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arxiv: 2605.18345 · v1 · pith:HVVCZ6MTnew · submitted 2026-05-18 · 🪐 quant-ph · cs.LG

Hybrid Quantum-Classical Neural Architecture Search

Alberto Marchisio , Muhammad Kashif , Nouhaila Innan , Muhammad Shafique This is my paper

Pith reviewed 2026-05-20 11:32 UTC · model grok-4.3

classification 🪐 quant-ph cs.LG
keywords hybrid quantum-classical neural networksneural architecture searchFLOPs-aware optimizationquantum machine learningNISQ hardware constraintshardware-aware design
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The pith

FLOPs-aware neural architecture search produces accurate yet computationally efficient hybrid quantum-classical networks.

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

The paper sets out to show how neural architecture search can be adapted to hybrid quantum-classical neural networks by incorporating FLOPs as a direct proxy for computational cost during the search. It argues that this hardware-aware extension automates the otherwise manual and difficult choices around data encoding, circuit structure, measurements, and classical-quantum coupling. A sympathetic reader would care because current NISQ devices impose strict resource limits, making manually designed models often too costly or impractical to run. By treating FLOPs as an explicit search objective, the method aims to discover architectures that remain accurate while staying within practical computational budgets.

Core claim

The central claim is that FLOPs-aware search constitutes an important hardware-aware direction for HQNNs, enabling the automatic construction of networks that are accurate, computationally efficient, and practically deployable on current quantum hardware by using FLOPs counts as a sufficient proxy for overall complexity.

What carries the argument

FLOPs-aware neural architecture search, which extends classical NAS techniques to hybrid quantum-classical settings by adding computational cost as an explicit objective alongside accuracy.

If this is right

  • Manual design of HQNNs becomes unnecessary once FLOPs-aware search is applied.
  • The resulting architectures balance prediction accuracy with reduced computational demands suitable for NISQ hardware.
  • Classical NAS methods can be directly reused in quantum-hybrid contexts when cost metrics are included.
  • Deployability of quantum machine learning models increases because efficiency is optimized during discovery rather than after the fact.

Where Pith is reading between the lines

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

  • The same search procedure could be extended to other hardware metrics such as circuit depth or noise resilience if those become measurable proxies.
  • Combining FLOPs-aware search with error-mitigation techniques might further improve the practical performance of the discovered HQNNs.
  • The approach suggests that resource-constrained quantum machine learning may benefit from treating hardware cost as a first-class search variable rather than a post-design check.

Load-bearing premise

That FLOPs counts serve as a sufficient proxy for actual computational complexity and hardware constraints when searching hybrid quantum-classical architectures.

What would settle it

A side-by-side execution of FLOPs-aware versus non-aware searched architectures on the same NISQ simulator or device, measuring whether the FLOPs-selected models show measurably lower actual runtime, gate count, or energy use while preserving comparable accuracy.

Figures

Figures reproduced from arXiv: 2605.18345 by Alberto Marchisio, Muhammad Kashif, Muhammad Shafique, Nouhaila Innan.

Figure 1
Figure 1. Figure 1: Functionality of a HQNN, composed of both classical layers and quantum layers, equipped with classical optimization and parameter update. in classification settings, is minimized using classical optimization, while gradients through the quantum block are obtained with differentiable quantum techniques such as the parameter-shift rule. This allows the quantum module to be integrated into familiar deep learn… view at source ↗
Figure 2
Figure 2. Figure 2: Overview of the standard NAS workflow, including the search space, search strategy, candidate evaluation, and architecture selection. 2.3 Evaluation Metrics We consider both predictive performance and computational efficiency as key evaluation criteria. In standard NAS, the primary objective is typically accuracy, which reflects how reliably a model performs on a given task. Accuracy measures the proportio… view at source ↗
Figure 3
Figure 3. Figure 3: Detailed methodology for FLOPs-aware HQNN architecture search. search process iteratively evolves candidate solutions using crossover (p = 0.8), mutation (p = 0.2), and Pareto-optimal architectures that balance accuracy and computational cost. The search stops evaluating further architectures if there is no improvement in the objectives for two consecutive generations. An overview of the complete methodolo… view at source ↗
Figure 4
Figure 4. Figure 4: Iris Dataset: Accuracy versus FLOPs for all candidate HQNN architectures (blue dots), and pareto-optimal architectures (red stars). Classical FLOPs vs accuracy (left), quantum FLOPs vs accuracy (middle), and Total FLOPs vs accuracy (right). 100%, beyond which larger quantum circuits offer no benefit. Classical FLOPs show weak correlation with accuracy, with Pareto-optimal solutions appearing across both lo… view at source ↗
Figure 5
Figure 5. Figure 5: Digits Dataset: Accuracy versus FLOPs for all candidate HQNN architectures (blue dots), and pareto-optimal architectures (red stars). Classical FLOPs vs accuracy (left), quantum FLOPs vs accuracy (middle), and Total FLOPs vs accuracy (right). Overall, the accuracy improvements in HQNNs are primarily driven by quantum FLOPs, while classical FLOPs remain largely fixed due to the constrained design of classic… view at source ↗
read the original abstract

