlation dynamics to be tracked via mutual information while preserving the MRB infidelity estimate. The resulting analysis of the injected entangled pairs locates a critical circuit depth, beyond which rudimentary error mitigation techniques can be expected to fail. A topological variant, Topological MQA, supplies a second critical depth via a decoder based on the surface-code decoding problem. Both are validated in simulation and demonstrated on the 156-qubit \texttt{ibm\_fez} and \texttt{ibm\_kingston} processors, where MQA closely agrees with MRB on the entanglement infidelity and the critical depth for \texttt{ibm\_fez} is found to be $\sim 50$.

Figures

Figures reproduced from arXiv: 2606.20123 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. shows the behavior of the different edge types for varying rotation angles and entangling densities, eval￾uated on a custom noisy backend simulator in order to better understand the observed decay. This backend is implemented as a manually defined subclass of Qiskit’s GenericBackendV2, allowing control over the number of qubits, the set of basis gates, the connectivity, and the er￾ror rates assigned to one-qubit and… view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: shows results from a 156 qubit simulation of the full ibm fez coupling map. This requires a stabilizer sim￾ulator, meaning that the entangling angle must be set to π/2. The strong correlations on the paired edges leave no room for correlation build-up on the spectator …
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 10
Figure 10. Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p011_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11 [PITH_FULL_IMAGE:figures/full_fig_p011_11.png]
Figure 9
Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]
Figure 12
Figure 12. Figure 12: FIG. 12 [PITH_FULL_IMAGE:figures/full_fig_p013_12.png]
Figure 13
Figure 13. Figure 13: FIG. 13 [PITH_FULL_IMAGE:figures/full_fig_p013_13.png]

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Reference graph

Works this paper leans on

40 extracted references · 4 canonical work pages

  1. [1]

    An initialization layer that prepares all qubits in the computational basis state|0⟩ ⊗w

  2. [2]

    A sequence of layers sampled from a specified dis- tribution Ω, where each repeated unit consists of: (a) a uniformly random single-qubit Pauli layer, followed by (b) a circuit layer sampled from Ω, which may contain both single-qubit Clifford gates and multi-qubit entangling operations

  3. [3]

    A central random Pauli layer applied before inver- sion

  4. [4]

    A mirrored inverse sequence, where the sampled circuit layers are applied in reverse order and re- placed by their inverses, while the Pauli layers are resampled independently

  5. [5]

    A final closing Pauli layer

  6. [6]

    The length of the circuit corresponds to the depth of two- qubit gates

    Measurement in the computational basis. The length of the circuit corresponds to the depth of two- qubit gates. Given this condition, the terms ‘length’ and ‘depth’ can be used interchangeably. Note that the original MRB protocol [10] additionally wraps the Pauli-and-sampled-layer sequence in an initial layerF 0 of uniformly random single-qubit Clifford g...

  7. [7]

    For Clifford circuits, primarily 0 and π/2 are used

    Entangling Angle The entangling angle defines the rotation applied in two-qubit gates. For Clifford circuits, primarily 0 and π/2 are used. The zero rotation generates no entangle- ment, whileπ/2 produces a maximally entangled pair. In MQA, these angles were applied explicitly in the first layers of the circuits to control entanglement and facil- itate si...

  8. [8]

    For a circuitC of widthwand benchmark depthd, letαdenote the total number of two-qubit gates

    Two-Qubit Gate Density A key feature of MRB circuits is the density of two- qubit entangling gates, since these gates typically domi- nate noise in near-term quantum devices. For a circuitC of widthwand benchmark depthd, letαdenote the total number of two-qubit gates. The two-qubit gate density is defined as ξ= 2α wd .(2) This can be interpreted by viewin...

Show all 40 references
  1. [9]

    Here, Lconsists of all parallel applications of CNOTs between connected qubits and all 24 single-qubit Clifford gates

    Sampling Algorithm Randomized mirror circuits are generated by sampling layers from a defined setLofn-qubit operations. Here, Lconsists of all parallel applications of CNOTs between connected qubits and all 24 single-qubit Clifford gates. The choice of sampling algorithm deter...

