CyberSec Research

In the Hamiltonian formulation, Quantum Field Theory calculations scale exponentially with spatial volume, making real-time simulations intractable on classical computers and motivating quantum computation approaches. In Hamiltonian quantisation, bosonic fields introduce the additional challenge of an infinite-dimensional Hilbert space. We present a scalable quantum algorithm for Quantum Electrodynamics (QED), an Abelian gauge field theory in higher than one spatial dimensions, designed to address this limit while preserving gauge invariance. In our formulation, Gauss's law is automatically satisfied when the implementation remains fully gauge invariant. We demonstrate how gauge invariance is maintained throughout the lattice discretisation, digitisation, and qubitisation procedures, and identify the most efficient representation for extending to large Hilbert space dimensions. Within this framework, we benchmark several quantum error mitigation techniques and find the calibration method to perform most effectively. The approach scales naturally to larger lattices, and we implement and test the 2+1 and 3+1 dimensional setups on current quantum hardware. Our results indicate that next-generation quantum platforms could enable reliable, fully quantum simulations of large-scale QED dynamics.

We present the first next-to-leading-logarithmic QCD analysis of the electromagnetic corrections to the semileptonic weak Hamiltonian, including the mixed $\mathcal{O}(\alpha\,\alpha_s^2)$ corrections to the vector coupling $g_V$. The analysis combines the evaluation of three-loop anomalous dimensions and two-loop matching corrections with a consistent factorization of short-distance QCD effects. The latter is implemented through a scheme change based on a $d$-dimensional operator product expansion performed inside the loop integrals. The resulting renormalization-group--improved expression for the radiative correction $\Delta^V_R = 2.432(16)\%$ can be systematically refined using input from lattice QCD and perturbation theory and improves the consistency of first-row CKM unitarity tests.

A representation of Lattice Gauge Theories (LGT) suitable for simulations with tensor network state methods or with quantum computers requires a truncation of the Hilbert space to a finite dimensional approximation. In particular for U(1) LGTs, several such truncation schemes are known, which we compare with each other using tensor network states. We show that a functional basis obtained from single plaquette Hamiltonians -- which we call plaquette state basis -- outperforms the other schemes in two spatial dimensions for plaquette, ground state energy and mass gap, as it is delivering accurate results for a wide range of coupling strengths with a minimal number of basis states. We also show that this functional basis can be efficiently used in three spatial dimensions. Green's function Monte Carlo appears to be a highly useful tool to verify tensor network states results, which deserves further investigation in the future.

Gauge invariance requires physical states to be composite, even in the weak sector of the Standard Model (SM). The Fr\"ohlich-Morchio-Strocchi (FMS) mechanism resolves this subtlety and predicts additional Higgs contributions in SM processes. While this has been supported by theoretical investigations in the bosonic sector, its impact on fermionic observables remains largely unexplored. We use non-perturbative lattice techniques within a gauge-invariant framework to study a proxy theory of the weak sector with dynamical fermions. We determine the physical spectrum of the theory and interpret the results in the context of the FMS mechanism. Additionally, we identify suitable simulation points for a scattering analysis as a first step toward cross-sections relevant to (future lepton) colliders.

In this work, we perform a lattice QCD calculation of the branching ratios and the form factors of radiative leptonic decays $P \to \ell \nu_\ell \gamma$ ($P = \pi, K$) using $N_f=2+1$ domain wall fermion ensembles generated by the RBC and UKQCD collaborations at the physical pion mass. We adopt the infinite volume reconstruction (IVR) method, which extends lattice data to infinite volume and effectively controls the finite volume effects. This study represents a first step toward a complete calculation of radiative corrections to leptonic decays using the IVR method, including both real photon emissions and virtual photon loops. For decays involving a final state electron, collinear radiative corrections, enhanced by the large logarithmic factors such as $\ln(m_\pi^2/m_e^2)$ and $\ln(m_K^2/m_e^2)$, can reach the level of $O(10\%)$ and are essential at the current level of theoretical and experimental precision. After including these corrections, our result for $\pi \to e\nu_e\gamma$ agrees with the PIBETA measurement; for \(K \to e\nu_e\gamma\), our results are consistent with the KLOE data and exhibit a $1.7\sigma$ tension with E36; and for $K \to \mu\nu_\mu\gamma$, where radiative corrections are negligible, our results confirm the previously observed discrepancies between lattice results and the ISTRA/OKA measurements at large photon energies, and with the E787 results at large muon photon angles.

