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arXiv:1908.07051 · Physical review. D/Physical review. D.

Deeply inelastic scattering structure functions on a hybrid quantum computer

Niklas Mueller, Andrey Tarasov, Raju Venugopalan B

Published Jul 13, 2020• 78 citations
arXivHTMLPDF

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 $0+1$-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.

DOI
10.1103/physrevd.102.016007

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We study different aspects the worldline path integrals with gauge fields using quantum computing. We use the Variational Quantum Eigensolver (VQE) and Evolution of Hamiltonian (EOH) quantum algorithms and IBM QISKit to perform our computations. We apply these methods to the path integral of a particle moving in a Abelian and non-Abelian background gauge field associated with a constant magnetic field and the field of a chromo-magnetic field. In all cases we found excellent agreement with the classical computation. We also discuss the insertion of vertex operators into the worldline path integrals to study scattering and show how to represent them using unitary operators and quantum gates on near term quantum computers.
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