Jet evolution in a quantum computer: quark and gluon dynamics

TL;DR

This work demonstrates the feasibility of simulating in-medium jet evolution for SU(3) partons on quantum simulators by mapping the 2D transverse dynamics to a mixed position-momentum representation and discretizing the medium into slices. The authors derive an in-medium Hamiltonian $H_{q/g}(x^+) = \hat{K} + \hat{V}(x^+)$ and implement a Trotterized time-evolution with kinetic and potential terms acting in complementary bases, then extract the transverse momentum distribution and the jet-quenching parameter $\hat{q}$ from measurements. Results show that, for moderate saturation scales $Q_s^2$ and on simulators, the quark and gluon propagation agree with analytical baselines, with controlled-methods outperforming tensorial ones and real-device runs hindered by noise. The work identifies lattice-spacing and finite-size effects as key limitations and outlines steps toward a full quantum simulation of jet quenching on fault-tolerant hardware, including possible color-qutrit representations and error-mitigation strategies.

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.

Figures (17)

• Figure 1: Schematic representation of the jet evolution in a QGP medium.
• Figure 2: Quantum circuit for the quantum simulation of a parton propagating in a QGP medium, where $n_c$ is the number of colour qubits and $n_q$ is the number of position/momentum qubits per direction. The first step is the initialization, the second step is the application of the time evolution operator, and the third step is the measurement of the final system state. The $U_{K}$ and $U_{V}$ are the kinetic and potential evolution operators, respectively, and the $QFT$ and $QFT^\dagger$ are the gate representation of the QFT and its inverse, respectively. Inside the dashed box, one iteration of the time evolution operator is shown.
• Figure 3: Squared momentum distribution for a SU(3) quark with $N_{\perp} = 8$, $L_{\perp} = 4.8$ GeV-1, $m_g=0.8$ GeV, $N_{\eta} = 4$, $p^+=+\infty$ GeV, $g^2\mu = 0.5$ GeV$\frac{3}{2}$ and $N_{reps} =1$. For this plot, three individual executions of the quantum circuit are presented, with the height of the bins being the mean of the three individual executions and the error bars being the respective standard deviation. Each execution corresponds to a different background field configuration. The vertical dashed line represents the saturation scale of that simulation.
• Figure 4: Jet quenching parameter $\hat{q}$ as a function of the saturation scale $Q_s^2$ for a SU(3) quark with $N_{\perp} = 8$, $L_{\perp} = 4.8$ GeV-1, $m_g=0.8$, $N_{\eta} = 16$ for several values of $p^+$. For each set of parameters, three different executions of the quantum circuit are performed, for different background field configurations, consequently, each point in the plot is the mean of the three individual executions and the error bars are the respective standard deviation. The solid lines represent the analytical expectations.
• Figure 5: Jet quenching parameter $\hat{q}$ as a function of the saturation scale $Q_s^2$ for a SU(3) quark with $N_{\perp} = 4$, $L_{\perp} = 4.8$ GeV-1, $N_{reps} = 1$, $m_g=0.8$ GeV for several values of $p^+$ and $N_\eta$. For each set of parameters, three different executions of the quantum circuit are performed, for different background field configurations, consequently, each point in the plot is the mean of the three individual executions and the error bars are the respective standard deviation. The solid lines represent the analytical expectations.