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arxiv: 2604.15132 · v1 · submitted 2026-04-16 · ✦ hep-lat · hep-th· nucl-th· quant-ph

Recognition: unknown

A minimal implementation of Yang-Mills theory on a digital quantum computer

Georg Bergner , Masanori Hanada , Emanuele Mendicelli
Authors on Pith no claims yet

Pith reviewed 2026-05-10 09:47 UTC · model grok-4.3

classification ✦ hep-lat hep-thnucl-thquant-ph
keywords Yang-Mills theoryquantum simulationdigital quantum computerSU(N) gauge theoryorbifold latticenoncompact variablesKogut-Susskind Hamiltoniangauge theory
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The pith

Simplified Hamiltonians enable a minimal implementation of SU(N) Yang-Mills theory for digital quantum simulation.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper develops a minimal way to simulate SU(N) pure Yang-Mills theory on digital quantum computers in 3+1 dimensions. It builds on the orbifold lattice protocol that scales logarithmically with local Hilbert-space truncation and introduces further simplified Hamiltonians plus methods that improve convergence to the infinite-mass limit. For SU(2) it exploits the embedding of the group manifold into four-dimensional space to cut resources more. Monte Carlo simulations of the Euclidean path integral benchmark the accuracy of these analytical changes. The results strengthen the case for the noncompact-variable-based approach as a practical framework for quantum simulation of non-Abelian gauge theories.

Core claim

The authors show that simplified Hamiltonians together with improved convergence techniques allow the orbifold lattice formulation to reach the Kogut-Susskind Hamiltonian without a large scalar mass. For SU(2) the isomorphism SU(2) congruent to S^3 embedded in R^4 reduces the local degrees of freedom further. These modifications are validated by Euclidean Monte Carlo benchmarks that confirm the modified theories approach standard Yang-Mills in the appropriate limit.

What carries the argument

The orbifold lattice simulation protocol with logarithmic scaling in local Hilbert-space truncation, combined with simplified Hamiltonians and convergence methods to the infinite-mass limit of the Kogut-Susskind Hamiltonian.

If this is right

  • Resource requirements for digital quantum simulation of SU(N) Yang-Mills are reduced beyond the original logarithmic scaling.
  • Simulations become viable without auxiliary large scalar masses.
  • SU(2) calculations gain an additional reduction via the R^4 embedding of the group manifold.
  • Monte Carlo benchmarks establish that the new analytical improvements preserve the target continuum limit.
  • The noncompact-variable approach gains concrete support as a route toward quantum simulations of non-Abelian gauge theories.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The framework could be tested on present-day quantum hardware for small lattices to measure actual qubit and gate counts.
  • Similar Hamiltonian simplifications might apply to other non-Abelian groups or to theories that include dynamical fermions.
  • If the error bounds hold, the method opens a path to studying confinement and other strong-coupling phenomena with quantum resources.
  • Connections to alternative noncompact lattice formulations could be checked by comparing spectra or correlation functions.

Load-bearing premise

The simplified Hamiltonians and convergence methods accurately reproduce the Kogut-Susskind Hamiltonian in the infinite-mass limit without introducing uncontrolled errors.

What would settle it

A direct quantum simulation or Monte Carlo comparison that produces plaquette expectation values or Wilson-loop observables deviating from the standard Kogut-Susskind theory in the infinite-mass limit would falsify the accuracy claim.

Figures

Figures reproduced from arXiv: 2604.15132 by Emanuele Mendicelli, Georg Bergner, Masanori Hanada.

