# Quark Matter 2019 - the XXVIIIth International Conference on Ultra-relativistic Nucleus-Nucleus Collisions

3-9 November 2019
Wanda Reign Wuhan Hotel
Asia/Shanghai timezone

## Computing real time correlation functions on a hybrid classical/quantum computer

5 Nov 2019, 14:40
20m
HongKong Room (Wanda Reign Wuhan Hotel)

### HongKong Room

#### Wanda Reign Wuhan Hotel

Oral Presentation New theoretical developments

### Speaker

Niklas Mueller (Brookhaven National Laboratory)

### Description

Nuclear structure functions and parton Wigner distributions of protons and nuclei are principal components of QCD phenomenology. Their first principle computation is an outstanding problem in QCD, because they involve non-perturbative nucleon/nuclear matrix elements of electromagnetic currents that are light-like separated in Minkowskian spacetime. Real-time correlation functions are a difficult problem for lattice computations, which are only feasible in Euclidean space time. To overcome restrictions of classical computing, we outline a strategy to compute nuclear structure functions in the high energy Regge limit of QCD using a hybrid quantum computer [1]. 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 world-lines in background gauge fields [2]. While extremely challenging in general, the problem simplifies in the Regge limit, where the interaction of the world-lines with gauge fields is strongly localized in proper time and the corresponding quantum circuits can be written down. As a proof principle, we employ the Color Glass Condensate effective theory of high energy QCD to construct the algorithm for a first straightforward application of the framework, specifically, the problem of computing the well-known dipole model result for the structure function $F_2$ [3]. We outline how this computation can be systematically scaled up in complexity and extended in scope to other real-time correlation functions, for example to describe non-equilibrium transport of quarks and gluons in a Quark-Gluon-Plasma, where the restrictions of euclidean lattice computations are evident.

[1] N. Mueller, A. Tarasov, R. Venugopalan, in preparation
[2] N. Mueller, R. Venugopalan, Phys.Rev. D99 (2019) no.5, 056003
[3] A. Tarasov, R. Venugopalan, arXiv:1903.11624 [hep-ph]

### Primary authors

Raju Venugopalan (Brookhaven National Laboratory) Niklas Mueller (Brookhaven National Laboratory)