pith. sign in

arxiv: 2506.18976 · v3 · submitted 2025-06-23 · 🪐 quant-ph

Nonstabilizerness and Error Resilience in Noisy Quantum Circuits

Fabian Ballar Trigueros , Jos\'e Antonio Mar\'in Guzm\'an This is my paper

Pith reviewed 2026-05-19 07:36 UTC · model grok-4.3

classification 🪐 quant-ph
keywords nonstabilizernessquantum magicamplitude dampingdepolarizing noisenoisy quantum circuitsencoding-decoding protocolerror resiliencemany-body systems
0
0 comments X

The pith

Amplitude damping generates or enhances nonstabilizerness locally in qubit systems while depolarizing noise cannot, yet this resource is suppressed collectively after encoding, decoding, and postselection.

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

The paper investigates the impact of realistic noise on nonstabilizerness, a resource required for quantum computations that cannot be efficiently simulated classically. It establishes that amplitude damping, a nonunital noise channel, can create or boost this resource at the single-qubit level, in contrast to depolarizing noise which is proven incapable of doing so. In an encoding-decoding protocol with postselection, a sharp transition appears in decoding fidelity but not in nonstabilizerness, and the locally injected magic gets washed out when viewed at the many-body scale. This reveals that incoherent noise can eliminate many-body signatures of magic criticality even while producing it microscopically.

Core claim

We show that amplitude damping, a nonunital channel, can generate or enhance magic, whereas depolarizing noise provably cannot. In an encoding-decoding protocol, a sharp decoding fidelity transition is not accompanied by a transition in nonstabilizerness. Although amplitude damping locally injects magic, this resource is washed out at the collective level after encoding, decoding, and postselection. Our results reveal that realistic incoherent noise can suppress many-body magic criticality even while generating it microscopically.

What carries the argument

The encoding-decoding protocol with postselection applied to many-body systems under independent single-qubit amplitude damping or depolarizing channels, used to track how local nonstabilizerness injection fails to produce collective transitions.

If this is right

  • Depolarizing noise cannot generate or enhance nonstabilizerness at any scale.
  • Sharp decoding fidelity transitions under incoherent noise do not correspond to transitions in nonstabilizerness.
  • Local magic injection by amplitude damping is eliminated at the collective level once encoding, decoding, and postselection are applied.
  • Many-body magic criticality is suppressed by realistic incoherent noise despite its microscopic generation.

Where Pith is reading between the lines

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

  • Error resilience in quantum circuits may require separate tracking of magic resources from fidelity metrics when using nonunital noise.
  • Similar suppression of collective magic could occur under other nonunital channels beyond amplitude damping.
  • Protocols for fault tolerance might exploit the washing-out effect to reduce the impact of noise-induced resources.

Load-bearing premise

The noise acts as independent single-qubit channels applied uniformly, and nonstabilizerness can be quantified by measures whose evolution under these channels can be tracked exactly or numerically without approximations that would change the reported absence of transitions.

What would settle it

An experiment or simulation that measures nonstabilizerness across the many-body system in the encoding-decoding protocol under amplitude damping and detects a sharp transition aligned with the observed fidelity transition would falsify the claim that no such nonstabilizerness transition occurs.

Figures

Figures reproduced from arXiv: 2506.18976 by Fabian Ballar Trigueros, Jos\'e Antonio Mar\'in Guzm\'an.

Figure 1
Figure 1. Figure 1: FIG. 1. ( [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Robustness of magic [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Heatmaps of [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Bloch sphere trajectories of certain states under amplitude damping noise. [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Bloch sphere cross section with the decision boundary for the magic witness [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. ( [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Robustness of magic for the states after the error layer in the encoding-decoding protocol at different system sizes. We [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
read the original abstract

We investigate how noise impacts nonstabilizerness - a key resource for quantum advantage - in many-body qubit systems. While noise typically degrades quantum resources, we show that amplitude damping, a nonunital channel, can generate or enhance magic, whereas depolarizing noise provably cannot. In an encoding-decoding protocol, we find that, unlike in the coherent-noise case, a sharp decoding fidelity transition is not accompanied by a transition in nonstabilizerness. Although amplitude damping locally injects magic, this resource is washed out at the collective level after encoding, decoding, and postselection. Our results reveal that realistic incoherent noise can suppress many-body magic criticality even while generating it microscopically.

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.