Figure 1
Figure 1. Figure 1: Plot of ⟨Tr(ZZZ¯Z¯)⟩ versus 1/m2 for H, H1, and H2 embedded in R 8 . Monte Carlo simulation measurements are shown for a lattice size of 83 with two different lattice spacings: at = a = 0.1 [left] and 0.3 [right]. The multiplicative factor of 4 accounts for the difference in coupling conventions between the orbifold and Wilson formulations. The blue, red, and green solid lines show quadratic fits to these … view at source ↗
Figure 2
Figure 2. Figure 2: Plot of ⟨Tr(UUU¯U¯)⟩spatial versus 1/m2 for H, H1, and H2 embedded in R 8 . Monte Carlo simulation measurements are shown for a lattice size of 83 with two different lattice spacings: at = a = 0.1 [left] and 0.3 [right]. 0.000 0.002 0.004 0.006 0.008 1/m2 = 1/m2 U(1) 1.87 1.88 1.89 1.90 1.91 hTr(UU ¯U ¯U ) itemporal Wilson H H m2 = ∞ H1 H1 m2 = ∞ H2 H2 m2 = ∞ at = a = 0.1 0.000 0.002 0.004 0.006 0.008 1/m2… view at source ↗
Figure 3
Figure 3. Figure 3: Plot of ⟨Tr(UUU¯U¯)⟩temporal versus 1/m2 for H, H1, and H2 embedded in R 8 . Monte Carlo simulation measurements are shown for a lattice size of 83 with two different lattice spacings: at = a = 0.1 [left] and 0.3 [right]. 21 [PITH_FULL_IMAGE:figures/full_fig_p021_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Plot of ⟨Tr(W − 1N ) 2 ⟩ versus 1/m2 for H, H1, and H2 embedded in R 8 . Monte Carlo simulation measurements are shown for a lattice size of 83 with two different lattice spacings: at = a = 0.1 [left] and 0.3 [right]. 5.2 Minimal embedding into R 4 We repeat the analysis of the previous section with SU(2) embedded into R 4 instead of R 8 , using the same simulation parameters. The results (Figs. 5–8) show … view at source ↗
Figure 5
Figure 5. Figure 5: Plot of ⟨Tr(ZZZ¯Z¯)⟩ versus 1/m2 for H, H1, and H2 embedded in R 4 . Monte Carlo simulation measurements are shown for a lattice size of 83 with two different lattice spacings: at = a = 0.1 [left] and 0.3 [right]. The multiplicative factor of 4 accounts for the difference in coupling conventions between the orbifold and Wilson formulations. 0.000 0.002 0.004 0.006 0.008 1/m2 1.86 1.87 1.88 1.89 1.90 1.91 1… view at source ↗
Figure 6
Figure 6. Figure 6: Plot of ⟨Tr(UUU¯U¯)⟩spatial versus 1/m2 for H, H1, and H2 embedded in R 4 . Monte Carlo simulation measurements are shown for a lattice size of 83 with two different lattice spacings: at = a = 0.1 [left] and 0.3 [right]. 23 [PITH_FULL_IMAGE:figures/full_fig_p023_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Plot of ⟨Tr(UUU¯U¯)⟩temporal versus 1/m2 for H, H1, and H2 embedded in R 4 . Monte Carlo simulation measurements are shown for a lattice size of 83 with two different lattice spacings: at = a = 0.1 [left] and 0.3 [right]. 0.000 0.002 0.004 0.006 0.008 1/m2 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 hTr( W − 1) 2 i H H m2 = ∞ H1 H1 m2 = ∞ H2 H2 m2 = ∞ at = a = 0.1 0.000 0.002 0.004 0.006 0.008 1/… view at source ↗
Figure 8
Figure 8. Figure 8: Plot of ⟨Tr(W − 1N ) 2 ⟩ versus 1/m2 for H, H1, and H2 embedded in R 4 . Monte Carlo simulation measurements are shown for a lattice size of 83 with two different lattice spacings: at = a = 0.1 [left] and 0.3 [right]. 24 [PITH_FULL_IMAGE:figures/full_fig_p024_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: The Hˆ Hamiltonian embedded in R 8 , on 83 and a = at = 0.1, with m2 = 50. [Left] ⟨Tr(W − 1N )⟩ versus γ. The red line is a quadratic fit. The green dashed line indicates the target value of zero. [Right] Plaquette expectation value versus ⟨Tr(W − 1N )⟩. Symbols denote the three plaquette observables (see text for color conventions). 25 [PITH_FULL_IMAGE:figures/full_fig_p025_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: The Hˆ 1 Hamiltonian embedded in R 8 , on 83 and a = at = 0.1, with m2 = 50. [Left] ⟨Tr(W −1N )⟩ versus γ. The red line is a quadratic fit. The green dashed line indicates the target value of zero. [Right] Plaquette expectation value versus ⟨Tr(W −1N )⟩. Symbols denote the three plaquette observables (see text for color conventions). −22 −20 −18 −16 −14 −12 γ −0.075 −0.050 −0.025 0.000 0.025 0.050 0.075 0… view at source ↗
Figure 11
Figure 11. Figure 11: The Hˆ 2 Hamiltonian embedded in R 8 , on 83 and a = at = 0.1, with m2 = 500. [Left] ⟨Tr(W −1N )⟩ versus γ. The red line is a quadratic fit. The green dashed line indicates the target value of zero. [Right] Plaquette expectation value versus ⟨Tr(W −1N )⟩. Symbols denote the three plaquette observables (see text for color conventions). 26 [PITH_FULL_IMAGE:figures/full_fig_p026_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: The Hˆ Hamiltonian embedded in R 4 , on 83 lattice and lattice spacing a = at = 0.1, with m2 = 50. [Left] ⟨Tr(W − 1N )⟩ versus γ. The red line is a quadratic fit. The green dashed line indicates the target value of zero. [Right] Plaquette expectation value versus ⟨Tr(W − 1N )⟩. Symbols denote the three plaquette observables (see text for color conventions). 27 [PITH_FULL_IMAGE:figures/full_fig_p027_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: The Hˆ 1 Hamiltonian embedded in R 4 , on 83 and a = at = 0.1, with m2 = 50. [Left] ⟨Tr(W −1N )⟩ versus γ. The red line is a quadratic fit. The green dashed line indicates the target value of zero. [Right] Plaquette expectation value versus ⟨Tr(W −1N )⟩. Symbols denote the three plaquette observables (see text for color conventions). −20.5 −20.0 −19.5 −19.0 −18.5 −18.0 γ −0.4 −0.3 −0.2 −0.1 0.0 0.1 0.2 hT… view at source ↗
Figure 14
Figure 14. Figure 14: The Hˆ 2 Hamiltonian embedded in R 4 , on 83 and a = at = 0.1, with m2 = 500. [Left] ⟨Tr(W −1N )⟩ versus γ. The red line is a quadratic fit. The green dashed line indicates the target value of zero. [Right] Plaquette expectation value versus ⟨Tr(W −1N )⟩. Symbols denote the three plaquette observables (see text for color conventions). 28 [PITH_FULL_IMAGE:figures/full_fig_p028_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: The original Hamiltonian Hˆ , R 4 embedding, m2 = 80, 83 lattice, γ = 0, with varying a = at . [Left] Effective spacing aeff versus the lattice spacing a. [Center] Pla￾quette expectation value versus a = at . Three plaquette observables from Hˆ are shown. [Right] Plaquette expectation value versus a = at . Two plaquette observables from Hˆ , their counterparts from the anisotropic Wilson action with the c… view at source ↗
Figure 16
Figure 16. Figure 16: The Hˆ 1 Hamiltonian, R 4 embedding, m2 = 80, 83 lattice, γ = 0, with varying a = at . [Center] Plaquette expectation value versus a = at . Three plaquette observables from Hˆ 1 are shown. [Right] Plaquette expectation value versus a = at . Two plaquette observables from Hˆ 1, their counterparts from the anisotropic Wilson action with the corre￾sponding effective lattice spacings, and the values from the … view at source ↗
Figure 17
Figure 17. Figure 17: The Hˆ 2 Hamiltonian, R 4 embedding, m2 = 150, 83 lattice, γ = 0, with varying a = at . [Left] Effective spacing aeff versus the lattice spacing a. [Center] Plaquette expectation value versus a = at . Three plaquette observables from Hˆ 2 are shown. [Right] Plaquette expectation value versus a = at . Two plaquette observables from Hˆ 2, their counterparts from the anisotropic Wilson action with the corres… view at source ↗
Figure 18
Figure 18. Figure 18: Plot of various quantities as function of 1 [PITH_FULL_IMAGE:figures/full_fig_p034_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Plot of various quantities as function of 1 [PITH_FULL_IMAGE:figures/full_fig_p035_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: [Left] Same as [PITH_FULL_IMAGE:figures/full_fig_p036_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: [Left] Same as [PITH_FULL_IMAGE:figures/full_fig_p037_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: The original Hamiltonian Hˆ , R 4 embedding, m2 = 150, 83 lattice, γ = 0, with varying a = at . [Left] Effective spacing aeff versus the lattice spacing a. [Center] Plaquette expectation value versus a = at . Three plaquette observables from Hˆ are shown. [Right] Plaquette expectation value versus a = at . Two plaquette observables from Hˆ , their counterparts from the anisotropic Wilson action with the c… view at source ↗
Figure 23
Figure 23. Figure 23: The original Hamiltonian Hˆ 1, R 4 embedding, m2 = 150, 83 lattice, γ = 0, with varying a = at . [Left] Effective spacing aeff versus the lattice spacing a. [Center] Plaquette expectation value versus a = at . Three plaquette observables from Hˆ are shown. [Right] Plaquette expectation value versus a = at . Two plaquette observables from Hˆ , their counterparts from the anisotropic Wilson action with the … view at source ↗
read the original abstract

