openQ*D code: a versatile tool for QCD+QED simulations

Agostino Patella; Alberto Ramos; Isabel Campos; Marina Krstic Marinkovic; Martin Hansen; Nazario Tantalo; Patrick Fritzsch

REVIEW 2 major objections 5 minor 4 cited by

openQ*D code: a versatile tool for QCD+QED simulations

T0 review · 2 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A new open-source code makes lattice QCD+QED simulations practical.

desk verdict A solid, genuinely useful code paper; the phase-quenched sign assumption is the one gap that should be explicitly scoped before acceptance. read the letter →

arxiv 1908.11673 v1 pith:CHNE2TG6 submitted 2019-08-30 hep-lat

Isabel Campos , Patrick Fritzsch , Martin Hansen , Marina Krstic Marinkovic , Agostino Patella , Alberto Ramos , Nazario Tantalo This is my paper · ORCID

classification hep-lat PACS 11.15.-q11.15.Ha12.20.-m12.38.Gc12.38.-t02.70.-c02.70.Uu

keywords latticeQCDQEDC*boundaryconditionsrationalhybridMonteCarloFourieraccelerationisospinbreakingopensourcecodeWilsonfermions

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper presents openQ*D-1.0, an open-source lattice simulation package designed to make QCD+QED calculations practical: it generates gauge-field configurations for quantum chromodynamics coupled to quantum electrodynamics, with or without C* boundary conditions. The payoff is a local, gauge-invariant way to compute isospin-breaking effects and QED radiative corrections to hadronic observables from first principles, avoiding the non-local actions that most existing approaches use to handle charged particles on a finite torus. The paper argues that the implementation of the C* orbifold, rational hybrid Monte Carlo with reweighting, multiple deflation subspaces, and Fourier acceleration for the U(1) field is correct, and it supports this with low-level tests, Hamiltonian-conservation checks, solver benchmarks, and a stable dynamical test run.

What carries the argument

The load-bearing mechanism is the C* orbifold: spatial directions are closed by C-parity boundary conditions, implemented by allocating a doubled lattice and mapping the mirror copy through shifted boundary conditions, which turns the fermion determinant into a Pfaffian and makes charged states accessible without non-local gauge fixing. Around this sit three algorithmic pieces: the rational hybrid Monte Carlo (RHMC) with a rational approximation of fractional powers of the Dirac operator and twisted-mass reweighting; multiple deflation subspaces so that quarks with different electric charges each receive their own low-mode subspace; and Fourier acceleration of the U(1) molecular-dynamics update, where the kinetic term uses an inverse Laplacian preconditioning. The package also provides O(a) improvement terms (Sheikholeslami-Wohlert) and a choice of SU(3) gauge actions.

What would settle it

Compute the average sign of the Pfaffian on the Q*D1 ensemble, or at lighter pseudoscalar masses, by evaluating $\mathrm{pf}(C T D)$ on a sample of configurations; if the average sign departs from +1 by more than a few percent, or fluctuates strongly, the ensembles require sign reweighting and the code's stated assumption of a mild sign problem would fail at those parameters.

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Extended reading notes

Core claim

The central claim is that a single open-source program, openQ*D-1.0, can simulate QCD, QED, and QCD+QED with O(a)-improved Wilson fermions under periodic or C* boundary conditions, and that the implementation of the C* orbifold, the rational hybrid Monte Carlo with reweighting, multiple deflation subspaces, and Fourier acceleration for the U(1) field is correct and efficient. With C* boundary conditions, fields obey a charge-conjugation relation across the spatial boundary, implemented by simulating a doubled lattice; this yields the Pfaffian target distribution and provides a local gauge-invariant framework in which electrically charged hadrons can be studied on a finite volume. The paper reports that the dynamical test run Q*D1 is stable, and that the reweighting factors stay close to one, supporting the practical viability of the approach.