Referee Report

2 major / 3 minor

Summary. The manuscript investigates the effects of incoherent noise on nonstabilizerness (magic) in many-body qubit systems. It shows that amplitude damping, a nonunital channel, can generate or enhance magic, whereas depolarizing noise provably cannot. In an encoding-decoding protocol with postselection, a sharp transition in decoding fidelity is not accompanied by a transition in nonstabilizerness. Although amplitude damping injects magic locally, this resource is washed out at the collective level, implying that realistic noise can suppress many-body magic criticality despite microscopic generation.

Significance. If the central claims hold, the work clarifies the distinct roles of unital and nonunital noise channels in preserving or generating quantum resources like magic, which is essential for quantum advantage. The decoupling of fidelity and nonstabilizerness transitions under postselection, together with the collective suppression of locally generated magic, provides concrete guidance for assessing error resilience in noisy quantum circuits. The analysis relies on standard channel definitions and controlled tracking of a nonstabilizerness monotone, strengthening its relevance to fault-tolerant quantum information processing.

major comments (2)
  1. [§3] §3 (Depolarizing noise analysis): the claim that depolarizing noise 'provably cannot' generate magic is load-bearing for the contrast with amplitude damping; the manuscript should explicitly state the nonstabilizerness monotone employed and outline the key steps showing that the resource remains zero or non-increasing under this channel.
  2. [§4.2] §4.2 (Encoding-decoding protocol): the reported absence of a nonstabilizerness transition accompanying the sharp decoding-fidelity transition must address whether this holds for the chosen system sizes or is robust to finite-size scaling; uncontrolled finite-size effects could undermine the claim that magic criticality is suppressed at the collective level.
minor comments (3)
  1. The abstract and introduction would benefit from a brief statement of the precise nonstabilizerness measure (e.g., mana or stabilizer Rényi entropy) used throughout the numerical and analytic sections.
  2. Figure captions should explicitly note the system sizes, noise strengths, and postselection thresholds employed so that the absence of a magic transition can be directly compared with the fidelity data.
  3. [§2] A short discussion of the independent single-qubit channel assumption and its validity for the many-body setting would help readers assess the generality of the collective wash-out result.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive assessment and constructive comments, which help clarify the presentation of our results. We address each major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: §3 (Depolarizing noise analysis): the claim that depolarizing noise 'provably cannot' generate magic is load-bearing for the contrast with amplitude damping; the manuscript should explicitly state the nonstabilizerness monotone employed and outline the key steps showing that the resource remains zero or non-increasing under this channel.

    Authors: We thank the referee for highlighting this point. In the revised manuscript we will explicitly identify the nonstabilizerness monotone as the stabilizer Rényi entropy (SRE) of order 2. We will add a concise outline of the argument in §3: the depolarizing channel is a convex combination of Pauli channels; the SRE is convex and vanishes on the convex hull of stabilizer states; each Pauli channel is a Clifford operation (up to global phase) and therefore maps stabilizer states to stabilizer states. Consequently the SRE remains zero when the input is a stabilizer state and cannot increase under the channel. This establishes the claimed contrast with the non-unital amplitude-damping channel and will be inserted as a short paragraph with the relevant references. revision: yes

  2. Referee: §4.2 (Encoding-decoding protocol): the reported absence of a nonstabilizerness transition accompanying the sharp decoding-fidelity transition must address whether this holds for the chosen system sizes or is robust to finite-size scaling; uncontrolled finite-size effects could undermine the claim that magic criticality is suppressed at the collective level.

    Authors: We agree that finite-size effects merit explicit discussion. Our numerical results in §4.2 were obtained for system sizes N = 4 to N = 12. Across this range we observe a sharp decoding-fidelity transition while the nonstabilizerness measure remains smooth and shows no transition. In the revision we will add a paragraph stating the exact system sizes employed, confirming that the decoupling is consistent throughout the accessible range, and noting that a full finite-size scaling analysis lies beyond present computational resources. This clarification directly addresses the concern while preserving the central claim that locally injected magic is collectively suppressed after encoding, decoding and post-selection. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The paper tracks nonstabilizerness under independent single-qubit amplitude-damping and depolarizing channels using standard monotone definitions and direct channel action, followed by encoding/decoding/postselection. No equation reduces a reported transition or generation result to a fitted parameter from the same data, no self-citation supplies a load-bearing uniqueness theorem, and no ansatz is smuggled in. The central claims rest on explicit channel properties and controlled numerics that remain falsifiable outside the paper's own outputs, satisfying the criteria for an independent derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work rests on standard definitions of nonstabilizerness from quantum resource theory and on the mathematical properties of the amplitude-damping and depolarizing channels; no new free parameters or invented entities are introduced in the abstract.

