Compton Form Factor Extraction using Quantum Deep Neural Networks

TL;DR

This work addresses the challenge of extracting Compton form factors (CFFs) from DVCS data by combining a twist-2 forward model with quantum-inspired deep neural networks (QDNNs) trained on a state-vector simulator. By contrasting CDNNs and progressively optimized Full QDNNs within a common physics-informed loss, the study demonstrates that QDNNs can yield tighter uncertainties and competitive accuracy, especially in sparse or highly nonlinear kinematic regions. A data-driven DVCS quantum qualifier, incorporating nonlinearity and experimental noise, guides per-bin model selection and enables a hybrid local-global extraction pipeline that aligns with, and in many cases improves upon, established global analyses like KM15. The resulting local CFF extractions, when assembled into a global parameterization, show reduced uncertainties and robust agreement with prior results, signaling a promising avenue for multidimensional hadronic structure investigations and future extensions to additional CFFs and polarization observables, including evolution and higher-order effects.

Abstract

We extract Compton form factors (CFFs) from deeply virtual Compton scattering measurements at the Thomas Jefferson National Accelerator Facility (JLab) using quantum-inspired deep neural networks (QDNNs). The analysis implements the twist-2 Belitsky-Kirchner-Müller formalism and employs a fitting strategy that emulates standard local fits. Using pseudodata, we benchmark QDNNs against classical deep neural networks (CDNNs) and find that QDNNs often deliver higher predictive accuracy and tighter uncertainties at comparable model complexity. Guided by these results, we introduce a quantitative selection metric that indicates when QDNNs or CDNNs are optimal for a given experimental fit. After obtaining local extractions from the JLab data, we perform a standard neural-network global CFF fit and compare with previous global analyses. The results support QDNNs as an efficient and complementary tool to CDNNs for CFF determination and for future multidimensional studies of parton distributions and hadronic structure.

Figures (14)

• Figure 1: Schematic of the CDNN used for local CFF regression. The network takes a three-dimensional kinematic input $(x_B,Q^2,t)$ and maps it through an input layer, eight fully connected hidden layers (64 neurons each) with ReLU activations, to a four-dimensional output $(\Re e\,\mathcal{H},\Re e\,\mathcal{E},\Re e\,\widetilde{\mathcal{H}},\mathrm{DVCS})$. Only the first and last hidden layers are shown explicitly; intermediate layers are omitted for clarity.
• Figure 2: Schematic of the QDNN used for local CFF regression. A classical preprocessing layer maps $(x_B,Q^2,t)$ to $n=6$ qubits via angle embedding. The circuit applies $L=8$ Strongly Entangling Layers (SELs); only a subset is drawn for clarity. Pauli-$Z$ expectation values are measured on each qubit to form a 6-dimensional classical vector, which is passed to a small classical head to produce four outputs $(\Re e\,\mathcal{H},\Re e\,\mathcal{E},\Re e\,\widetilde{\mathcal{H}},\mathrm{DVCS})$.
• Figure 3: Distributions of the extracted $\Re e\mathcal{E}$ from noisy replicas of cross section pseudodata generated from kinematics $k=5.75$ GeV, $Q^2 = 2.22$ GeV$^2$, $x_B = 0.333$, $t = -0.16$ GeV$^2$ (Set 144). The histograms display improved accuracy and precision by the QDNN.
• Figure 4: Predicted cross sections from the (a) CDNN and (b) QDNN fits of noisy replicas of cross section pseudodata (red points) generated from kinematics $k=8.521$ GeV, $Q^2 = 3.65$ GeV$^2$, $x_B = 0.367$, $t = -0.20459$ GeV$^2$ (Set 26).
• Figure 5: Predicted cross sections from the (a) CDNN and (b) QDNN fits of noisy replicas of cross section pseudodata (red points) generated from kinematics $k=5.75$ GeV, $Q^2 = 2.48$ GeV$^2$, $x_B = 0.399$, $t = -0.45$ GeV$^2$ (Set 165). In both cases there is a small improvement in proximity to the true with a clear narrowing of the error band for the QDNN.