We present a minimal implementation of SU($N$) pure Yang-Mills theory in $3+1$ dimensions for digital quantum simulation, designed to enable quantum advantage. Building on the orbifold lattice simulation protocol with logarithmic scaling in the local Hilbert-space truncation, we introduce further simplified Hamiltonians. Furthermore, we test simple methods that improve the convergence to the infinite mass limit, thereby removing the requirement of a large scalar mass to obtain the Kogut-Susskind Hamiltonian. For the SU(2) theory, we can cut the resource requirement further by utilizing the embedding of $\mathrm{SU}(2)\cong\mathrm{S}^3$ into $\mathbb{R}^4$. Monte Carlo simulations of the Euclidean path integral were used to benchmark the accuracy of these new analytical improvements to the theory. These results provide further support for the noncompact-variable-based approach as a practical framework for quantum simulation of non-Abelian gauge theories.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript presents a minimal implementation of SU(N) pure Yang-Mills theory in 3+1 dimensions designed for digital quantum computers. It extends the orbifold lattice protocol by introducing simplified Hamiltonians and convergence improvement methods to achieve the Kogut-Susskind Hamiltonian in the infinite-mass limit without requiring large scalar masses. For SU(2), it leverages the SU(2) ≅ S^3 embedding in R^4 to further reduce resources. The analytical improvements are benchmarked using Monte Carlo simulations of the Euclidean path integral, which the authors argue provide support for the noncompact-variable approach as a practical quantum simulation framework.

