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Ether of Orbifolds

Henry Lamm

Abstract

Whose world is this? The orbifold lattice has been proposed as a bridge to practical quantum simulation of Yang--Mills theory, claiming exponential speedup over all known approaches. Through analytical derivations, Monte Carlo simulation, and explicit circuit construction, we identify compounding hidden costs entirely absent in Kogut--Susskind formulations: a mass-dependent Trotter overhead that scales as $m^4$, gauge-violating dynamics that grow as $m^2$ and worsen 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. The bridge is not built. The gap is the foundation.

Ether of Orbifolds

Abstract

Whose world is this? The orbifold lattice has been proposed as a bridge to practical quantum simulation of Yang--Mills theory, claiming exponential speedup over all known approaches. Through analytical derivations, Monte Carlo simulation, and explicit circuit construction, we identify compounding hidden costs entirely absent in Kogut--Susskind formulations: a mass-dependent Trotter overhead that scales as , gauge-violating dynamics that grow as and worsen with penalty terms, and a mandatory mass extrapolation. Monte Carlo simulations of SU(3) establish a universal scaling: the continuum limit forces , binding the Trotter step to the lattice spacing through a cost unique to orbifolds. For a fiducial calculation, the orbifold is -- times more expensive than every published alternative. The bridge is not built. The gap is the foundation.

Paper Structure

This paper contains 7 sections, 13 equations, 1 figure, 5 tables.

Table of Contents

  1. Introduction
  2. The mass--Trotter catastrophe
  3. Gauge violation & penalty traps
  4. Explicit circuits and T-gate costs
  5. Resource landscape
  6. On claims about the KS Hamiltonian
  7. Discussion

Figures (1)

  • Figure 1: (a) Unitarity violation vs. $m^2$ for SU(3) orbifold MC on the largest volumes ($16^3$ for 3d, $8^4$ for 4d). Open markers: $(2{+}1)$d; filled: $(3{+}1)$d. Each color/symbol denotes a distinct (dimension, $a$) pair. Smaller volumes ($8^3$, $4^4$) agree to $<\!1\%$ (Table \ref{['tab:mc']}). (b) Scaling collapse: all four datasets plotted against $a\!\cdot\!m^2$. The dashed line shows $\propto\!(a\!\cdot\!m^2)^{-0.95}$.