-->PONE-D-26-26966-->-->PsiAudit: An open-source toolkit for auditing symmetry-organised complexity in equivariant quantum neural networks-->-->PLOS One

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Reviewer #1: Yes

Reviewer #2: Yes

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Reviewer #2: Yes

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-->5. Review Comments to the Author

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Reviewer #1: Well written, presented and supported. It was a pleasure to read; this reviewer appreciates the care and effort of the authors to develop the project and manuscript.

The scope and impact of the paper are difficult to predict in its current state.

A clear description of the software is helpful and can serve as a useful guide for researchers following in the authors' path.

Explaining symmetry 'organized' complexity is important and should be examined.

There is much to test and report in this area.

Automation is needed if we wish to explore the domain. It so follows that the authors' work reported in this paper is useful in the construction effort for tools to this purpose.

'PsiAudit' as a name for the toolkit is confusing and collides with tradition for naming of tools among various disciplines from engineering to psychology. A great scope of work in psychology, neuroscience, accounting, and social sciences exists, in which names for methods and tools collide with the name that has been chosen here.

For something as important as examining symmetry a better name can be be found.

This work needs to be viewed as a possible gatekeeper for exploration of circuits.

41 > ""The choice of ansatz affects trainability, resource requirements, inductive bias, and the range of states the model can reach [5, 6, 7].

Regardless of the tool aspect, the concept that -

619 > ""Our results show this captures information that expressibility, gradient variance, and Meyer-Wallach Q do not, since ansätze that look alike under those measures can separate clearly in the component profile

- this is valuable in the presentation of a direction for exploration.

Assuming that an efficient path is to simulate a structure or design before going further, and as PsiAudit is a simulator, it then conditions later exploration. Imprecision in a simulator will influence choices about what to explore.

This reviewer can not evaluate the precision of the PsiAudit simulator.

As a tool it is a valuable contribution.

Researchers need to read the details on how this PsiAudit is validated.

ie.

965 > .... The tests pass at all system sizes used in this paper.

Recommendations -

This reviewer did not find anything wrong with the paper, and would hope only that the authors take extra care in advising the reader on the scope and limitations of the simulator.

From the name of the toolkit, the reviewer would not guess its purpose, and it seems misnamed for those who have other 'Psi/Psy ... ' prefixed tools already in use, or 'audit' tools. This reviewer encounters both and assumes Psi/Psy to be psychology/neuroscience and Audit to be psychology/engineering/accounting.

Reviewer #2: The authors have introduced an open-source Python diagnostic toolkit, PsiAudit designed to evaluate symmetry-organised complexity within Equivariant Quantum Neural Networks. This toolkit addresses a critical diagnostic blind spot in Quantum Machine Learning (QML) by introducing four distinct, normalized structural axes: sector occupation entropy, cross-sector coherence, sectoral fluctuation, and generator-sum compliance.

The framework successfully breaks diagnostic degeneracy by distinguishing between equivariant and symmetry-broken architectures in scenarios where standard metrics yield overlapping results.

The core primitives are rigorously bounded within a zero-to-one interval using appropriate statistical normalization techniques, ensuring cross-architecture comparability.

The architecture functions out-of-the-box across highly diverse structural group paradigms, including Abelian, non-Abelian Lie, and finite-discrete groups.

Computing metrics via operator and projector actions on pure state vectors rather than forming dense density matrices keeping execution efficient and highly scalable on standard CPU hardware.

The inclusion of a public repository containing raw data, parameters, configuration seeds, and an executable Jupyter Notebook fully satisfies open-science standards.

However, there is still distinct room for improvement, and the following points should be addressed:

* The proxy-based generator-sum calculation demonstrates a blind spot, yielding an overly high compliance score for circuits with late-stage local symmetry-breaking gates.

* The parameter-averaged commutator deviation check successfully flags subtle symmetry-breaking defects. Authors can consider promoting this metric from an optional validation step in the discussion to a primary, configurable choice within the core pipeline.

* The internal cross-sector coherence factor hits artificial numerical saturation boundaries at larger qubit counts. Authors must clarify how users should interpret or adjust the weights of the coherence indices when scaling up circuits.

* The current permutation audit maps basic Hamming-weight orbits but cannot isolate individual multiplicity spaces for higher-order irreducible representations. Authors must outline a developmental path for incorporating a true Schur-Weyl decomposition engine to resolve complex representation structures.

* The toolkit relies entirely on ideal state-vector simulations. Authors must address how environmental decoherence, readout noise, or sampling error on real near-term quantum hardware affect the baseline values of the composite score.

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Reviewer #1: No

Reviewer #2: No

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PsiAudit: An open-source toolkit for auditing symmetry-organised complexity in equivariant quantum neural networks

PONE-D-26-26966R1

Dear Dr. Ugail,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

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Kind regards,

Zeheng Wang

Academic Editor

PLOS One

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