Significance. Should the benchmarks confirm that the simplifications introduce no uncontrolled errors in recovering the standard Kogut-Susskind formulation, this work would represent a meaningful advance in reducing the computational resources needed for quantum simulations of non-Abelian gauge theories. The logarithmic scaling and minimal implementation could help bridge the gap to quantum advantage in this area. The use of independent Monte Carlo benchmarks to validate the approach is a constructive element, though stronger quantitative validation would enhance its significance.

major comments (1)
  1. [Benchmarking with Monte Carlo simulations] The central support for the claim that the simplified Hamiltonians and convergence methods accurately reproduce the Kogut-Susskind Hamiltonian in the infinite-mass limit comes from Monte Carlo benchmarks of the Euclidean path integral. However, no explicit quantitative error analysis, finite-mass comparison plots against the unmodified KS Hamiltonian, or statements on how truncation or orbifold artifacts are controlled are provided. This leaves the systematic errors unquantified and is load-bearing for the quantum-simulation applicability asserted in the abstract.
minor comments (1)
  1. [Abstract] The abstract states that 'Monte Carlo simulations ... were used to benchmark the accuracy of these new analytical improvements' but omits any mention of specific error metrics, resource counts, or comparison baselines, which would strengthen the summary of the results.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive feedback. We agree that additional quantitative details on the Monte Carlo benchmarks would strengthen the support for our claims and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Benchmarking with Monte Carlo simulations] The central support for the claim that the simplified Hamiltonians and convergence methods accurately reproduce the Kogut-Susskind Hamiltonian in the infinite-mass limit comes from Monte Carlo benchmarks of the Euclidean path integral. However, no explicit quantitative error analysis, finite-mass comparison plots against the unmodified KS Hamiltonian, or statements on how truncation or orbifold artifacts are controlled are provided. This leaves the systematic errors unquantified and is load-bearing for the quantum-simulation applicability asserted in the abstract.

    Authors: We acknowledge the referee's concern. The Monte Carlo results presented in the manuscript already illustrate convergence of the simplified Hamiltonians toward the expected Kogut-Susskind behavior as the scalar mass is increased, with statistical errors shown. However, we agree that the current presentation would benefit from more explicit quantitative error analysis, direct comparison plots at finite mass against the unmodified Kogut-Susskind Hamiltonian, and additional statements clarifying how truncation and orbifold artifacts are controlled. In the revised version we will add these elements, including error bars on the deviation from the target Hamiltonian and a dedicated discussion of artifact suppression. revision: yes

Circularity Check

0 steps flagged

No significant circularity; central benchmarks use independent Monte Carlo simulations

full rationale

The paper builds on an orbifold lattice protocol and introduces simplified Hamiltonians plus convergence methods to reach the Kogut-Susskind limit. Accuracy of these improvements is benchmarked via Monte Carlo simulations of the Euclidean path integral. These benchmarks are external to the quantum simulation protocol and do not reduce any result to a fitted parameter or self-defined quantity by construction. No load-bearing step equates a prediction to its input via definition, fitting, or unverified self-citation chain. The claim of support for the noncompact approach therefore rests on independent validation rather than internal reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The approach rests on standard assumptions of lattice gauge theory and digital quantum simulation; no new free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption Orbifold lattice simulation protocol provides logarithmic scaling in local Hilbert-space truncation
    Explicitly stated as the foundation for the minimal implementation.
  • domain assumption Simplified Hamiltonians converge to the Kogut-Susskind Hamiltonian in the infinite mass limit
    Central to removing the large scalar mass requirement.

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discussion (0)

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Forward citations

Cited by 1 Pith paper

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  1. Comments on "Ether of Orbifolds"

    hep-lat 2026-04 unverdicted

    ε_g in the orbifold lattice formulation measures the shift in effective lattice spacing generated dynamically by complex matrix VEVs, not gauge symmetry breaking.

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