We apply the recently proposed Sample-based Krylov Quantum Diagonalization (SKQD) method to lattice gauge theories, using the Schwinger model with a $\theta$-term as a benchmark. SKQD approximates the ground state of a Hamiltonian, employing a hybrid quantum-classical approach: (i) constructing a Krylov space from bitstrings sampled from time-evolved quantum states, and (ii) classically diagonalizing the Hamiltonian within this subspace. We study the dependence of the ground-state energy and particle number on the value of the $\theta$-term, accurately capturing the model's phase structure. The algorithm is implemented on trapped-ion and superconducting quantum processors, demonstrating consistent performance across platforms. We show that SKQD substantially reduces the effective Hilbert space, and although the Krylov space dimension still scales exponentially, the slower growth underscores its promise for simulating lattice gauge theories in larger volumes.

We present an application of Physics-Informed Neural Networks (PINNs) to the study of $\mathrm{SU}(N_c)$ lattice gauge theories. Our method enables the learning of eigenfunctions and eigenvalues at arbitrary gauge couplings, smoothly moving from the analytically known strong-coupling regime towards weaker couplings. By encoding the Schr\"odinger equation and the symmetries of the eigenstates directly into the loss function, the network performs an unsupervised exploration of the spectrum. We validate the approach on the single-plaquette $\mathrm{U}(1)$ and $\mathrm{SU}(2)$ pure-gauge theories, showing that the PINNs successfully reproduce the hierarchy of energy levels and their corresponding wavefunctions.

Understanding how quarks are spatially arranged inside exotic pentaquarks remains one of the key open problems in contemporary hadron spectroscopy. The electromagnetic multipole moments of hadrons provide a direct probe of their internal quark--gluon geometry and spatial charge distributions. Motivated by this, we employ QCD light-cone sum rules to compute the magnetic dipole, electric quadrupole, and magnetic octupole moments of the $J^P = 3/2^-$ pentaquark with strangeness $S = -1$. Five distinct diquark--diquark--antiquark interpolating currents are constructed to explore possible internal configurations. The resulting electromagnetic moments exhibit pronounced sensitivity to the underlying quark arrangement: magnetic dipole moments range from $-2.28\mu_N$ to $+3.36\mu_N$, establishing this observable as a key discriminator among configurations with identical quantum numbers. Nonzero electric quadrupole and magnetic octupole moments indicate clear deviations from spherical symmetry, while a detailed decomposition shows that light quarks dominate the magnetic response and the charm quark drives quadrupole deformation. These findings position electromagnetic multipole moments as quantitative and discriminating probes of exotic hadron structure, providing concrete benchmarks for forthcoming LHCb, Belle~II, and lattice QCD studies.

A reliable calculation of radiative corrections to $\tau\to\pi\pi\nu_\tau$ decays is an important prerequisite for using hadronic $\tau$ decays for a data-driven evaluation of the hadronic-vacuum-polarization contribution to the anomalous magnetic moment of the muon, $a_\mu^\text{HVP, LO}[\pi\pi,\tau]$. In this Letter, we present an improved model-independent analysis of these radiative corrections, including, for the first time, effects beyond point-like pions in the evaluation of the loop diagrams. These structure-dependent corrections, implemented via a dispersive representation of the pion form factor, lead to significant changes compared to previous calculations due to enhancements near the $\rho(770)$ resonance. We also devise strategies for the matching to chiral perturbation theory and a stable implementation of the real corrections down to the two-pion threshold, which shows that some higher-order isospin-breaking corrections need to be kept due to a strong threshold enhancement. Finally, we perform dispersive fits to the currently available $\tau\to\pi\pi\nu_\tau$ spectra and discuss the consequences for isospin-breaking corrections in the evaluation of $a_\mu^\text{HVP, LO}[\pi\pi,\tau]$.