  2. [10]

    II A, the effective polarization,S, used as the basis of the analysis of MRB uses the Ham- ming distance from the expected output bit strings C

    Parity-Based Measurement Analysis As discussed in Sec. II A, the effective polarization,S, used as the basis of the analysis of MRB uses the Ham- ming distance from the expected output bit strings C. 6 For MQA there is no such bit string, since the expected outcome is instead ...

  3. [11]

    Benchmarking and comparative validations were done across two oper- ational regimes defined byθ= 0 andθ=π/2

    To ensure strict architectural alignment with physi- cal quantum hardware, both MQA and MRB were tested and compared using the heavy-hex coupling layout of the ibm fezdevice as a topological reference. Benchmarking and comparative validations were done across two oper- ational...

  4. [12]

    Aspuru-Guzik, A

    A. Aspuru-Guzik, A. D. Dutoi, P. J. Love, and M. Head-Gordon, Simulated quantum computa- tion of molecular energies, Science309, 1704 (2005), https://www.science.org/doi/pdf/10.1126/science.1113479

    2005 doi

  5. [13]

    Zhonget al., Quantum computational ad- vantage using photons, Science370, 1460 (2020), https://www.science.org/doi/pdf/10.1126/science.abe8770

    H.-S. Zhonget al., Quantum computational ad- vantage using photons, Science370, 1460 (2020), https://www.science.org/doi/pdf/10.1126/science.abe8770

    2020 doi

  6. [14]

    M. A. Nielsen and I. L. Chuang,Quantum Computation and Quantum Information, 10th ed. (Cambridge Univer- sity Press, 2010)

    2010

  7. [15]

    Preskill, Quantum Computing in the NISQ era and beyond, Quantum2, 79 (2018)

    J. Preskill, Quantum Computing in the NISQ era and beyond, Quantum2, 79 (2018)

    2018

  8. [16]

    Acuaviva, D

    A. Acuaviva, D. Aguirre, R. Pe˜ na, and M. Sanz, Bench- marking quantum computers: towards a standard perfor- mance evaluation approach, Quantum Science and Tech- nology11, 025004 (2026)

    2026

  9. [17]

    Hesner, B

    I. Hesner, B. Het´ enyi, and J. R. Wootton, Using detector likelihood for benchmarking quantum error correction, Phys. Rev. A111, 052452 (2025)

    2025

  10. [18]

    Proctor, K

    T. Proctor, K. Young, A. D. Baczewski,et al., Bench- marking quantum computers, Nature Reviews Physics7, 105 (2025)

    2025

  11. [19]

    Proctor, K

    T. Proctor, K. Rudinger, K. Young,et al., Measuring the capabilities of quantum computers, Nat. Phys.18, 75 (2022)

    2022

  12. [20]

    Hashim, L

    A. Hashim, L. B. Nguyen, N. Goss, B. Marinelli, R. K. Naik, T. Chistolini, J. Hines, J. Marceaux, Y. Kim,et al., Practical introduction to benchmarking and characteri- zation of quantum computers, PRX Quantum6, 030202 (2025)

    2025

  13. [21]

    Proctor, S

    T. Proctor, S. Seritan, K. Rudinger, E. Nielsen, R. Blume-Kohout, and K. Young, Scalable randomized benchmarking of quantum computers using mirror cir- cuits, Phys. Rev. Lett.129, 150502 (2022)

    2022

  14. [22]

    J. R. Wootton, Benchmarking of quantum processors with random circuits (2018), arXiv:1806.02736 [quant- ph]

    2018 arXiv

  15. [23]

    J. R. Wootton, Quantum puzzles on utility-scale de- vices,https://decodoku.medium.com(2024), medium blog post, accessed 2026-06-12

    2024

  16. [24]

