Preparations for Quantum Computing in Hadron Physics

TL;DR

This paper surveys how quantum computing could impact hadron physics by focusing on niche, ab initio problems where conventional methods face fundamental barriers, such as real-time Minkowski dynamics, high-density QCD, fragmentation, and jet evolution. It explains the distinctions between digital and analogue quantum simulations, reviews current hardware capabilities, and elaborates in detail on lattice-gauge formulations and particle-based encodings for QCD on quantum devices, including fermion and gauge-boson mappings and gauge fixing. The authors present progress toward neutron-star equation-of-state calculations, fragmentation-function access via light-front QCD and NJL/Schwinger models, and time-evolution studies of jets and scattering in simplified settings, while highlighting methodologies like RGPEP for renormalization and effective Hamiltonians. Although hardware remains in its infancy, the review argues that targeted quantum simulations could offer valuable, ab initio insights within a decade, complementing lattice results and providing new perspectives on nonperturbative hadron dynamics. Overall, the work lays out a structured roadmap for translating QCD into quantum-computing language, identifying concrete encoding schemes, algorithmic strategies, and near-term benchmarks to progress toward realistic quantum QCD calculations.

Abstract

Quantum computers are coming online and will quickly impact hadron physics once certain fidelity, decoherence and memory thresholds are met, quite possibly within a decade. We review a selected number of topics where ab-initio QCD-level information about hadrons can be obtained with this computational tool that is hard to come by from other methods. This includes high baryon-density systems such as neutron-star matter (with a sign problem in lattice gauge theory); fragmentation functions; Monte Carlo generation of particles which accounts for quantum correlations in the final state; entropy production in jets; and generally, any application where time evolution in Minkowski space (as opposed to a Euclidean formulation) or where large chemical potentials play an important dynamical role. For other problems, such as the prediction of very highly excited hadron spectroscopy, they will not be a unique, but a complementary tool.

Figures (11)

• Figure 1: Bottomonium meson spectrum computed with Lattice Gauge Theory and its comparison with experimental data. Reprinted Ryan:2020iog under the terms of the Creative Commons 4.0 License,https://creativecommons.org/licenses/by/4.0/
• Figure 2: Status of the Equation of State of Neutron Star Matter Alarcon:2024hljLopeOter:2025fbt. To the left, low--density side, chiral interactions, nucleon scattering and nuclear data are quite constraining. To the right, at asymptotically high densities (beyond the presumed range of neutron--star ones) pQCD gives a controlled uncertainty band. However, through a large swath of the diagram, only causality and stability (as well as integral constraints from the $n-\mu$ plane, shown in different shades) are available. It is at these densities, unreachable by Lattice techniques that a quantum computer could make a significant contribution. Copyright: American Physical Society. Reproduced with permission.
• Figure 3: The gluon parton distribution function $xg(x)$ inside the kaon computed from LGT compares very well with Dyson-Schwinger estimates and experimental data--driven extractions above $x\geq 0.2$ and seems qualitatively correct over the entire $x$ range. Reprinted from Lin:2025hka with publisher's permission.
• Figure 4: From left to right: a) Typical ALICE ALICE:2016jjg experimental data and Monte Carlo simulation of two-meson correlation against $\varphi$, with a peak at $\phi_1-\phi_2=0$ indicating that the mesons are positively correlated. b) and c) In the experiment, the baryon-baryon and antibaryon-antibaryon correlations dip below 1, implying anti-correlation. In this baryon case, Monte Carlo simulations disagree with the experimental data. This is true for both identical and different baryon species. Copied from ALICE:2016jjg by the ALICE collaboration under the terms of the Creative Commons License 4.0 (http://creativecommons.org/licenses/by/4.0/); no changes have been effected.
• Figure 5: Left: Energy--level scheme of a quantised harmonic oscillator $H={\rm constant}+\hbar\omega(a+a^\dagger)$ (implementable as a microscopic oscillating $LC$ circuit). Microwaves which excite the $|0\rangle \leftrightarrow |1\rangle$ transition can also excite higher levels. Right: to implement a two--level "transmon" qubit, a nonanharmonicity is needed, which is achieved by swapping the linear inductor by a non-linear Josephson junction. The Hamiltonian receives nonharmonic terms such as $-\hbar \omega'(a+a^\dagger)^4$, and the equispacing is broken, so that no further excitation of the oscillator is possible with the same microwave pulse.