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arxiv: 2606.24260 · v1 · pith:A6FEBU4Nnew · submitted 2026-06-23 · 💻 cs.SE

Architecting Hybrid Quantum-Classical Software Systems: Exploration of the Design Trade-off Space with Quantitative Guarantees

\'Alvaro M. Aparicio-Morales , Jose Garcia-Alonso , Javier C\'amara , Juan M. Murillo This is my paper

Pith reviewed 2026-06-25 23:13 UTC · model grok-4.3

classification 💻 cs.SE
keywords hybrid quantum-classical systemsarchitectural styletrade-off analysisservice-oriented architecturesNISQ constraintsQoS criteriadesign space explorationquantitative guarantees
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The pith

A formalization of hybrid quantum-classical architectural styles enables trade-off analysis that identifies decision boundaries for QoS-based configuration selection.

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

This paper introduces a method to explore the design space of hybrid quantum-classical software systems by formalizing an architectural style that blends service-oriented architecture principles with the constraints of noisy intermediate-scale quantum hardware. The formalization supports trade-off analysis that provides quantitative guarantees about system performance under different configurations. A reader would care because it moves the choice between quantum and classical components from intuition to a structured process that respects quality-of-service requirements. The results show the method can identify decision boundaries for selecting the most suitable setup dynamically.

Core claim

The paper claims that a formalization of an architectural style for hybrid applications allows the exploration of the design trade-off space, successfully identifying decision boundaries that enable the dynamic selection of the most suitable hybrid or classical configuration based on the user's QoS criteria, while providing quantitative guarantees.

What carries the argument

Formalization of an architectural style for hybrid quantum-classical applications that incorporates NISQ constraints and SOA structural/behavioral properties to support trade-off analysis with quantitative guarantees.

If this is right

  • The method identifies decision boundaries in the design space of hybrid systems.
  • It enables dynamic selection of hybrid or classical configurations based on QoS criteria.
  • It delivers quantitative guarantees for system configurations under prescribed levels of uncertainty.
  • It addresses challenges arising from NISQ idiosyncrasies such as algorithm-machine specificity and disparate quality metrics.

Where Pith is reading between the lines

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

  • The decision boundaries could be embedded in runtime adaptation mechanisms for deployed hybrid services.
  • Analogous formal styles might be developed for other mixed-paradigm systems, such as classical-edge-quantum combinations.
  • Empirical calibration against real device noise models would test whether the modeled constraints suffice for production use.

Load-bearing premise

The formalization of the architectural style for hybrid applications adequately captures the constraints of NISQ hardware and the structural and behavioral properties of SOA systems so that the resulting trade-off analysis yields reliable quantitative guarantees.

What would settle it

Running the selected hybrid or classical configurations on actual NISQ hardware and observing that measured QoS metrics fall outside the predicted quantitative bounds would falsify the reliability of the guarantees.

Figures

Figures reproduced from arXiv: 2606.24260 by \'Alvaro M. Aparicio-Morales, Javier C\'amara, Jose Garcia-Alonso, Juan M. Murillo.

Figure 1
Figure 1. Figure 1: Architecture of the HSA System [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: HaiQ Signature Examples const MAX_TIMEOUTS ; abstract sig PU { services : some Service } </ formula cpulogicalperformancefactor ; formula cpuram ; formula cpubandwidth ; formula cpucostfactor ; formula qpuprize ; formula clops ; formula readoutminerror ; formula readoutmaxerror ; formula cpuerrorrate ; / > abstract sig QPU extends PU {} </ formula cpulogicalperformancefactor ; formula cpuram ; formula cpub… view at source ↗
Figure 3
Figure 3. Figure 3: Design Trade-off Space with Quantitative Guarantees Analyzer System for Hybrid Service Applications [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Architecture of the WFHS System [PITH_FULL_IMAGE:figures/full_fig_p017_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Design Space of Hybrid Search App [PITH_FULL_IMAGE:figures/full_fig_p018_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Decision region representation of the optimal configurations for the Hybrid Search Application across [PITH_FULL_IMAGE:figures/full_fig_p019_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Solution Space of Weather Forecast Hybrid System [PITH_FULL_IMAGE:figures/full_fig_p020_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Comparison of dimensions by configuration type [PITH_FULL_IMAGE:figures/full_fig_p021_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Normal Forecast Scenario - Optimal Solutions [PITH_FULL_IMAGE:figures/full_fig_p022_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Emergency Forecast Scenario - Optimal Solutions [PITH_FULL_IMAGE:figures/full_fig_p023_10.png] view at source ↗
read the original abstract

