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arXiv:2211.07826

Generalized Parton Distribution Functions via Quantum Simulation of Quantum Field Theory in Light-front Coordinates

Carter M. Gustin, Gary R. Goldstein

Published Nov 15, 2022• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.2211.07826

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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.
Quantum chromodynamics (QCD) describes the structure of hadrons such as the proton at a fundamental level. The precision of calculations in QCD limits the precision of the values of many physical parameters extracted from collider data. For example, uncertainty in the parton distribution function is the dominant source of error in the WWW mass measurement at the Large Hadron Collider. Improving the precision of such measurements is essential in the search for new physics. Quantum simulation offers an efficient way of studying quantum field theories (QFTs) such as QCD nonperturbatively. Previous quantum algorithms for simulating QFTs have qubit requirements that are well beyond the most ambitious experimental proposals for large-scale quantum computers. Can the qubit requirements for such algorithms be brought into range of quantum computation with several thousand logical qubits? We show how this can be achieved by using the light-front formulation of quantum field theory. This work was inspired by the similarity of the light-front formulation to quantum chemistry, first noted by Wilson [Nucl. Phys. B, Proc. Suppl. 17, 82 (1990)].
Quantum computing has demonstrated the potential to revolutionize our understanding of nuclear, atomic, and molecular structure by obtaining forefront solutions in nonrelativistic quantum many-body theory. In this work, we show that quantum computing can be used to solve for the structure of hadrons, governed by strongly interacting relativistic quantum field theory. Following our previous work on light unflavored mesons as a relativistic bound-state problem within the nonperturbative Hamiltonian formalism, we present the numerical calculations on simulated quantum devices using the basis light-front quantization approach. We implement and compare the variational quantum eigensolver and the subspace-search variational quantum eigensolver to find the low-lying mass spectrum of the light meson system and its corresponding light-front wave functions as quantum states from ideal simulators, noisy simulators, and IBM quantum computers. Based on obtained quantum states, we evaluate the meson decay constants and parton distribution functions directly on the quantum circuits. Our calculations on the quantum computers and simulators are in reasonable agreement with accurate numerical solutions solved on classical computers when noises are moderately small, and our overall results are comparable with the available experimental data.
We present a quantum algorithm for simulating Generalized Parton Distributions (GPDs) in the Schwinger model. Unlike the staggered fermions widely utilized in current quantum simulations, we employ Wilson fermions for lattice discretization. This choice is critical for the quantum computation of GPDs due to their strict preservation of charge conjugation symmetry. We construct a comprehensive algorithmic framework that includes the preparation of hadronic states with non-zero momentum and the measurement of light-cone correlation functions incorporating Wilson lines. We provide a complexity analysis, demonstrating that the resources required for our algorithm scale polynomially with both the number of qubits and the desired precision ε\varepsilonε. Finally, we benchmark our approach using exact diagonalization, extracting mass spectra and GPDs (also parton distribution functions) that are consistent with theoretical expectations and fundamental physical constraints.
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.
Generalized Parton Distribution functions (GPDs) are off-diagonal light-cone matrix elements that encode the internal structure of hadrons in terms of quark and gluon degrees of freedom. In this work, we present the first nonperturbative study of quasi-GPDs in the massive Schwinger model, quantum electrodynamics in 1+1 dimensions (QED2), within the Hamiltonian formulation of lattice field theory. Quasi-distributions are spatial correlation functions of boosted states, which approach the relevant light-cone distributions in the luminal limit. Using tensor networks, we prepare the first excited state in the strongly coupled regime and boost it to close to the light-cone on lattices of up to 400 lattice sites. We compute both quasi-parton distribution functions and, for the first time, quasi-GPDs, and study their convergence for increasingly boosted states. In addition, we perform analytic calculations of GPDs in the two-particle Fock-space approximation and in the Reggeized limit, providing qualitative benchmarks for the tensor network results. Our analysis establishes computational benchmarks for accessing partonic observables in low-dimensional gauge theories, offering a starting point for future extensions to higher dimensions, non-Abelian theories, and quantum simulations.
Parton distribution functions (PDFs) describe the inner, nonperturbative structure of hadrons. Their computation involves matrix elements with a Wilson line along a direction on the light cone, posing significant challenges in Euclidean lattice calculations, where the time direction is not directly accessible. We propose implementing the light-front Wilson line within the Hamiltonian formalism using tensor network techniques. The approach is demonstrated in the massive Schwinger model (quantum electrodynamics in 1 + 1 dimensions), a toy model that shares key features with quantum chromodynamics. We present accurate continuum results for the fermion PDF of the vector meson at varying fermion masses, obtained from first-principle calculations directly in Minkowski space. Our strategy also provides a useful path for quantum simulations and quantum computing.