Deeply inelastic scattering structure functions on a hybrid quantum computer

Abstract

We outline a strategy to compute deeply inelastic scattering structure functions using a hybrid quantum computer. Our approach takes advantage of the representation of the fermion determinant in the QCD path integral as a quantum mechanical path integral over 0 þ 1-dimensional fermionic and bosonic worldlines. The proper time evolution of these worldlines can be determined on a quantum computer. While extremely challenging in general, the problem simplifies in the Regge limit of QCD, where the interaction of the worldlines with gauge fields is strongly localized in proper time and the corresponding quantum circuits can be written down. As a first application, we employ the color glass condensate effective theory to construct the quantum algorithm for a simple dipole model of the F 2 structure function. We outline further how this computation scales up in complexity and extends in scope to other real-time correlation functions.

Worldline master formulas for the dressed electron propagator. Part I. Off-shell amplitudes

“…In the non-Abelian case, it may be helpful to generate the particle color factor, and take care of the path ordering, by adding suitable auxiliary fields, in the same way as Grassmann variables take care of the spin factor and path ordering in (1.19) -see, for example, [47][48][49][50]. Further applications to QCD-related topics can be found in references [51][52][53].…”

Thermalization of Gauge Theories from their Entanglement Spectrum

“…Apart from the importance of 'simpler' (2+1) dimensional gauge theories in the context of, e.g., topological entanglement for universal topological quantum computation [65,79], and condensed matter physics [80,81], the Entanglement structure of Abelian and non-Abelian gauge theories, such as QCD, may be crucial to make sense of thermalization in high energy and nuclear physics, where it is largely unexplored. Examples are the apparent quick thermalization and hydrodynamization of the Quark-Gluon-Plasma in ultra-relativistic heavy ion collisions [14] or the structure of QCD bound states in deeply inelastic scattering experiments [82][83][84].…”

Gauge protection in non-abelian lattice gauge theories

“…On the other hand, the vast majority of experimental results was achieved for abelian lattice gauge theories [28, 30-32, 45, 61, 64-67]. Although strong efforts have been devoted to proposals for quantum simulating non-abelian gauge theories [43,[68][69][70][71][72][73][74][75][76][77][78][79][80], only a few proofs of principle for non-abelian theories have been achieved in the laboratory by exploiting the gauge constraint to limit the system to the gauge Hilbert space [77,[81][82][83][84][85]. Other implementation strategies for non-abelian gauge theories still remain unexplored within laboratory experiments, and it still remains a challenge to achieve scaling in system size similar to what has been demonstrated for abelian gauge theories, while keeping the reliability of the quantum simulator.…”