Neural network wavefunctions for SU(2) lattice gauge theory in the Hamiltonian formulation

In this talk I will cover our recent preprint arXiv:2509.12323 where we propose a neural network approach to finding the ground state wavefunction of SU(2) lattice gauge theory. Specifically, we demonstrate that the use of bespoke SU(2)-gauge-equivariant neural network layers increases the extent to which our variational ansatz can represent the ground state of this system. During this talk I will contrast the Hamiltonian and Euclidean formalisms of lattice gauge theories, highlighting the promises that the former offers but also the difficulties: noting briefly the issues of parameterising the continuous Hilbert space that plague tensor network and quantum simulation approaches and how our approach alleviates this. I will try and present our method pedagogically as we are very interested in learning its uses but also the limits of its validity, before closing with some remarks on scaling to larger systems and different gauge groups.