A quantum-mechanical system comes naturally equipped with a convex space: each (Hermitian) operator has a (real) expectation value, and the expectation value of the square any Hermitian operator must be non-negative. This space is of exponential (e.g.~in volume) dimension, but low-dimensional projections can be efficiently explored by standard algorithms. Such approaches have been used to precisely constrain critical exponents of conformal field theories ("conformal bootstrap") and, more recently, to constrain the ground state physics of various quantum-mechanical systems, including lattice field theories. In this talk we discuss related approaches to systematically constraining the real-time dynamics of quantum systems, which are otherwise obstructed from study by sign problems and the ill-posed nature of analytic continuation.

We report on tensor renormalization group calculations of entanglement entropy in one-dimensional quantum systems. The reduced density matrix of a Gibbs state can be represented as a $1 + 1$-dimensional tensor network, which is analogous to the tensor network representation of the partition function. The HOTRG method is used to approximate the reduced density matrix for arbitrary subsystem sizes, from which we obtain the entanglement entropy. We test our method in the quantum Ising model and obtain the entanglement entropy of the ground state by taking the size of time direction to infinity. The central charge $c$ is obtained as $c = 0.49997(8)$ for a bond dimension $D=96$, which agrees with the theoretical value $c=1/2$ within the error.

The expressive power of neural networks in modelling non-trivial distributions can in principle be exploited to bypass topological freezing and critical slowing down in simulations of lattice field theories. Some popular approaches are unable to sample correctly non-trivial topology, which may lead to some classes of configurations not being generated. In this contribution, we present a novel generative method inspired by a model previously introduced in the ML community (GFlowNets). We demonstrate its efficiency at exploring ergodically configuration manifolds with non-trivial topology through applications such as triple ring models and two-dimensional lattice scalar field theory.

Markov Chain Monte Carlo simulations of lattice Quantum Chromodynamics (QCD) are the only known tool to investigate non-perturbatively the theory of the strong interaction and are required to perform precision tests of the Standard Model of Particle Physics. As the Markov Chain is a serial process, the sole option for improving the sampling rate is accelerating each individual update step. Heterogeneous clusters of GPU-accelerated nodes offer large total memory bandwidth which can be used to speed-up our application, openQxD-1.1, which is dominated by inversions of the Dirac operator, a large sparse matrix. In this work we investigate offloading the inversion to GPU using the lattice-QCD library QUDA, and our early results demonstrate a significant potential speed-up in the time-to-solution for state-of-the-art problem sizes. Minimal extensions to the existing QUDA library are required for our specific physics programme while greatly enhancing the performance portability of our code and retaining the reliability and robustness of existing applications in openQxD-1.1. Our new interface will enable us to utilize pre-exascale infrastructure and reduce the systematic uncertainty in our physics predictions by incorporating the effects of quantum electromagnetism (QED) in our simulations.

The recent BESIII announcement of a pseudoscalar glueball candidate makes an update on glueballs from lattice QCD timely. A brief review of how glueballs are studied in lattice QCD is given, and the reasons that glueballs are difficult to study both in lattice QCD with dynamical quarks and in experiments are outlined. Recent glueball studies in lattice QCD are then presented, and an exploratory investigation of the scalar glueball using glueball, meson, and meson-meson operators is summarized, suggesting that no scalar state below 2 GeV or so can be considered to be predominantly a glueball state.

We study QCD at finite temperature and non-zero chemical potential to derive the critical temperature at the chiral phase transition (crossover). We solve a set of Dyson--Schwinger partial differential equations using the exact solution for the Yang--Mills quantum field theory based on elliptical functions. Assuming a Nambu-Jona--Lasino (NJL) model of the quarks, we obtain a very good agreement with recent lattice computations regarding the dependence of the critical temperature on the strong coupling scale. The solution depends on a single scale parameter, as typical for the theory and already known from studies about asymptotic freedom. The analysis is analytically derived directly from QCD.