In this talk, I will review recent works related on how to harness programmable simulators based on waveguide QED [1] and fermionic optical lattices [2,3]. 

First, I will briefly show how the tunable-range interactions appearing in waveguide QED can be used to construct wavefunction ansätze that approximate the ground state of quantum spin models [1].

Second, I will discuss how to harness the latest experimental advances in programmable optical lattices to simulate fermionic Hamiltonians relevant in condensed-matter physics [2]. In particular, we construct variational circuits for ground-state preparation and apply them to local and extended Fermi-Hubbard models with and without doping, showing considerable improvements with respect to adiabatic state preparation. 

Finally, we will discuss how to improve the estimation of ground-state properties of relevant many-body Hamiltonians using only global control and classical post-processing [3].

[1] C Tabares, A Muñoz de Las Heras, L Tagliacozzo, D Porras, A. González-Tudela.  Physical Review Letters 131 (7), 073602 (2023).

[2] C. Tabares, C. Kokail, P. Zoller, D. González-Cuadra and A. González-Tudela, PRX Quantum  6 (3), 030356 (2025).

[3] C Tabares, DS Wild, JI Cirac, P Zoller, A González-Tudela, D. González-Cuadra. arXiv:2511.04434.

Inviter: Tao Shi