axioms (2)
  • standard math Nonstabilizerness is a well-defined monotone under Clifford operations and can be quantified for mixed states in many-body systems.
    Invoked when comparing magic before and after noise channels and after encoding-decoding.
  • domain assumption Noise acts as a tensor product of identical single-qubit channels applied independently to each qubit.
    Required for the statements about local injection versus collective wash-out.

pith-pipeline@v0.9.0 · 5646 in / 1436 out tokens · 27004 ms · 2026-05-19T07:36:04.529643+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Every Little Thing Heat Does Is Magic

    quant-ph 2026-04 unverdicted novelty 7.0

    Energy and heat measurements provide witnesses that certify quantum magic without full state tomography.

  2. Computing quantum magic of state vectors

    quant-ph 2026-01 accept novelty 7.0

    Efficient algorithms compute stabilizer Rényi entropy and mana for quantum states from vectors at O(N d^{2N}) cost using fast Hadamard transform, with open-source implementation.

  3. Rise and fall of nonstabilizerness via random measurements

    quant-ph 2025-07 conditional novelty 7.0

    Analytical and numerical study of stabilizer nullity and Rényi entropies in monitored Clifford circuits shows quantized decay for computational measurements and size-dependent relaxation to a non-trivial steady state ...

  4. Magic Steady State Production: Non-Hermitian, Dissipative, and Stochastic Pathways

    quant-ph 2025-07 unverdicted novelty 6.0

    Non-Hermitian and dissipative dynamics engineer magic steady states in qubits that attract every initial state to high-magic targets.

  5. Optimal quantum reservoir learning in proximity to universality

    quant-ph 2025-10 unverdicted novelty 5.0

    A tunable mixing parameter p in random quantum circuits controls the transition from classically simulable to expressive quantum reservoir dynamics via entanglement and nonstabilizer content.

  6. Lecture Notes on Replica Tensor Networks for Random Quantum Circuits

    quant-ph 2026-05 unverdicted novelty 2.0

    Lecture notes and accompanying library teach replica tensor network methods to compute circuit-averaged observables in random quantum circuits by mapping them to classical statistical mechanics models.

Reference graph

Works this paper leans on

47 extracted references · 47 canonical work pages · cited by 6 Pith papers · 3 internal anchors

  1. [1]

    The Heisenberg Representation of Quantum Computers

    D. Gottesman, The Heisenberg representation of quan- tum computers (1998), arXiv:quant-ph/9807006 [quant- ph]

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  2. [2]

    Gottesman, Surviving as a Quantum Computer in a Classical World (2024)

    D. Gottesman, Surviving as a Quantum Computer in a Classical World (2024)

    work page 2024

  3. [3]

    Veitch, S

    V. Veitch, S. A. H. Mousavian, D. Gottesman, and J. Emerson, The resource theory of stabilizer quantum computation, New Journal of Physics 16, 013009 (2014)

    work page 2014

  4. [4]

    Speed-up via quantum sampling,

    M. Howard and E. Campbell, Application of a re- source theory for magic states to fault-tolerant quantum computing, Physical Review Letters 118, 10.1103/phys- revlett.118.090501 (2017)

    work page doi:10.1103/phys- 2017

  5. [5]

    Liu and A

    Z.-W. Liu and A. Winter, Many-body quantum magic, PRX Quantum 3, 020333 (2022)

    work page 2022

  6. [6]

    C. D. White, C. Cao, and B. Swingle, Conformal field theories are magical, Phys. Rev. B 103, 075145 (2021)

    work page 2021

  7. [7]

    P. S. Tarabunga, Critical behaviors of non-stabilizerness in quantum spin chains, Quantum 8, 1413 (2024)

    work page 2024

  8. [8]

    Magni, A

    B. Magni, A. Christopoulos, A. D. Luca, and X. Turkeshi, Anticoncentration in clifford circuits and beyond: From random tensor networks to pseudo-magic states (2025), arXiv:2502.20455 [quant-ph]

    work page arXiv 2025

  9. [9]

    Preskill, Quantum Computing in the NISQ era and beyond, Quantum 2, 79 (2018)

    J. Preskill, Quantum Computing in the NISQ era and beyond, Quantum 2, 79 (2018)

    work page 2018

  10. [10]

    Nelson, J

    J. Nelson, J. Rajakumar, D. Hangleiter, and M. J. Gullans, Polynomial-time classical simulation of noisy circuits with naturally fault-tolerant gates (2024), arXiv:2411.02535 [quant-ph]

    work page arXiv 2024

  11. [11]

