Rare $b\to s\ell^+\ell^-$ decays provide some of the most sensitive tests of the Standard Model and require precise and systematically improvable hadronic input from lattice QCD. For the phenomenologically important channel $B\to K^*\ell^+\ell^-$ this entails a first-principles treatment of a resonant $K\pi$ final state together with controlled heavy-quark dynamics. We present the status of a new exploratory lattice calculation that combines a variational determination of finite-volume $K\pi$ states with the $1+J\to2$ finite-volume formalism to access the relevant matrix elements. The computation is carried out on an RBC/UKQCD domain-wall fermion ensemble with $a^{-1} \approx 2.7\,\mathrm{GeV}$ and employs a dual heavy-quark strategy, using both a relativistic heavy-quark action tuned to the physical $b$ mass and domain-wall heavy masses extrapolating from charm. All correlation functions are computed using (stochastic) distillation, providing a versatile setup that supports a broad range of heavy-to-light transitions into resonant final states. We show first two-point results for the $K^*\leftrightarrow K\pi$ system and discuss the accessible kinematic region, which allows for a controlled study at high $q^2$. The outlook for extending the calculation to lower $q^2$ and for incorporating effects from charmonium resonances is outlined.

Generalised Parton Distributions (GPDs) provide multidimensional insight into hadron structure and are particularly relevant for the pion, whose dynamics are intimately linked to chiral symmetry breaking. We introduce a novel modelling strategy for pion GPDs that satisfies all QCD constraints by construction: support, polynomiality, positivity, and the soft-pion theorem. The approach is illustrated with a simple algebraic model, which is evolved and used to compute deeply virtual Compton scattering (DVCS) Compton Form Factors at next-to-leading order. Our results indicate that gluons dominate the pion response at the Electron Ion Collider kinematics.

We study the pseudoscalar ($J^{PC}=0^{-+}$) and vector ($1^{--}$) top--antitop (toponium) systems within the rainbow--ladder truncation of the Dyson--Schwinger and Bethe--Salpeter equations, employing the Qin--Chang effective interaction. After validating the framework in the charmonium and bottomonium sectors, we extend it consistently to the top sector, incorporating renormalisation-group running of the current quark mass and a careful treatment of the number of active flavours. We compute masses and leptonic decay constants for $N_f=5$ and $6$, then analyse their dependence on the renormalisation scale in the range $\mu=400-800\,\text{GeV}$. The resulting toponium masses lie near $344-346\,\text{GeV}$ with hyperfine splittings below $0.14-0.17\,\text{GeV}$, while the decay constants are large, $6-7\,\text{GeV}$, and exhibit the expected heavy-quark scaling behaviour. We find only mild sensitivity to the renormalisation point and a systematic reduction of binding when increasing $N_f$. Although the physical top quark decays weakly before hadronisation, our results demonstrate that, within a Poincaré-covariant nonperturbative framework, quantum chromodynamics (QCD) generates tightly correlated pseudoscalar and vector toponium systems in that extreme heavy-quark limit.

Strongly correlated fermionic systems are of great interest in condensed matter physics and numerical methods are indispensable tools for their study. However, existing approaches such as exact diagonalization (ED) and stochastic quantum Monte Carlo methods each suffer from fundamental limitations: ED is hindered by exponential scaling in system size, while Monte Carlo methods are plagued by sign problems and long autocorrelation times. These limitations restrict the accessible parameter space and developing algorithms that efficiently alleviate them remains a central challenge in computational physics. In this work, we propose a hybrid algorithm that combines ED and Hamiltonian Monte Carlo (HMC) to simulate 2D arrays of coupled quantum wires, modeled as interacting fermionic Hubbard chains. We demonstrate how our hybrid implementation of HMC, which we dub H$^2$MC, outperforms either method alone across several key simulation facets. When compared to pure ED, H$^2$MC has a much more favorable computational scaling, which allows us to push simulations to much larger 2D arrays. H$^2$MC also greatly alleviates the sign problem and reduces autocorrelation times when compared to pure HMC formulations utilizing either real or imaginary auxiliary fields. Our formalism demonstrates how complementary strengths of seemingly disparate methods can be leveraged to enable feasible simulations in an extended parameter space.

We introduce the CaRBM algorithm for fixed-depth thermal state preparation. Our algorithm is based on thermal state purification and uses the Restricted Boltzmann Machine (RBM) block-encoding scheme to implement the imaginary-time propagator $e^{-\beta H}$, which is implemented in the quantum circuit in a fixed-depth manner via Cartan decomposition. Our algorithm performs best at high temperatures, with the success probability of the block encoding decreasing as the temperature decreases. To increase the success probability, we have devised a correction scheme for the block-encoding that increases the temperature range our algorithm reliably probes. We demonstrate our algorithm by calculating the partition function zeros of the XXZ model and the phase diagram of the Gross-Neveu model, which is a model of strongly interacting relativistic fermions.