Load-bearing premise

The load-bearing premise is that the sign of the fermion determinant and Pfaffian is mild enough to be ignored at the simulated parameters; if that sign is not negligible, the generated ensembles would not represent the target QCD+QED path integral.

Editorial extensions

If this is right

Radiative corrections to hadronic observables can be computed from first principles on the lattice without non-local QED actions, because C* boundary conditions provide a local, gauge-invariant framework for charged states.
The code makes it practical to simulate QCD+QED with up- and down-type quarks of different electric charge, since each flavour can have its own deflation subspace and the solver performance stays charge-insensitive.
The demonstrated stability of the dynamical run Q*D1 and the smallness of the reweighting factors indicate that production ensembles at moderate quark masses are within reach.
Users can pick periodic, Schrödinger-functional, open, or open-SF boundary conditions in time, so the package can support scale-setting and step-scaling studies in addition to spectrum calculations.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A direct test of the sign assumption would be to evaluate the Pfaffian sign on the Q*D1 ensembles and at lighter quark masses; a non-negligible average sign would require reweighting and would refine the paper's statement about the mildness of the sign problem.
The modular design, with the Dirac operator taking the electric charge as a parameter and the U(1) action kept separate, suggests the code could be extended to non-compact QED or arbitrary charge assignments without changing the core solver machinery.
If ensembles like Q*D1 are pushed to the physical point, the C*-boundary setup could become a standard first-principles route to isospin-breaking corrections, complementing methods that treat QED perturbatively.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Here's my take on arXiv:1908.11673. The real content is the code release: openQ*D is the first open-source package that does dynamical QCD+QED with C* boundary conditions, and it extends its parent codes with multiple deflation subspaces (needed for quarks of different charge), Fourier acceleration for the U(1) field, rational approximations of arbitrary powers, and twisted-mass reweighting within RHMC. The paper documents the implementation carefully and ships a real test suite: low-level checks for C* boundary conditions, Dirac operators with generic charge, rational approximants, forces, plus Hamiltonian-conservation scalings that match the expected integrator orders and a stable dynamical run (Q*D1). That is genuine, reproducible work and should be credited.

The soft spots are in the testing, not the code. The phase-quenched approximation in Eq. (2.4) is the one that matters: the simulated distribution replaces determinant and Pfaffian by their absolute values, and the paper asserts the sign is mild citing [18], but nothing in Sec. 4 probes it. The Hamiltonian test tests the integrator; the solver benchmarks test linear algebra; the reweighting factors W_q quantify rational-approximation error, not the sign. At the test parameters (alpha_0 ~ 7 alpha_phys, m_PS ~ 660 MeV) that assumption is live. The paper itself says the sign will be investigated in future work, so it is not hiding the issue—but it means the central claim should be worded as 'generates ensembles for the phase-quenched theory' unless the sign is shown to be negligible. That is a fixable, addressable gap, not a fatal one.

Minor: the benchmarks use one representative configuration without repeated-run error bars, and the raw data behind the figures are not shipped—annoying for reproducibility but not disqualifying. The scale setting for Q*D1 is admittedly rough. The citation pattern is fine; refs [18] and [20] are the authors' own theoretical framework, which is appropriate here since the code implements that framework.

Who is this for? Any lattice group wanting to do QCD+QED with C* boundaries or with charged hadrons in finite volume. I'd take it seriously and would send it to a competent referee familiar with HMC and the C* formulation. It deserves peer review and, after the sign issue is either addressed or clearly scoped, likely publication as a code/tools paper. I'd cite it if I worked in this area.