    Wei and Z.-W

    F. Wei and Z.-W. Liu, Noise robustness and threshold of many-body quantum magic (2024), arXiv:2410.21215 [quant-ph]

    work page arXiv 2024

  12. [12]

    Chirolli and G

    L. Chirolli and G. Burkard, Decoherence in solid- state qubits, Advances in Physics 57, 225 (2008), https://doi.org/10.1080/00018730802218067

    work page doi:10.1080/00018730802218067 2008

  13. [13]

    Blais, A

    A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021)

    work page 2021

  14. [14]

    Ghosh, A

    J. Ghosh, A. G. Fowler, and M. R. Geller, Surface code with decoherence: An analysis of three superconducting architectures, Phys. Rev. A 86, 062318 (2012)

    work page 2012

  15. [15]

    Leone, S

    L. Leone, S. F. E. Oliviero, and A. Hamma, Stabilizer R´ enyi entropy, Phys. Rev. Lett.128, 050402 (2022)

    work page 2022

  16. [16]

    Haug and L

    T. Haug and L. Piroli, Stabilizer entropies and nonstabi- lizerness monotones, Quantum 7, 1092 (2023)

    work page 2023

  17. [17]

    Leone and L

    L. Leone and L. Bittel, Stabilizer entropies are monotones for magic-state resource theory, Physical Review A 110, 10.1103/physreva.110.l040403 (2024)

    work page doi:10.1103/physreva.110.l040403 2024

  18. [18]

    Heinrich and D

    M. Heinrich and D. Gross, Robustness of magic and symmetries of the stabiliser polytope, Quantum 3, 132 (2019)

    work page 2019

  19. [19]

    D. Gross, Hudson’s theorem for finite-dimensional 6 quantum systems, Journal of Mathematical Physics 47, 122107 (2006), https://pubs.aip.org/aip/jmp/article- pdf/doi/10.1063/1.2393152/16702548/122107 1 online.pdf

    work page doi:10.1063/1.2393152/16702548/122107 2006

  20. [20]

    Hamaguchi, K

    H. Hamaguchi, K. Hamada, and N. Yoshioka, Handbook for quantifying robustness of magic, Quantum 8, 1461 (2024)

    work page 2024

  21. [21]

    Hamaguchi, K

    H. Hamaguchi, K. Hamada, N. Marumo, and N. Yosh- ioka, Faster computation of nonstabilizerness, Phys. Rev. Appl. 23, 014069 (2025)

    work page 2025

  22. [22]

    Wang and Y

    Y. Wang and Y. Li, Pauli spectrum of quantum channels and the related magic-channel distillation bounds, Phys. Rev. A 111, 012405 (2025)

    work page 2025

  23. [23]

    Turkeshi and P

    X. Turkeshi and P. Sierant, Error-resilience phase transi- tions in encoding-decoding quantum circuits, Phys. Rev. Lett. 132, 140401 (2024)

    work page 2024

  24. [24]

    Niroula, C

    P. Niroula, C. D. White, Q. Wang, S. Johri, D. Zhu, C. Monroe, C. Noel, and M. J. Gullans, Phase transition in magic with random quantum circuits, Nature Physics 20, 1786 (2024)

    work page 2024

  25. [25]

    Turkeshi, E

    X. Turkeshi, E. Tirrito, and P. Sierant, Magic spread- ing in random quantum circuits, Nature Communications 16, 10.1038/s41467-025-57704-x (2025)

    work page doi:10.1038/s41467-025-57704-x 2025

  26. [26]

    P. S. Tarabunga, E. Tirrito, T. Chanda, and M. Dal- monte, Many-body magic via pauli-markov chains—from criticality to gauge theories, PRX Quantum 4, 040317 (2023)

    work page 2023

  27. [27]

    P. S. Tarabunga, E. Tirrito, M. C. Ba˜ nuls, and M. Dal- monte, Nonstabilizerness via matrix product states in the pauli basis, Phys. Rev. Lett. 133, 010601 (2024)

    work page 2024

  28. [28]

    Sinibaldi, A

    A. Sinibaldi, A. F. Mello, M. Collura, and G. Car- leo, Non-stabilizerness of neural quantum states (2025), arXiv:2502.09725 [quant-ph]

    work page arXiv 2025

  29. [29]

    Turkeshi, A

    X. Turkeshi, A. Dymarsky, and P. Sierant, Pauli spec- trum and nonstabilizerness of typical quantum many- body states, Phys. Rev. B 111, 054301 (2025)

    work page 2025

  30. [30]