We present a nonperturbative determination of the pion valence parton distribution function (PDF) moment ratios $\left\langle x^{n-1} \right\rangle / \left\langle x \right\rangle$ up to $n=6$, using the gradient flow in lattice QCD. As a testing ground, we employ SU($3$) isosymmetric gauge configurations generated by the OpenLat initiative with a pseudoscalar mass of $m_\pi \simeq 411~\text{MeV}$. Our analysis uses four lattice spacings and a nonperturbatively improved action, enabling full control over the continuum extrapolation, and the limit of vanishing flow time, $t\to0$. The flowed ratios exhibit O($a^2$) scaling across the ensembles, and the continuum-extrapolated results, matched to the $\overline {\text{MS}}$ scheme at $\mu = 2$ GeV using next-to-next-to-leading order matching coefficients, show only mild residual flow-time dependence. The resulting ratios, computed with a relatively small number of configurations, are consistent with phenomenological expectations for the pion's valence distribution, with statistical uncertainties that are competitive with modern global fits. These findings demonstrate that the gradient flow provides an efficient and systematically improvable method to access partonic quantities from first principles. Future extensions of this work will target lighter pion masses toward the physical point, and applications to nucleon structure such as the proton PDFs and the gluon and sea-quark distributions.

We construct a generative network for Monte-Carlo sampling in lattice field theories and beyond, for which the learning of layerwise propagation is done and optimised independently on each layer. The architecture uses physics-informed renormalisation group flows that provide access to the layerwise propagation step from one layer to the next in terms of a simple first order partial differential equation for the respective renormalisation group kernel through a given layer. Thus, it transforms the generative task into that of solving once the set of independent and linear differential equations for the kernels of the transformation. As these equations are analytically known, the kernels can be refined iteratively. This allows us to structurally tackle out-of-domain problems generally encountered in generative models and opens the path to further optimisation. We illustrate the practical feasibility of the architecture within simulations in scalar field theories.

We employ quantum variational methods to investigate a single-site interacting fermion-boson system -- an example of a minimal supersymmetric model that can exhibit spontaneous supersymmetry breaking. Our study addresses the challenges inherent in calculating mixed fermion-boson systems and explores the potential of quantum computing to advance their analysis. By using adaptive variational techniques, we identify optimal ans\"atze that scale efficiently, allowing for reliable identification of spontaneous supersymmetry breaking. This work lays a foundation for future quantum computing investigations of more complex and physically rich fermion-boson quantum field theories in higher dimensions.

We present a first joint extraction of the Collins-Soper kernel (CSK) combining experimental and lattice QCD data in the context of an analysis of transverse-momentum-dependent distributions (TMDs). Based on a neural-network parametrization, we perform a Bayesian reweighting of an existing fits of TMDs using lattice data, as well as a joint TMD fit to lattice and experimental data. We consistently find that the inclusion of lattice information shifts the central value of the CSK by approximately 10% and reduces its uncertainty by 40-50%, highlighting the potential of lattice inputs to improve TMD extractions.

Obtaining hadronic two-point functions is a central step in spectroscopy calculations in lattice QCD. This requires solving the Dirac equation repeatedly, which is computationally demanding. The distillation method addresses this difficulty by using the lowest eigenvectors of the spatial Laplacian to construct a subspace in which the Dirac operator can be fully inverted. This approach is efficient for nonlocal operators such as meson-meson and baryon-baryon operators. However, local multiquark operators with four or more (anti)quarks are computationally expensive in this framework: the cost of contractions scales with a high power of the number of Laplacian eigenvectors. We present a position-space sampling method within distillation that reduces this cost scaling by performing the momentum projection only over sparse grids rather than the full spatial lattice. We demonstrate the efficiency of this unbiased estimator for single-meson, single-baryon and local tetraquark operators. Using Wilson-clover fermions at the $SU(3)$-flavour-symmetric point, we apply this method to study the importance of local tetraquark operators for the finite-volume $T_{cc}(3875)^+$ spectrum. To this end, we extend a large basis of bilocal $DD^*$ and $D^*D^*$ scattering operators by including local tetraquark operators. The inclusion of local operators leads to significant shifts in several energy levels. Finally, we show the effect of these shifts on the $DD^*$ scattering phase shift from a single-channel $s$-wave L\"uscher analysis.

