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arXiv:2011.01275 · Physical review. D/Physical review. D.

Quantum simulation of light-front parton correlators

Miguel G. Echevarría, I. L. Egusquiza, E. Rico, G. Schnell

Published Jul 30, 2021• 37 citations
arXivHTMLPDF

Abstract

The physics of high-energy colliders relies on the knowledge of different nonperturbative parton correlators, such as parton distribution functions, that encode the information on universal hadron structure and are thus the main building blocks of any factorization theorem of the underlying process in such collision. These functions are given in terms of gauge-invariant light-front operators, that are nonlocal in both space and real time, and thus intractable by standard lattice techniques due to the well-known sign problem. In this paper, we propose a quantum algorithm to perform a quantum simulation of these type of correlators, and illustrate it by considering a space-time Wilson loop. We discuss the implementation of the quantum algorithm in terms of quantum gates that are accessible within actual quantum technologies such as cold atoms setups, trapped ions or superconducting circuits.

DOI
10.1103/physrevd.104.014512

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We present a systematic quantum algorithm, which integrates both the hadronic state preparation and the evaluation of the real-time light-front correlations, to study the parton distribution functions (PDFs). As a proof-of-concept, we realize the first direct simulation of the PDFs in the 1+1 dimensional Nambu-Jona-Lasinio (NJL) model. We show the results obtained by numerical diagonalization and by quantum computation using classical hardware. The agreement between these two distinct methods and the qualitative consistency with the QCD PDFs validate the proposed quantum algorithms. Our work suggests the encouraging prospects of calculating the QCD PDFs on current and near-term quantum devices. The presented quantum algorithm is expected to have many applications in high energy particle and nuclear physics.
Quantum simulation of quantum field theories offers a new way to investigate properties of the fundamental constituents of matter. We develop quantum simulation algorithms based on the light-front formulation of relativistic field theories. The process of quantizing the system in light-cone coordinates will be explained for a Hamiltonian formulation, which becomes block diagonal, each block approximating the Fock space with a certain harmonic resolution K. We analyze a QCD theory in 2+1D. We compute the analogue of parton distribution functions, the generalized parton distribution functions for mesonic composite particles, like hadrons, in these theories. The dependence of such analyses on the scaling of the number of qubits is compared with other schemes and conventional computations. There is a notable advantage to the light-front formulation.
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We present a systematic quantum algorithm that combines hadronic state preparation with the evaluation of real-time light-front correlators to investigate the parton distribution function (PDF) and light cone distribution amplitude (LCDA). As a proof of concept, we simulate both the PDF and LCDA in the 1+1 dimensional Nambu-Jona-Lasinio model. The results obtained from exact diagonalization and quantum computation on classical hardware show strong agreement, validating the effectiveness of the proposed algorithm. Our findings highlight the promising potential for calculating partonic collinear structure on current and near-term quantum devices. This quantum algorithm is anticipated to have broad applications in high-energy particle and nuclear physics.