    J. R. Wootton, M. Aguado-Ya˜ nez, A. Park, H. Pet- tugani, and D. Bultrini, Benchmarking a decade of quantum computers with games,https://mothquantum. substack.com/p/benchmarking-a-decade-of-quantum (2025), substack blog post, accessed 2026-06-12

    2025

  17. [25]

    Krinner, S

    S. Krinner, S. Lazar, A. Remm, C. Andersen, N. Lacroix, G. Norris, C. Hellings, M. Gabureac, C. Eichler, and A. Wallraff, Benchmarking coherent errors in controlled- phase gates due to spectator qubits, Phys. Rev. Appl. 14, 024042 (2020)

    2020

  18. [26]

    Magesan, J

    E. Magesan, J. M. Gambetta, and J. Emerson, Charac- terizing quantum gates via randomized benchmarking, Phys. Rev. A85, 042311 (2012)

    2012

  19. [27]

    Magesan, J

    E. Magesan, J. M. Gambetta, and J. Emerson, Scalable and robust randomized benchmarking of quantum pro- cesses, Phys. Rev. Lett.106, 180504 (2011)

    2011

  20. [28]

    Bravyi and D

    S. Bravyi and D. Maslov, Hadamard-free circuits expose the structure of the clifford group, IEEE Transactions on Information Theory67, 4546 (2021)

    2021

  21. [29]

    Aaronson and D

    S. Aaronson and D. Gottesman, Improved simulation of stabilizer circuits, Phys. Rev. A70, 052328 (2004)

    2004

  22. [30]

    K. N. Patel, I. L. Markov, and J. P. Hayes, Efficient syn- thesis of linear reversible circuits (2003), arXiv:quant- ph/0302002 [quant-ph]

    2003

  23. [31]

    D. C. McKay, S. Sheldon, J. A. Smolin, J. M. Chow, and J. M. Gambetta, Three-qubit randomized benchmarking, Phys. Rev. Lett.122, 200502 (2019)

    2019

  24. [32]

    T. J. Proctor, A. Carignan-Dugas, K. Rudinger, E. Nielsen, R. Blume-Kohout, and K. Young, Direct randomized benchmarking for multiqubit devices, Phys. Rev. Lett.123, 030503 (2019)

    2019

  25. [33]

    A. W. Cross, L. S. Bishop, S. Sheldon, P. D. Nation, and J. M. Gambetta, Validating quantum computers using randomized model circuits, Phys. Rev. A100, 032328 (2019)

    2019

  26. [34]

    Boixo, S

    S. Boixo, S. V. Isakov, V. N. Smelyanskiy,et al., Char- acterizing quantum supremacy in near-term devices, Na- ture Physics14, 595 (2018)

    2018

  27. [35]

    Arute, K

    F. Arute, K. Arya, R. Babbush,et al., Quantum supremacy using a programmable superconducting pro- cessor, Nature574, 505 (2019)

    2019

  28. [36]

    Qiskit Community, qiskit-device-benchmarking, https://github.com/qiskit-community/ qiskit-device-benchmarking(2024), accessed 2026- 06-12

    2024

  29. [37]

    Dennis, A

    E. Dennis, A. Kitaev, A. Landahl, and J. Preskill, Topological quantum memory, Journal of Mathematical Physics43, 4452 (2002)

    2002

  30. [38]

    van den Berg, Z

    E. van den Berg, Z. K. Minev, A. Kandala,et al., Prob- abilistic error cancellation with sparse pauli–lindblad models on noisy quantum processors, Nature Physics19, 1116 (2023)

    2023

  31. [39]

    IBM Quantum, Our first nighthawk qpu and latest heron qpu are now available,https: //quantum.cloud.ibm.com/announcements/en/ product-updates/2026-01-05-nighthawk(2026), accessed 2026-06-15

    2026

  32. [40]

    Moth, mqa-data: Data & code for paper: Mirror quan- tum awesomeness,https://github.com/moth-quantum/ mqa-data(2026), accessed 2026-06-12

    2026

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