Quantum Simulation of SU(3) Lattice Yang Mills Theory at Leading Order in Large N

TL;DR

This paper presents a simplified quantum simulation approach for SU(3) lattice gauge theory at leading order in large N, enabling real-time dynamics simulation on current quantum hardware.

Contribution

It introduces a leading-order expansion in 1/N_c for SU(3) gauge fields, simplifying the Hilbert space and interactions for quantum simulation.

Findings

Simulated SU(3) lattice gauge theory on 5x5 and 8x8 lattices.

Achieved a CNOT depth of 113 on ibm_torino.

Provided explicit constructions for qubit and qutrit representations.

Abstract

Quantum simulations of the dynamics of QCD have been limited by the complexities of mapping the continuous gauge fields onto quantum computers. By parametrizing the gauge invariant Hilbert space in terms of plaquette degrees of freedom, we show how the Hilbert space and interactions can be expanded in inverse powers of N_c. At leading order in this expansion, the Hamiltonian simplifies dramatically, both in the required size of the Hilbert space as well as the type of interactions involved. Adding a truncation of the resulting Hilbert space in terms of local energy states we give explicit constructions that allow simple representations of SU(3) gauge fields on qubits and qutrits. This formulation allows a simulation of the real time dynamics of a SU(3) lattice gauge theory on a 5x5 and 8x8 lattice on ibm_torino with a CNOT depth of 113.