Referee Report

2 major / 5 minor

Summary. This paper presents openQ*D-1.0, an open-source lattice QCD+QED simulation package built on openQCD-1.6 and NSPT-1.4. The code supports SU(3), U(1), and SU(3)×U(1) theories with O(a) improved Wilson fermions, periodic or C* spatial boundary conditions, several temporal boundary conditions, RHMC with rational approximations and frequency splitting, multiple deflation subspaces, and Fourier acceleration for the U(1) field. The manuscript gives the theoretical background for the actions and algorithms, a user guide for the dynamical simulation program iso1, and a set of tests: low-level code checks, Hamiltonian conservation tests with and without Fourier acceleration, solver benchmarks in an electroquenched setup, and a stable dynamical test run labeled Q*D1. The central claim is that openQ*D-1.0 is a stable, well-tested package that can generate QCD+QED configurations with C* boundary conditions.

Significance. If the claims hold, this is a valuable software contribution: it is the first open-source package of its kind for dynamical QCD+QED with C* boundary conditions, and it makes the framework of ref. [18] concretely usable. The strengths of the paper are that the code is publicly released, the low-level test suite covers C* boundary conditions, Dirac operators with generic electric charge, rational approximations and forces, and the Hamiltonian-conservation test reproduces the expected integrator orders. The authors also report a stable dynamical test run, which is a nontrivial algorithmic milestone. The main caveat is that the sign of the fermion determinant/Pfaffian is dropped in the simulated distribution, so the paper's claims must be read as claims about the phase-quenched theory unless the sign is shown to be negligible; this is acknowledged in the text but not quantified.

major comments (2)

[Sec. 2, Eq. (2.4); Sec. 4.5] The treatment of the determinant/Pfaffian sign is a load-bearing assumption for the paper's central claim. Equation (2.4) replaces det D_f and pf(CT D_f) by their absolute values, so the simulated distribution rho_sim in Eq. (2.6) is the phase-quenched theory rather than the target rho_tar of Eqs. (2.2)-(2.3). The text says that the sign problem is mild, citing ref. [18], and that it becomes irrelevant sufficiently close to the continuum, but no numerical evidence is given at the parameters of the Q*D1 run (alpha_0 = 0.05 ~ 7 alpha_phys, m_PS ~ 660 MeV, a ~ 0.074 fm). The tests in Sec. 4 do not probe the sign: Hamiltonian conservation (Fig. 4) tests the integrator, the solver benchmarks (Figs. 6-7) test linear algebra, and the reweighting factors W_q in Fig. 8 quantify only the rational-approximation error, not the sign. If the sign is non-negligible at these parameters, the Q*D1 ensemble is biased with respect to the QCD+QED path integral, and the statement that openQ*D can generate QCD+QED configurations is not demonstrated. I ask the authors either to provide a quantitative estimate of the sign, for example by computing the stochastic estimate of the sign on a subset of generated configurations, or to explicitly and consistently recast the claims as applying to the phase-quenched theory, with the sign reweighting identified as a necessary additional ingredient that is not yet implemented.
[Sec. 4.5 and Summary] The Q*D1 run is presented as evidence that the code is stable for dynamical QCD+QED, but the run is explicitly an unphysical version of Nf=2+1 QCD+QED: the two down-type quarks are degenerate and the up-type quark is significantly heavier because the bare masses were taken equal. This is acknowledged in Sec. 4.5, and the run is described as sufficient to probe observables and performance. That is acceptable for a tools paper, but the wording of the abstract and Summary ('designed to perform lattice simulations of QCD+QED') should be qualified so that a reader does not infer that the package has been demonstrated to produce physical QCD+QED ensembles. The distinction between a code that can generate ensembles for the phase-quenched theory and a code that has been validated for the target QCD+QED distribution should be made prominent in the introduction or abstract.

minor comments (5)

