Exponential speedup in quantum simulation of Kogut-Susskind Hamiltonian via orbifold lattice

TL;DR

This paper introduces an orbifold lattice approach that naturally reproduces the Kogut-Susskind Hamiltonian, enabling exponential speedup in quantum simulations of SU(N) gauge theories by overcoming previous implementation challenges.

Contribution

The authors show that the orbifold lattice Hamiltonian can reproduce the Kogut-Susskind Hamiltonian as a limit, providing a new, efficient framework for quantum simulation of gauge theories.

Findings

Orbifold lattice Hamiltonian reproduces Kogut-Susskind Hamiltonian in a controlled limit.

Numerical evidence for SU(2) and SU(3) Yang-Mills theories in (2+1) dimensions.

Quantified convergence rate using Euclidean path integral methods.

Abstract

We demonstrate that the orbifold lattice Hamiltonian -- an approach known for its efficiency in simulating SU($N$) Yang-Mills theory and QCD on digital quantum computers -- can reproduce the Kogut-Susskind Hamiltonian in a controlled limit. While the original Kogut-Susskind approach faces significant implementation challenges on quantum hardware, we show that it emerges naturally as the infinite scalar mass limit of the orbifold lattice formulation, even at finite lattice spacing. Our analysis provides both a general analytical framework applicable to SU($N$) gauge theories in arbitrary dimensions and specific numerical evidence for $(2+1)$-dimensional SU($N$) Yang-Mills theories ($N=2,3$). Using Euclidean path integral methods, we quantify the convergence rate by comparing the standard Wilson action with the orbifold lattice action, matching lattice parameters, and systematically extrapolating results as the bare scalar mass approaches infinity. This reformulation resolves longstanding technical obstacles and offers a straightforward implementation protocol for digital quantum simulation of the Kogut-Susskind Hamiltonian with exponential speedup compared to classical methods and previously known quantum methods.