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arXiv:2604.08622

Comments on "Ether of Orbifolds"

Masanori Hanada

hep-latquant-phSubmitted Apr 9, 2026• Announced Apr 10, 2026
v1 · Apr 9, 2026v2 · Apr 20, 2026
arXivHTMLPDF

Abstract

We comment on a recent manuscript "Ether of Orbifolds" by Henry Lamm. In the first version, it was mistakenly claimed that the orbifold lattice Hamiltonian is not gauge invariant, and a quantity $ε_g$, which has nothing to do with a non-existent "gauge violation", was introduced. The scaling of this $ε_g$ was used to claim a huge simulation cost. In fact, $ε_g$ characterizes the shift of the effective lattice spacing -- because, in the orbifold lattice formulation, the lattice is generated dynamically from the vacuum expectation value of the complex matrices. In the second version, the claim about the gauge symmetry was partially corrected, based on our comments. However, $ε_g$ is still mistakenly interpreted as a measure of "departure from SU($N$)", inconsistently with the foundational results by Kaplan, Katz, and Ünsal, and also by Arkani-Hamed, Cohen, and Georgi. This interpretation plays a central role in sustaining the argument introduced in the first version.

Comments
Comments on arXiv:2603.29091

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We comment on a recent manuscript "Ether of Orbifolds" by Henry Lamm. In the first version, it was mistakenly claimed that the orbifold lattice Hamiltonian is not gauge invariant, and a quantity εgε_gεg​, which has nothing to do with a non-existent "gauge violation", was introduced. The scaling of this εgε_gεg​ was used to claim a huge simulation cost. In fact, εgε_gεg​ characterizes the shift of the effective lattice spacing -- because, in the orbifold lattice formulation, the lattice is generated dynamically from the vacuum expectation value of the complex matrices. In the second version, the claim about the gauge symmetry was partially corrected, based on our comments. However, εgε_gεg​ is still mistakenly interpreted as a measure of "departure from SU(NNN)", inconsistently with the foundational results by Kaplan, Katz, and Ünsal, and also by Arkani-Hamed, Cohen, and Georgi. This interpretation plays a central role in sustaining the argument introduced in the first version.
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 m4m^4m4, non-singlet contamination that grows as m2m^2m2 and worsens with penalty terms, and a mandatory mass extrapolation. Monte Carlo simulations of SU(3) establish a universal scaling: the continuum limit forces m2∝1/am^2 \propto 1/am2∝1/a, binding the Trotter step to the lattice spacing through a cost unique to orbifolds. For a fiducial 10310^3103 calculation, the orbifold is 10410^4104--101010^{10}1010 times more expensive than every published alternative. These results indicate that the claimed computational advantages do not at present survive quantitative scrutiny.
Abstract We propose a new framework for simulating U(k) Yang-Mills theory on a universal quantum computer. This construction uses the orbifold lattice formulation proposed by Kaplan, Katz, and Unsal, who originally applied it to supersymmetric gauge theories. Our proposed approach yields a novel perspective on quantum simulation of quantum field theories, carrying certain advantages over the usual Kogut-Susskind formulation. We discuss the application of our constructions to computing static properties and real-time dynamics of Yang-Mills theories, from glueball measurements to AdS/CFT, making use of a variety of quantum information techniques including qubitization, quantum signal processing, Jordan-Lee-Preskill bounds, and shadow tomography. The generalizations to certain supersymmetric Yang-Mills theories appear to be straightforward, providing a path towards the quantum simulation of quantum gravity via holographic duality.
The Hamiltonian formulation of lattice gauge theories plays a central role in quantum simulations of gauge theories, and understanding their spectrum and other properties is expected to become crucial in the upcoming years. The relevant Hamiltonians in this framework possess local symmetry at each lattice site and may exhibit higher-form symmetries. There are then an exponentially large number of dynamically disconnected symmetry sectors, most of which are not translation-invariant. An exponential number of dynamically disconnected sectors, i.e., Hilbert space fragmentation, can also occur in systems in which no such symmetries have been identified. In this contribution, we describe an emergent gauge symmetry that is valid only in a subset of sectors of the fragmented S=1S=1S=1 dipole-conserving spin chain. These non-invertible symmetries can label exponentially many of the model's sectors. Simulating this Hamiltonian, which is not gauge-invariant, yields an exact quantum simulation of a gauge theory.
The development of quantum technology and the advent of quantum computation have renewed interest in Hamiltonian formulations of lattice gauge theories. In contrast to Euclidean Monte Carlo calculations, Hamiltonian simulation requires a direct representation of the physical Hilbert space, an efficient treatment of enforcing Gauss' law as constraints, and a formulation of real-time dynamics in terms of degrees of freedom that can be encoded on quantum or quantum-inspired classical platforms. The starting point corresponds to finding a suitable basis for Hamiltonian lattice gauge theories. The existing literature focuses on several complementary approaches: electric basis, magnetic basis, gauge-fixed, quantum-link, qubit-regularised, finite-group, and orbifold formulations. This article primarily focuses on the prepotential and loop--string--hadron formulations, where non-Abelian Gauss laws are solved locally and the dynamics is written directly in terms of gauge-invariant loop, string and hadron excitations. The discussion covers the SU(2) and SU(3) constructions in one spatial dimension, the role of residual Abelian Gauss laws, and the extension to higher dimensions through point splitting. We conclude by highlighting its direct applications: eliminating redundant gauge degrees of freedom makes exact diagonalisation and tensor network calculations feasible for studying real-time dynamics, provides insights into thermalisation properties, enables mapping of physical degrees of freedom onto analog and digital quantum hardware, and enables quantum simulation of dynamics.