Quantum Computing Derives Hadron Fragmentation Functions, Enabling First Ab Initio Results in Light-Front Quantum Chromodynamics

Understanding how strongly interacting particles, such as protons and neutrons, break apart into other particles remains a fundamental challenge in nuclear physics. Juan José Gálvez-Viruet, Felipe J. Llanes-Estrada, and Nicolás Martínez de Arenaza, all from the Complutense University of Madrid, alongside María Gómez-Rocha from the University of Granada and Timothy J. Hobbs from Argonne National Laboratory, now present a breakthrough in calculating fragmentation functions, which describe these particle breakups. Their work demonstrates, for the first time, a method to calculate these functions directly from the underlying theory of strong interactions, known as Chromodynamics, without relying on approximations. This achievement utilises a novel computational approach, successfully applied to the fragmentation of charm quarks into charmonium, and opens the door to more accurate predictions of particle behaviour in high-energy collisions and a deeper understanding of the strong force itself.

Quantum Chromodynamics (QCD) in Light-front Quantization, discretised and truncated in both Fock- and momentum-spaces with a particle-register encoding, forms the foundation for this work. The research demonstrates, for the first time, a method to calculate fragmentation functions, a problem previously intractable using first-principles approaches. The authors are using a classical simulation to mimic what a quantum computer could do, allowing them to test their methods and demonstrate the feasibility of the approach. The goal is to move beyond traditional methods, such as perturbative QCD, that have limitations in certain regimes. The document details numerical results for the fragmentation function, calculated using different parameters, including variations in color group structure and Hamiltonian complexity, and presents a thorough uncertainty analysis addressing potential sources of error.

The analysis considers the effects of Fock space truncation, Trotter decomposition, infrared cutoffs, and the choice of renormalization scale. Results demonstrate the feasibility of using quantum computing to calculate fragmentation functions, potentially overcoming limitations of traditional methods. The computational cost remains a significant challenge, highlighting the need for efficient algorithms and powerful quantum computers. The thorough uncertainty analysis validates the results and assesses their reliability, while the scaling challenges underscore the need for further advancements in hardware and algorithms.

This research reveals the promise of quantum computing for handling strong coupling regimes and exploring non-perturbative regimes in hadron physics. Quantum simulations could allow researchers to calculate a wide range of hadronic properties, such as masses, decay constants, and form factors. Remaining challenges include building powerful quantum hardware, developing efficient algorithms, and scaling up calculations to more realistic scenarios.

Charm Fragmentation Modeled Via Quantum Dynamics

This work presents a breakthrough in calculating fragmentation functions, a longstanding challenge in particle physics previously intractable using first-principles approaches. The team achieved this by simulating quantum dynamics on a classical computer, representing the interactions of quarks and gluons within the framework of Chromodynamics and Light-front Quantization. The core of this achievement lies in a novel approach to tracking the evolution of particles over time.

Researchers monitored the system’s entropy, a measure of disorder, to determine when the simulation had reached a stable state representing the final fragmentation products. By observing the spreading of probability among different particle configurations, they identified a plateau in entropy, signaling the completion of the process and allowing extraction of the fragmentation function. This method circumvents the need for excessively long simulations and provides a practical way to model complex particle interactions. Results demonstrate that the calculated fragmentation function closely aligns with established Nonrelativistic QCD computations, providing strong validation of the new method.

The simulation employed a system representing two quarks, one antiquark, and a gluon, utilizing 25 to 29 qubits to represent the system’s state. 63 ±0. 07 GeV−1, consistent with the meson’s radius of 0. 321 ±0.

014 fm. This work establishes a pathway toward more accurate and detailed modeling of particle fragmentation using quantum computers. While current simulations are limited by computational resources, the team anticipates that with access to a few hundred well-functioning qubits, the calculations could be extended to include a greater number of particles and explore a wider range of energy scales.

Light-Front Quantization Calculates Fragmentation Functions

This research presents a significant advance in calculating fragmentation functions, a longstanding challenge in quantum chromodynamics. Scientists successfully deployed a light-front quantization approach, discretised and adapted for simulation, to achieve this calculation from first principles. The team demonstrated this capability through a proof-of-concept simulation of charm-to-charmonium fragmentation, yielding results comparable to established perturbative evaluations. The study also investigated the impact of computational parameters on the accuracy of these calculations. Researchers found that the introduction of a cutoff on Hamiltonian matrix elements had a limited effect on the scaling of computational resources, while the number of encoded momentum fractions exerted a stronger influence.

Furthermore, the team explored the convergence of results with varying time-step sizes and cutoff values, revealing oscillations in the fragmentation function that could be reduced with increased computational memory. The results demonstrate the feasibility of this approach and provide valuable insights into the systematic uncertainties inherent in truncating the complexity of quantum calculations. The observed oscillations indicate a need for larger quantum memory to fully dampen these effects and achieve even greater precision in future studies.