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arXiv:2106.03865 · Physical review. D/Physical review. D.

Partonic collinear structure by quantum computing

Tianyin Li, Xingyu Guo, Wai Kin Lai, Xiaohui Liu, Enke Wang, Hongxi Xing, Dan-Bo Zhang, Shi-Liang Zhu

Published Jun 13, 2022• 50 citations
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Abstract

We present a systematic quantum algorithm, which integrates both the hadronic state preparation and the evaluation of real-time light-front correlators, to study parton distribution functions (PDFs). As a proof of concept, we demonstrate the first direct simulation of the PDFs in the $1+1$ dimensional Nambu-Jona-Lasinio model. We show the results obtained by exact diagonalization and by quantum computation using classical hardware. The agreement between these two distinct methods and the qualitative consistency with QCD PDFs validate the proposed quantum algorithm. Our work suggests the encouraging prospects of calculating 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.

DOI
10.1103/physrevd.105.l111502

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We perform the first quantum computation of parton distribution function (PDF) with a real quantum device by calculating the PDF of the lightest positronium in the Schwinger model with IBM quantum computers. The calculation uses 10 qubits for staggered fermions at five spatial sites and one ancillary qubit. The most critical and challenging step is to reduce the number of two-qubit gate depths to around 500 so that sensible results start to emerge. The resulting lightcone correlators have excellent agreement with the classical simulator result in central values, although the error is still large. Compared with classical approaches, quantum computation has the advantage of not being limited in the accessible range of parton momentum fraction xxx due to renormalon ambiguity, and the difficulty of accessing non-valence partons. A PDF calculation with 3+1 dimensional QCD near x=0x=0x=0 or x=1x=1x=1 will be a clear demonstration of the quantum advantage on a problem with great scientific impact. This work is a shortened version of our previous study "arXiv:2506.16829v2".
A bstract Calculations of the parton distribution function (PDF) and distribution amplitude (DA) are highly relevant to core experimental programs as they provide non-perturbative inputs to inclusive and exclusive processes, respectively. Direct computation of the PDFs and DAs remains challenging because they are non-perturbative quantities defined as light-cone correlators of quark and gluon fields, and are therefore inherently time-dependent. In this work, we use a uniform quantum strategy based on tensor network simulation techniques to directly extract these hadronic quantities from first principles using the matrix product state of the hadrons in the same setup. We present exemplary numerical calculations with the Nambu-Jona-Lasinio model in 1+1 dimensions and compare with available exact diagonalization and quantum circuit simulation results. Using tensor networks, we evaluate the PDF and DA at various strong couplings in the large-qubit limit, which is consistent with expectations at perturbative and non-relativistic limits.
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