Hybrid quantum-classical neural networks (HQNNs) are emerging as a practical approach for quantum machine learning in the noisy intermediate-scale quantum (NISQ) era, as they combine classical learning components with parameterized quantum circuits in an end-to-end trainable framework. However, their performance and efficiency depend strongly on architectural choices such as data encoding, circuit structure, measurement design, and the coupling between classical and quantum modules. This makes manual design increasingly difficult, especially when hardware limitations and resource constraints must also be taken into account. In this paper, we study the foundations of HQNNs and neural architecture search (NAS), discuss how NAS extends to quantum and hybrid settings, and demonstrate FLOPs-aware search (where FLOPs serve as a proxy for computational complexity), as an important hardware-aware direction for building HQNNs that are not only accurate but also computationally efficient and practically deployable.

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

1 major / 1 minor

Summary. The manuscript studies the foundations of hybrid quantum-classical neural networks (HQNNs) and neural architecture search (NAS), discusses how NAS extends to quantum and hybrid settings, and demonstrates FLOPs-aware search (using FLOPs as a proxy for computational complexity) as a hardware-aware direction for constructing HQNNs that are accurate, computationally efficient, and practically deployable on NISQ hardware.

Significance. If the demonstration establishes that FLOPs-aware NAS yields HQNN architectures with favorable accuracy-efficiency trade-offs, the work could be significant for systematizing the design of practical hybrid quantum-classical models under resource constraints, extending classical NAS techniques to the quantum domain.

major comments (1)
  1. [Abstract] Abstract, final paragraph: the central claim that FLOPs-aware search produces HQNNs that are 'practically deployable' rests on FLOPs serving as a faithful proxy for total computational complexity. In hybrid quantum-classical settings this is questionable, since quantum sub-circuits are dominated by gate depth, two-qubit gate count, and shot noise rather than classical floating-point operations; the search objective may therefore still select high-depth or high-measurement circuits that undermine NISQ deployability.
minor comments (1)
  1. [Abstract] The abstract supplies no quantitative results, baselines, error bars, or specific architectural outcomes from the FLOPs-aware demonstration, making it difficult to evaluate whether the claimed efficiency gains are realized.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thoughtful comments, which have helped us improve the clarity and precision of our manuscript. We address the major comment point by point below.

read point-by-point responses

  1. Referee: [Abstract] Abstract, final paragraph: the central claim that FLOPs-aware search produces HQNNs that are 'practically deployable' rests on FLOPs serving as a faithful proxy for total computational complexity. In hybrid quantum-classical settings this is questionable, since quantum sub-circuits are dominated by gate depth, two-qubit gate count, and shot noise rather than classical floating-point operations; the search objective may therefore still select high-depth or high-measurement circuits that undermine NISQ deployability.

    Authors: We agree that FLOPs is an imperfect proxy for the full computational complexity in hybrid quantum-classical systems, as quantum circuit execution is better characterized by metrics such as gate depth, two-qubit gate counts, and the number of shots required for measurement. Our use of FLOPs primarily captures the classical computational cost associated with the neural network components and data processing, which constitutes a significant portion of the overall resource requirements in hybrid models. To address this, we have revised the final paragraph of the abstract to remove the unqualified claim of 'practically deployable' and instead emphasize 'computationally efficient' with respect to classical FLOPs. Additionally, we have added a new subsection in the discussion that explicitly discusses the limitations of FLOPs as a proxy and proposes future extensions of the NAS framework to incorporate quantum hardware metrics such as circuit depth and gate count. We believe this strengthens the paper by acknowledging the referee's valid concern while maintaining the contribution of FLOPs-aware search as a practical starting point for hybrid NAS. revision: yes

Circularity Check

0 steps flagged

No circularity: discussion and demonstration paper with no load-bearing derivations

full rationale

The manuscript studies foundations of HQNNs and NAS, discusses extensions to hybrid quantum-classical settings, and demonstrates FLOPs-aware search as a hardware-aware direction. No equations, predictions, or first-principles derivations are presented that could reduce to inputs by construction. The central claims rest on conceptual discussion and empirical demonstration rather than any self-referential fit or self-citation chain, rendering the work self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that neural architecture search techniques transfer effectively to quantum-hybrid settings and that FLOPs is a meaningful proxy for deployability; no free parameters or invented entities are identifiable from the abstract.

axioms (1)
  • domain assumption NAS methods can be extended to quantum and hybrid quantum-classical settings while incorporating hardware constraints such as FLOPs
    Invoked in the abstract when stating that the paper discusses how NAS extends to quantum and hybrid settings and demonstrates FLOPs-aware search.

pith-pipeline@v0.9.0 · 5680 in / 1126 out tokens · 41137 ms · 2026-05-20T11:32:45.161803+00:00 · methodology

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Reference graph

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