Jet evolution in a quantum computer: quark and gluon dynamics

Abstract: The intrinsic quantum nature of jets and the Quark-Gluon Plasma makes the study of jet quenching a promising candidate to benefit from quantum computing power. Standing as a precursor of the full study of this phenomenon, we study the propagation of SU(3) partons in Quark-Gluon Plasma using quantum simulation algorithms. The algorithms are developed in detail, and the propagation of both quarks and gluons is analysed and compared with analytical expectations. The results, obtained with quantum simulators, demonstrate that the algorithm successfully simulates parton propagation, yielding results consistent with analytical baseline calculations.

• The paper presents a quantum simulation framework that accurately models jet evolution and quark-gluon interactions in a QGP medium.
• It employs quantum algorithms with controlled operations that enhance numerical stability over traditional tensorial approaches.
• Results highlight that precise lattice discretization and parameter tuning are essential for capturing jet quenching phenomena.

Quantum Simulations of Jet Evolution in a QGP Medium

This paper explores the development and implementation of quantum algorithms to simulate the propagation of SU(3) partons—quarks and gluons—traversing through a Quark-Gluon Plasma (QGP) medium. The study is positioned within the growing interest of leveraging quantum computing to tackle complex computational problems in high-energy physics, specifically focusing on jet quenching phenomena, where partons traverse QGP-consuming medium experience energy loss and momentum broadening.

Methodology

The approach adopted involves developing quantum algorithms that utilize quantum simulation techniques. The paper presents a detailed description of encoding parton dynamics onto quantum computers, carefully managing the intrinsic complexities of quantum chromodynamics (QCD) interactions governed by SU(3) symmetry. With quarks and gluons considered in both fundamental and adjoint representations, the study implements the Hamiltonian governing the parton evolution, discretized over a two-dimensional lattice capturing transverse kinematics.

The algorithms were executed using Noise Intermediate-Scale Quantum (NISQ) devices. Recognizing the limitations of current quantum devices, predominantly in terms of coherence time and noise susceptibility, the abstractions were tested primarily within quantum simulators. To simulate the interaction of partons with the QGP medium, evolving the system through the light-cone coordinates was emphasized as a computationally feasible strategy.

Key Findings

1. Parton Propagation Simulation: Results derived from quantum simulators demonstrated reasonable consonance with analytical baseline calculations for the jet quenching parameters, capturing the transverse momentum broadening akin to classical estimations. Specifically, outcomes for quarks showed a congruence for saturation scales up to about 30 GeV² before lattice effects became significant.
2. Algorithmic Considerations: The study implemented two methods for color evolution: a tensorial product approach and a controlled operations technique. The latter, leveraging controlled unitary operations, showed improved numerical stability and alignment with theoretical predictions, especially for SU(3) cases. Adjusting the algorithm to include kinetic and potential components separately, with fine-grained lattice discretization, was shown to substantiate parton dynamics close to physical realism.
3. Lattice Effects and Simulation Parameters: The examination of discrete lattice effects revealed that a fine balance between lattice spacing and medium parameters like gluon mass and coupling strengths is crucial for accurate simulations. The UV and IR cutoffs set by lattice boundaries substantially impacted the simulation, necessitating larger transverse lattice sizes for precise results akin to classical physics.

Implications

The outcomes highlight the capability of current quantum computing devices to simulate certain aspects of QCD dynamics with potentially useful accuracy, suggesting a scale where quantum approaches can complement classical numerical methods. Extending the Fock space for the simulation magisterially would pull the quantum simulations closer to full jet dynamics, a work still in nascency but expected to bloom as quantum devices mature.

Future Prospects

The paper sketches myriad opportunities for subsequent research. The most immediate is the extension to full jet simulations which involves a rich cascade of parton splitting and recombination, demanding further complexity and consideration of quantum coherence. Additionally, there exists potential in integrating quantum error mitigation strategies to mitigate noise inherent to NISQ devices, in hopes of achieving a nearer-term application of quantum computing to simulate high-energy particle interactions.

The study lays foundational insights that chart a roadmap towards quantum simulations not only augmenting but potentially pioneering novel computational strategies in particle physics. The authors advocate that near-term research should focus on error mitigation and advancing quantum algorithms that leverage both qubits and qutrits to natively represent the intricate structure of QCD.