[Sec. 4.5, text near Fig. 8] There is a typo: 'better rational appriximation' should read 'better rational approximation'.
[Sec. 4.4] The text uses 'Schwartz-Alternating-Procedure'; the standard spelling in lattice QCD is 'Schwarz' (as in Hermann Schwarz).
[Fig. 3 and Sec. 4.1] The scaling plots have no error bars or repeated-run information, and the y-axis notation '16·t[16 cores]/t' is slightly ambiguous; a sentence stating how many runs were averaged and how representative the single-node baseline is would improve reproducibility.
[Sec. 3.2.1] The instructions to modify 'lines 122-124 of main/Makefile' are tied to a specific line numbering that may change between versions; referencing the variable names (e.g., CFLAGS) would be more robust.
[Eq. (2.5) and Sec. 2.3] The derivation of the small-determinant action S_sdet is only sketched; a short explanation of the identity det(D_f) = det(D_f,oo) det(hat D_f) in the text would help readers who are not already familiar with even-odd preconditioning.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation: openQ*D is a code/tools paper whose tests are internal consistency and benchmark checks; the main self-citations supply the theoretical C* framework and the sign-ignoring assumption, but no fitted input is renamed as a prediction.

full rationale

The paper does not derive a physical constant from fitted inputs, so the classic circularity patterns (self-definitional identities, fitted inputs called predictions, renaming known results) do not apply. The target distribution in Eqs. (2.2)-(2.3) and the simulated distribution in Eq. (2.6) are related by explicitly stated rational-approximation and reweighting factors, Eqs. (2.7)-(2.9), and the reweighting factors are computed rather than assumed to be unity. The phase-quenched replacement in Eq. (2.4), where det and Pfaffian are replaced by absolute values, is explicitly acknowledged as an approximation: the text states that the sign 'should be separately calculated and included in the evaluation of observables as a reweighting factor' and that it is a 'mild sign problem [18]' with future work planned. This is an admitted theoretical assumption and a correctness risk at the Q*D1 parameters, not a circular step. The tests in Section 4 are internal consistency checks: Hamiltonian-conservation scaling tests the integrator, solver benchmarks test linear algebra, and the displayed reweighting factors quantify rational-approximation accuracy; none are presented as predictions from fitted parameters. The self-citations to refs. [18] and [20] are load-bearing for the theoretical motivation of C* boundary conditions, the qel=1/6 normalization, and the sign mildness, but they are prior published theoretical results rather than the paper's own inputs re-identified as outputs, and the code implementation is additionally checked against gauge covariance, gamma5-hermiticity, zero-field analytic expressions, and other low-level properties. There is thus no constructed circularity; the modest score reflects the same-group citation dependence in the theoretical framing, not a circular derivation.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The central claim is about a code, not a physical derivation, so the ledger contains no fitted constants used to obtain the result. The simulation parameters in the test runs are user inputs, not fitted outputs. The main load-bearing assumptions are theoretical inputs inherited from the same group's earlier papers.

assumptions (5)

domain assumption C* boundary conditions give a local, gauge-invariant formulation of QCD+QED in finite volume and allow charged states via the Pfaffian of CT D.
The whole code is built on the framework of ref. [18] by the same group; the paper cites rather than rederives it in the abstract and in section 2.1.
standard math The identity |pf(CT D)| = |det D|^(1/2) holds, justifying alpha_f = 1/4 in the pseudofermion action.
Invoked after equation (2.20); the paper says it is easily proved but gives no formal proof in this work.
domain assumption The sign of the Pfaffian and determinant is mild and can be ignored sufficiently close to the continuum.
Stated after equation (2.4) and deferred to future work. If false, the generated ensembles are biased.
domain assumption The elementary charge qel must be 1/6 to construct gauge-invariant interpolating operators for charged hadrons under C* boundary conditions.
Section 2.2 justifies this via refs. [18,20]; it determines the U(1) charge quantization in the code.
domain assumption Wilson fermions with O(a) improvement and standard even-odd preconditioning behave as usual when the U(1) field is coupled through the integer charge qhat.
Section 2.3 makes this a design choice inherited from openQCD; the devel test programs check gauge covariance and gamma5-hermiticity but do not prove equivalence to the continuum.