Addressing problems beyond classical computing limits is sparking an increasing interest in Quantum Computing. However, despite their adequacy to address specific problems, quantum algorithms cover a limited subset of the functionality required in real-world computing systems. Additionally, they require expensive specialized hardware. To overcome this issue, hybrid (quantum-classical) software systems are emerging as a promising way to integrate both computing paradigms by applying the principles of Service-Oriented Architectures (SOA). Still, the design and deployment of hybrid service-based systems faces unique challenges like the idiosyncrasies and constraints of NISQ computers (e.g., algorithms that can only run in specific machines, disparate quality attribute metrics), and the management of structural and behavioural properties of service-based applications. From the SOA perspective, architectural decisions need to be made by performing a trade-off analysis and providing quantitative guarantees of system configurations under prescribed levels of uncertainty. In this paper, a method to explore the design space of quantum-classical applications is provided by a formalization of an architectural style of hybrid applications. The obtained results demonstrate that the proposed method successfully identifies decision boundaries. It enables the dynamic selection of the most suitable hybrid or classical configuration based on the user's QoS criteria.

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 paper proposes a formalization of an architectural style for hybrid quantum-classical applications grounded in SOA principles. This formalization is used to explore the design trade-off space and identify decision boundaries that support dynamic selection between hybrid and classical configurations according to user-specified QoS criteria, while addressing NISQ hardware constraints and structural/behavioral properties of service-based systems.

Significance. If the formalization produces decision boundaries whose quantitative guarantees remain valid when mapped to actual NISQ constraints (algorithm-machine specificity and heterogeneous metrics), the work could provide a useful framework for architectural decision-making in an emerging area of quantum software engineering. The abstract, however, supplies no evidence of such validation or external benchmarks.

major comments (1)
  1. [Abstract] Abstract: The central claim that the method 'successfully identifies decision boundaries' with quantitative guarantees for QoS selection rests on the assumption that the architectural-style formalization encodes NISQ idiosyncrasies (algorithm-machine binding, disparate quality metrics) and SOA properties as endogenous elements. No description is given of how these constraints are incorporated rather than treated as exogenous parameters; if they are exogenous, the resulting trade-off surfaces are artifacts of the abstraction and do not constitute the claimed guarantees.
minor comments (1)
  1. [Abstract] The abstract would benefit from a concise statement of the formal method employed (e.g., the modeling formalism or analysis technique) and the nature of the 'obtained results' (e.g., specific metrics or case studies).

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address the major comment below and agree that the abstract requires clarification to better convey the formalization approach.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that the method 'successfully identifies decision boundaries' with quantitative guarantees for QoS selection rests on the assumption that the architectural-style formalization encodes NISQ idiosyncrasies (algorithm-machine binding, disparate quality metrics) and SOA properties as endogenous elements. No description is given of how these constraints are incorporated rather than treated as exogenous parameters; if they are exogenous, the resulting trade-off surfaces are artifacts of the abstraction and do not constitute the claimed guarantees.

    Authors: The manuscript's formalization of the hybrid architectural style incorporates NISQ idiosyncrasies (algorithm-machine binding, disparate metrics) and SOA structural/behavioral properties directly into the style definition and its primitives, rendering them endogenous rather than exogenous parameters. The trade-off surfaces and decision boundaries are generated from this integrated model, yielding quantitative guarantees relative to the formalized constraints. We agree, however, that the abstract is overly concise and provides no description of this incorporation. We will revise the abstract to explicitly note that the style formalization encodes these elements endogenously. We will also add a brief clarification in the introduction or discussion section on the model's assumptions when mapping to real NISQ hardware. revision: yes

Circularity Check

0 steps flagged

No circularity in derivation chain

full rationale

The provided abstract and description outline a formalization of an architectural style for hybrid quantum-classical SOA systems to explore design trade-offs and identify decision boundaries for QoS-based selection. No equations, parameters, or derivations are shown. No self-citations, fitted inputs, ansatzes, or uniqueness theorems are referenced that would reduce any claim to its own inputs by construction. The approach is presented as a modeling method whose outputs (decision boundaries) are not shown to be equivalent to inputs via any of the enumerated circular patterns; the central claim remains independent of the listed circularity mechanisms.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no specific free parameters, axioms, or invented entities can be extracted. The central claim rests on an unstated assumption that the architectural formalization is faithful to NISQ and SOA realities.

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