Charting the phase diagram of Quantum Chromodynamics (QCD) at large density is a challenging task due to the complex action problem in lattice simulations. Through simulations at imaginary baryon chemical potential $\mu_B$ we observe that, if the strangeness neutrality condition is imposed, both the strangeness chemical potential $\mu_S/\mu_B$ and the strangeness susceptibility $\chi_2^S$ take on constant values at the chiral transition for varying $\mu_B$. We present new lattice data to extrapolate contours of constant $\mu_S/\mu_B$ or $\chi_2^S$ to finite baryon chemical potential. We argue that they are good proxies for the QCD crossover because, as we show, they are only mildly influenced by criticality and by finite volume effects. We obtain continuum limits for these proxies up to $\mu_B = 400$ MeV, through a next-to-next-to-leading order (N$^2$LO) Taylor expansion based on large-statistics data on $16^3 \times 8$, $20^3 \times 10$ and $24^3 \times 12$ lattices with our 4HEX improved staggered action. We show that these are in excellent agreement with existing results for the chiral transition and, strikingly, also with analogous contours obtained with the hadron resonance gas (HRG) model. On the $16^3 \times 8$ lattice, we carry out the expansion up to next-to-next-to-next-to-next-to-leading order (N$^4$LO), and extend the extrapolation beyond $\mu_B=500$ MeV, again finding perfect agreement with the HRG model. This suggests that the crossover line constructed from this proxy starts deviating from the chemical freeze-out line near $\mu_B\approx500$ MeV, as expected but not yet observed.

We report a state-of-the-art lattice QCD calculation of the nucleon gluon parton distribution function employing large-momentum effective theory. The calculation is carried out on the 2+1 flavour CLQCD ensembles with three lattice spacings a={0.105,0.0897,0.0775} fm and pion mass of approximately 300 MeV, covering nulceon momenta up to 1.97 GeV. Distillation technique is applied to improve the signal of two-point correlators. We then apply the state-of-the-art hybrid renormalization and one-loop perturbative matching, and extrapolate the result to the continuum and infinite momentum limit. Our result is in agreement with that from global analysis within errors.

The vast majority of visible matter in our universe comes from protons and neutrons (the nucleons). Nucleon interactions are fundamental to how the universe developed after the Big Bang and govern all nuclear phenomena. The subtle balance in how two nucleons interact shapes the universe's hydrogen content that is central to our existence. Our objective is to compute the interaction strength while varying the parameters of nature to understand how delicate this balance is. We developed a new code using sophisticated physics algorithms and a highly optimized library for simulations on CPU-GPU parallel architectures. It has excellent weak scaling and impressive linear scaling for a fixed problem size with increasing number of nodes up to El Capitan's full $\sim$11,000 nodes. On Alps, El Capitan, Frontier, Jupiter, and Perlmutter supercomputers we achieve a maximum disruptive speed-up of $\sim$240 times the previous state-of-the-art, signaling a new era of supercomputing.

Near the critical point, Markov Chain Monte Carlo (MCMC) simulations of lattice quantum field theories (LQFT) become increasingly inefficient due to critical slowing down. In this work, we investigate score-based symmetry-preserving diffusion models as an alternative strategy to sample two-dimensional $\phi^4$ and ${\rm U}(1)$ lattice field theories. We develop score networks that are equivariant to a range of group transformations, including global $\mathbb{Z}_2$ reflections, local ${\rm U}(1)$ rotations, and periodic translations $\mathbb{T}$. The score networks are trained using an augmented training scheme, which significantly improves sample quality in the simulated field theories. We also demonstrate empirically that our symmetry-aware models outperform generic score networks in sample quality, expressivity, and effective sample size.