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Cite this review

Pith. "Pith review of openQ*D code: a versatile tool for QCD+QED simulations." pith.science (2026). https://pith.science/paper/CHNE2TG6

@misc{pith2026190811673,
  author       = {Pith},
  title        = {Pith review of: openQ*D code: a versatile tool for QCD+QED simulations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CHNE2TG6}},
  note         = {Machine review of arXiv:1908.11673}
}

read the original abstract

We present the open-source package openQ*D-1.0, which has been primarily, but not uniquely, designed to perform lattice simulations of QCD+QED and QCD, with and without C* boundary conditions, and O(a) improved Wilson fermions. The use of C* boundary conditions in the spatial direction allows for a local and gauge-invariant formulation of QCD+QED in finite volume, and provides a theoretically clean setup to calculate isospin-breaking and radiative corrections to hadronic observables from first principles. The openQ*D code is based on openQCD-1.6 and NSPT-1.4. In particular it inherits from openQCD-1.6 several core features, e.g. the highly optimized Dirac operator, the locally deflated solver, the frequency splitting for the RHMC, or the 4th order OMF integrator.

Figures

Figures reproduced from arXiv: 1908.11673 by the authors.

**Figure 1.** Summary of salient features of openQ*D. Some features inherited from openQCD and NSPT are highlighted. scalability tests, and studies of the performance of solvers for the Dirac equation for electrically charged fields. We also illustrate the outcome of some sample runs performed for testing purposes. In figure 1, we provide a schematic view of the openQ*D functionalities. 2 Theoretical background An overview of th… view at source ↗

**Figure 2.** Global geometry of extended lattice. The top diagram represents a section of the extended lattice along a (1, k) plane where k = 2, 3 is a direction with C ∗ boundary conditions. All fields are periodic along the extended direction 1. C ∗ boundary conditions in the direction k = 2, 3 are replaced by shifted boundary conditions in the extended lattice. Shifted boundary conditions are imposed by properly defining the … view at source ↗

**Figure 3.** Results for strong (left) and weak (right) scaling of the application of the Dirac operator and SAP preconditioner as explained in the text. The speedup factors for the Dirac operator are multiplied by a factor 10 for better visibility. The dashed lines indicate perfect scaling behaviour accordingly. 4 Performance and testing 4.1 Code performance on parallel machines For future reference and comparison, benchmark me… view at source ↗

Figures from the paper (5 more)

**Figure 4.** Figure 4: Violations of MD Hamiltonian conservation ∆H as a function of the MD integration step–size ∆τ , for all available integrators (LF, OMF2, OMF4), with and without Fourier Acceleration (FA). The lines represent the fit functions provided in the legend [PITH_FULL_IMAGE:f…

**Figure 5.** Figure 5: Mass of the Q¯0γ5Q valence pseudoscalar neutral meson has been calculated as a function of q and am0 = 1/(2κ) − 4. QCD+qQED setup: SU(3) configurations are taken from the QCD1 ensemble (table 1) and pure U(1) configurations are generated with α0 = 0.05 and qel = 1/6. T…

**Figure 6.** Figure 6: Comparison of performance of various solvers and various electric charges as a function of the mass mPS of the valence neutral pion. In all cases, the inverse of the even–odd preconditioned Dirac operator has been calculated on random sources. One representative QCD+q…

**Figure 7.** Figure 7: Comparison of performance of various solvers and various electric charges as a function of the twisted mass µ. In all cases, the inverse of (Dˆ †Dˆ +µ 2 ) has been calculated on random sources. The mass of the valence neutral pion (calculated at µ = 0) has been chosen …

**Figure 8.** Figure 8: Selected observables for simulation Q*D1 including thermalisation part. Left–right/top– bottom: HMC energy violations ∆H, average plaquette for SU(3) and U(1) gauge fields, energy density E(t) for SU(3), energy density for U(1), topological charge Q(t), lowest eigenval…

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Forward citations

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