Ether of Orbifolds

TL;DR

This paper critically examines the proposed quantum simulation approach using orbifold lattices for Yang--Mills theory, revealing significant hidden costs that negate claimed exponential speedups.

Contribution

It provides a detailed analysis showing that the orbifold lattice method has hidden costs, such as mass-dependent Trotter overhead and contamination, which undermine its computational advantages.

Findings

Orbifold lattice approach has a mass-dependent Trotter overhead scaling as m^4.

Non-singlet contamination grows as m^2 and worsens with penalty terms.

Continuum limit links m^2 to inverse lattice spacing, increasing costs.

Abstract

The orbifold lattice has been proposed as a route to practical quantum simulation of Yang--Mills theory, with claims of exponential speedup over all known approaches. Through analytical derivations, Monte Carlo simulation, and explicit circuit construction, we identify compounding costs entirely absent in Kogut--Susskind formulations: a mass-dependent Trotter overhead that scales as $m^4$, non-singlet contamination that grows as $m^2$ and worsens with penalty terms, and a mandatory mass extrapolation. Monte Carlo simulations of SU(3) establish a universal scaling: the continuum limit forces $m^2 \propto 1/a$, binding the Trotter step to the lattice spacing through a cost unique to orbifolds. For a fiducial $10^3$ calculation, the orbifold is $10^4$--$10^{10}$ times more expensive than every published alternative. These results indicate that the claimed computational advantages do not at present survive quantitative scrutiny.