Quantum Computing Hadron Fragmentation Functions in Light-Front Chromodynamics

TL;DR

The paper tackles the challenge of computing fragmentation functions, $D_j^h(z)$, from first principles by developing a light-front QCD (LFQCD) framework compatible with quantum computation. It introduces a particle-register encoding and discretized Fock/momentum spaces, with real-time evolution implemented via $U(x^+)=e^{-i x^+ P^-}$ in the gauge $A^+=0$, and demonstrates a proof-of-concept on classical simulators for SU(2) and SU(3) with modest qubit counts. As a benchmark, it extracts the fragmentation function for $c\to J/\psi$ using a simple longitudinal wavefunction and an annihilation gate to identify the meson, finding qualitative agreement with the NRQCD result Braaten et al. (1993) within the present cutoff and scheme uncertainties. The work provides an end-to-end workflow for ab initio fragmentation-function calculations via quantum simulation and outlines the scaling and hardware requirements needed to extend to more realistic multi-particle dynamics and full $p_\perp$ distributions.

Abstract

We deploy Quantum Chromodynamics (QCD) in Light-front Quantization (and Gauge), discretized and truncated in both Fock -- and momentum -- spaces with a particle-register encoding suited for quantum simulation; we show for the first time how to calculate fragmentation functions, a problem heretofore untractable in general from \emph{ab-initio} approaches. We provide a classical-simulator based proof-of-concept by computing the charm-to-charmonium fragmentation, $c\to J/ψ$, in a simplified setup, an interesting case where we can (reasonably) compare with the known 1993 perturbative evaluation within Nonrelativistic QCD.

Figures (2)

• Figure 1: $SU(2)$ simulation with up to four particles in an ($N=8$) $k^+$ lattice. Upper plot: the probability ( vs. time) for an initial $c$-quark with maximum grid momentum to not be accompanied by a bremsstrahlung gluon for $H$ restricted to $V_1$ interactions with a simulated quantum memory able to hold 1 or 2 gluons. Lower plot: The entropy, $S(t)$, increases with the average number of modes populated by radiation from the initial parton for $H$ restricted to the kinetic terms and $V$ interactions. Ideally, $D_j^h$ is to be extracted around saturation (maximum entropy); given that errors (upper plot) increase with time, we extract it when a plateau is found (between the red and blue vertical lines).
• Figure 2: Fragmentation function of a $c$-quark to a $J/\psi$ meson. $T$ denotes the total Hamiltonian ($V$ the vertex-type terms only); the $k^+$ momentum lattice size is set to $N=4$, (except for the case marked $N=8$). The continuous reference lines are the NRQCD computation of Braaten, Cheung and Yan Braaten:1993mp. The symbols were extracted from the classical simulation of what the quantum computer could do, as in Figure \ref{['fig:Entropy']}, at a few values of the $J/\psi$ momentum fraction $z$. The uncertainty raisers span only the two different times at which $D$ is extracted (lower plot of Figure \ref{['fig:Entropy']}).