Floquet evolution of the q-deformed \texorpdfstring{SU(3)${}_1$}{SU(3)1} Yang-Mills theory on a two-leg ladder

TL;DR

This paper demonstrates the simulation of Floquet dynamics of a q-deformed SU(3) lattice Yang-Mills theory on a two-leg ladder using IBM's quantum processor, showcasing the potential for quantum simulation of complex gauge theories.

Contribution

It introduces a quantum circuit tailored for simulating lattice Yang-Mills theory on noisy quantum hardware, enabling the study of Floquet thermalization dynamics.

Findings

Successful simulation of Floquet thermalization on 62 qubits

Error mitigation enables meaningful results on noisy hardware

Provides a benchmark for future quantum lattice gauge theory simulations

Abstract

We simulate Floquet time-evolution of a truncated SU(3) lattice Yang-Mills theory on a two-leg ladder geometry under open boundary conditions using IBM's superconducting 156-qubit device ibm\_fez. To this end, we derive the quantum spin representation of the lattice Yang-Mills theory, and compose a quantum circuit carefully tailored to hard wares, reducing the use of CZ gates. Since it is still challenging to simulate Hamiltonian evolution in present noisy quantum processors, we make the step size in the Suzuki-Trotter decomposition very large, and simulate thermalization dynamics in Floquet circuit composed of the Suzuki-Trotter evolution. We demonstrate that IBM's Heron quantum processor can simulate, by error mitigation, Floqeut thermalization dynamics in a large system consisting of $62$ qubits. Our work would be a benchmark for further quantum simulations of lattice gauge theories using real devices.