Toward selective quantum advantage in hadronic tomography:explicit cases from Compton form factors, GPDs, TMDs, and GTMDs

TL;DR

This paper explores the potential for quantum computing to provide advantages in hadronic tomography by analyzing specific observables like GPDs and TMDs, focusing on algorithmic, computational, and inference benefits.

Contribution

It identifies explicit quantum targets in hadronic physics and connects quantum advantages to formal objects, proposing benchmarks for credible quantum advantage claims.

Findings

Quantum algorithms can improve extraction of certain hadronic observables.

Direct quantum evaluation of correlators becomes feasible for some distributions.

Quantum Deep Neural Networks enhance extraction performance in noisy, sparse data regimes.

Abstract

We recast the case for quantum advantage in hadronic physics as an observable-by-observable question rather than a blanket claim about Quantum Chromo-Dynamics (QCD). Focusing on hadronic tomography, we analyze why Compton form factors (CFF), generalized parton distributions (GPDs), Transverse Momentum-dependent Distributions (TMDs), and Generalized Transverse Momentum-dependent Distributions (GTMDs) are natural quantum targets: they are defined by light-front, off-forward, or real-time correlation functions whose extraction from Euclidean calculations or sparse experimental data is often an ill-posed inverse problem. We separate three notions of advantage -- algorithmic, computational, and representational -- and connect each to explicit formal objects. At the algorithmic level, Hamiltonian simulation, linear-response algorithms, and amplitude-estimation primitives motivate gains for real-time and sign-problematic observables. At the computational level, direct quantum evaluation of matrix elements and correlators becomes plausible for PDFs, GPDs, timelike response, and high-energy evolution. At the inference level, recent Quantum Deep Neural Network (QDNN) studies of CFF extraction indicate improved performance in noisy and sparse regimes and motivate hybrid fits in which a quantum simulator supplies a physics prior while a classical network models detector and nuisance effects. We discuss why real-device execution is scientifically necessary, summarize current hardware milestones, and propose benchmark criteria for credible claims of quantum advantage in hadronic tomography.