In this work we examine a family of regularization invariant (RI) symmetric momentum (SMOM) schemes for semi-leptonic operators. By working with chirally symmetric and massless QCD, we relate the semi-leptonic operators with their corresponding flavor-changing vector currents, whose renormalization in pure QCD is protected by the Ward identity. For the latter, we extend the original RI/SMOM scheme [Sturm et al. 2009] to a family projectors suitable to be promoted to the semi-leptonic case and demonstrate their equivalence to Ref. [Gorbahn et al. 2023], relevant in particular for the perturbative calculation of the corresponding Wilson coefficients.

Quantum hardware platforms are getting increasingly sophisticated in their ability to simulate condensed matter, including but not limited to strongly-correlated, topological, and non-equilibrium phenomena. This review surveys recent progress in quantum-hardware-based simulations of condensed matter, primarily emphasizing gate-based digital quantum computer simulation, with analog experiments discussed as complementary benchmarks. We first review major hardware platforms, including superconducting qubits, trapped-ions, ultracold atoms, Rydberg arrays, photonic systems, and moire quantum materials. We then introduce the basic ingredients of digital quantum simulation. Building on this foundation, we discuss representative applications to condensed-matter physics, spanning ground-state problems, strongly correlated matter, topological phases, non-equilibrium dynamics, open-system physics, and high-energy-physics-inspired simulations. Finally, we summarize key methodological tools used in state-of-the-art quantum-simulation workflows. We emphasize that present noisy quantum simulations serve not only as near-term demonstrations, but also as prototypes for the encodings, diagnostic protocols and error-control strategies required for future fault-tolerant quantum simulation.

Predictions for tensor charges and form factors, elastic and transition, involving $\pi$- and $\rho$-mesons and their scalar and axialvector diquark partners, are delivered using a symmetry-preserving treatment of a vector*vector contact interaction (SCI). Two distinct SCI regularisation schemes are employed, with the results showing little sensitivity. Although, as typical in SCI analyses, the form factors are stiff; their infrared behaviour may be considered physically reliable. Notable amongst related quantities are the following: the pion tensor charge is approximately $0.36$ and the associated tensor form factor radius is practically the same as the pion charge radius; the $\rho$-meson tensor charge is roughly 80% of that for the proton; and diquark tensor charges and form factors are semiquantitatively alike with those of their $\pi$, $\rho$ partners. In addition to being interesting in themselves, the SCI predictions can serve as baselines for future studies with a closer connection to QCD.

The existence of geons, physical states of self-bound gravitons, has long been proposed. In the context of four-dimensional causal dynamical triangulation simulations we investigate this possibility by measuring curvature-curvature correlators of different gravitational operators. We find a behavior consistent with a massive state, independent of the operators considered, over a certain distance window. While at most a hint, this is tantalizing due to its possible implications for dark matter or (primordial) black holes. We also find indications that the phase of rapid expansion of the obtained de Sitter universe impacts the mass, and relates to quantum fluctuations of space-time.

As a first step towards machine identification of confining objects in thermalized lattice gauge configurations, we present our 2dVoId model for center vortex identification on pure SU(2) lattices in $D = 2$ dimensions. We create a training set by inserting thin Z2 vortices at various locations on a zero action lattice, and then distort those configurations by applying random SU(2) gauge transformations, noise, and by thickening the vortices via cooling. For moderate vortex visibility, our model is able to reliably identify the location of center vortices. We additionally demonstrate scalability through tiling strategies, which will enable generalization to higher dimensions while reducing training costs.