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# A model for studying the sign problem on quantum computers: Z(3) gauge theory with three fermion flavors in 1+1 dimensions

## March 8, 2024 @ 9:00 am - 10:00 am

**Quantum Matter in Mathematics and Physics Seminar**

**Speaker:** Semeon Valgushev (Iowa State University)

**Title:** A model for studying the sign problem on quantum computers: Z(3) gauge theory with three fermion flavors in 1+1 dimensions

**Abstract:** Many properties of quantum field theories can be understood with the help of classical numerical methods. Yet there are several outstanding problems — most remarkably the behaviour of nuclear matter at finite density and out-of-equilibrium real-time dynamics — that require the use of quantum algorithms. We present a simple yet physically rich toy model of QCD/nuclear matter at finite density, termed “QZD”, where Z stands for Z(3) gauge theory coupled to Nf = 3 fermion flavors, suitable for simulation on near-term quantum devices. We study it using tensor networks and find that in weak coupling the spectrum is that of the expected mesons and baryons, although the corrections in weak coupling are nontrivial. In strong coupling, besides the usual baryon, the singlet meson is a baryon anti-baryon state. For two special values of the coupling constant, the lightest baryon is degenerate with the lightest octet meson, and the lightest singlet meson, respectively.