Quantum Qualifiers for Neural Network Model Selection in Hadronic Physics

TL;DR

The paper tackles the problem of identifying when quantum deep neural networks (QDNNs) offer practical advantages over classical deep neural networks (CDNNs) in data-driven hadronic physics, highlighting DVCS-based Compton form factor extraction as a key testbed. It introduces a composite quantum qualifier $\hat{\Xi}$ built from data-characteristic metrics $\mathfrak{N}$, $\Phi$, $\mathfrak{D}$, $\mathfrak{M}$, and $\mathfrak{F}$ to estimate quantum outperformance $\Xi$, and develops a DVCS-specific variant $\hat{\Xi}_{DVCS}$ linked to cross-section fits $M_{DVCS}$. Across synthetic classification and regression benchmarks and a DVCS case study, the qualifier successfully predicts regimes where QDNNs outperform CDNNs, and maps these regimes in the $(Q^2,x_B)$ kinematic plane under varying noise. The proposed framework offers a scalable, interpretable diagnostic for deploying quantum ML in precision hadronic physics across observables and experimental conditions, ultimately guiding regime selection and data-informed model deployment.

Abstract

As quantum machine-learning architectures mature, a central challenge is no longer their construction, but identifying the regimes in which they offer practical advantages over classical approaches. In this work, we introduce a framework for addressing this question in data-driven hadronic physics problems by developing diagnostic tools - centered on a quantitative quantum qualifier - that guide model selection between classical and quantum deep neural networks based on intrinsic properties of the data. Using controlled classification and regression studies, we show how relative model performance follows systematic trends in complexity, noise, and dimensionality, and how these trends can be distilled into a predictive criterion. We then demonstrate the utility of this approach through an application to Compton form factor extraction from deeply virtual Compton scattering, where the quantum qualifier identifies kinematic regimes favorable to quantum models. Together, these results establish a principled framework for deploying quantum machine-learning tools in precision hadronic physics.

Figures (5)

• Figure 1: (a) Schematic of a CDNN for binary classification. Eight input features $x_i$ are passed through a hidden layer of 8 ReLU neurons, followed by a single sigmoid output neuron $\sigma(y)$ that returns the probability of belonging to Class 0 or Class 1. (b) Schematic of a QDNN for classification. Eight input qubits $|q_i\rangle$ are processed by a layer of quantum perceptrons $U^{(1)}_i$. The final measurement $M(|q_{\mathrm{out}}\rangle)$ determines the class label.
• Figure 2: Classification comparison between (a) a CDNN and (b) a QDNN using 1 function data with $0.2\sigma$ noise level and 8 input features. Two of the eight input features are plotted, with signal points in red and background points in blue. The QDNN outperforms the CDNN in classification accuracy.
• Figure 3: A function regression comparison between (a) a CDNN and (b) a QDNN using the target function $y = \cos 4x$ with 1$\sigma$ noise level and trained using 50 epochs.
• Figure 4: Comparison of the measured quantum outperformance $\Xi_{DVCS}$ and the DVCS quantum qualifier $\hat{\Xi}_{DVCS}$ across the experimental kinematic domain in $(Q^2,x_B)$ for three noise levels: (a,d)$0.5\sigma$, (b,e)$1\sigma$, and (c,f)$2\sigma$. Surfaces are constructed from ensemble-averaged values using interpolation and smoothing within the convex hull of the data. The comparison illustrates how the quantum qualifier tracks the large-scale structure of the observed quantum outperformance and identifies kinematic regions where quantum models are expected to be advantageous.
• Figure 5: Projections of the observed quantum outperformance surfaces $\Xi_{DVCS}(Q^2,x_B)$ for noise levels (a)$0.5\sigma$, (b)$1\sigma$, and (c)$2\sigma$. The solid black curve denotes the empirical crossover boundary $\Xi_{DVCS} = 0$, while the solid red curve denotes the predicted crossover boundary $\hat{\Xi}_{DVCS} = 0$ obtained from the quantum qualifier.