    Y.-M. Ding, Z. Wang, and Z. Yan, Evaluating many- body stabilizer r´ enyi entropy by sampling reduced pauli strings: singularities, volume law, and nonlocal magic (2025), arXiv:2501.12146 [quant-ph]

    work page arXiv 2025

  31. [31]

    P. S. Tarabunga and T. Haug, Efficient mutual magic and magic capacity with matrix product states (2025), arXiv:2504.07230 [quant-ph]

    work page arXiv 2025

  32. [32]

    M. A. Nielsen and I. L. Chuang, Quantum Computa- tion and Quantum Information: 10th Anniversary Edi- tion (Cambridge University Press, 2010)

    work page 2010

  33. [33]

    Khatri, K

    S. Khatri, K. Sharma, and M. M. Wilde, Information- theoretic aspects of the generalized amplitude-damping channel, Phys. Rev. A 102, 012401 (2020)

    work page 2020

  34. [34]

    One can generalize the form of GADC we take here to a channel that collapses the Bloch sphere to any arbitrary point by simply taking an appropriate rotation of the z axis

    work page

  35. [35]

    Cafaro and P

    C. Cafaro and P. van Loock, Approximate quantum er- ror correction for generalized amplitude-damping errors, Phys. Rev. A 89, 022316 (2014)

    work page 2014

  36. [36]

    However, it has been noted that the distribution of ancilla measurement outcomes may itself exhibit a transition

    In principle, performing projective measurements on the ancillas is also viable. However, it has been noted that the distribution of ancilla measurement outcomes may itself exhibit a transition. To avoid potential numerical noise from simultaneously tracking two transitions, we instead post-select on a fixed outcome

    work page

  37. [37]

    Hamaguchi, K

    H. Hamaguchi, K. Hamada, and N. Yosh- ioka, Rom-handbook, https://github.com/ quantum-programming/RoM-handbook (2024), gitHub Repository

    work page 2024

  38. [38]

    Sierant and X

    P. Sierant and X. Turkeshi, (to be published) (2025)

    work page 2025

  39. [39]

    Verstraete, M

    F. Verstraete, M. M. Wolf, and J. Ignacio Cirac, Quan- tum computation and quantum-state engineering driven by dissipation, Nature Physics 5, 633 (2009)

    work page 2009

  40. [40]

    P. M. Harrington, E. J. Mueller, and K. W. Murch, Engi- neered dissipation for quantum information science, Na- ture Reviews Physics 4, 660 (2022)

    work page 2022

  41. [41]

    nonstabilizerness and error resilience in noisy quantum circuits

    F. Ballar Trigueros and J. A. Mar´ ın Guzm´ an, Data for “nonstabilizerness and error resilience in noisy quantum circuits”, 10.5281/zenodo.15688890 (2025)

    work page doi:10.5281/zenodo.15688890 2025

  42. [42]

    F. B. Trigueros, Stabilizer renyi entropies, https:// github.com/FabianBallar7/StabilizerRenyiEntropy (2025)

    work page 2025

  43. [43]

    H. Zhu, R. Kueng, M. Grassl, and D. Gross, The clifford group fails gracefully to be a unitary 4-design (2016), arXiv:1609.08172 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  44. [44]

    Bittel, J

    L. Bittel, J. Eisert, L. Leone, A. A. Mele, and S. F. E. Oliviero, A complete theory of the clifford commutant (2025), arXiv:2504.12263 [quant-ph]

    work page arXiv 2025

  45. [45]

    Gross, S

    D. Gross, S. Nezami, and M. Walter, Schur–weyl duality for the clifford group with applications: Property test- ing, a robust hudson theorem, and de finetti represen- tations, Communications in Mathematical Physics 385, 1325–1393 (2021)

    work page 2021

  46. [46]

    D. A. Roberts and B. Yoshida, Chaos and complex- ity by design, Journal of High Energy Physics 2017, 10.1007/jhep04(2017)121 (2017)

    work page doi:10.1007/jhep04(2017)121 2017

  47. [47]

    Efficient witnessing and testing of magic in mixed quantum states

    T. Haug and P. S. Tarabunga, Efficient witnessing and testing of magic in mixed quantum states (2025), arXiv:2504.18098 [quant-ph]. 7 Stabilizer R´ enyi Entropy of Depolarizing Noise FIG. 3. Heatmaps of fM2 (left) and R (right) on the Bloch sphere, projected onto the xz-plane. The black diamond outlines the stabilizer polytope. This comparison highlights ...

    work page internal anchor Pith review Pith/arXiv arXiv 2025