Combining Hamiltonian Learning Techniques with Variational Quantm Algorithms

The emergence of programmable quantum simulation platforms has opened up new avenues for tackling the quantum many-body problem. These platforms provide us with valuable tools to explore questions in fundamental physics and also carry practical implications, particularly in areas like quantum chemistry and material design. In this presentation, I will showcase advancements in Hamiltonian learning techniques used for investigating highly correlated quantum many-body states on programmable quantum hardware. This will encompass a range of applications, including the verification and characterization of analog and digital quantum simulation platforms, as well as the analysis of entanglement properties in many-body states prepared on programmable quantum simulators. Notably, I will report on experiments involving 51 trapped ions, where we have successfully extract entanglement features of subsystems within an ion chain comprising up to 20 lattice sites. The latter part of the presentation will delve into the exciting prospects of combining Hamiltonian learning techniques with variational quantum algorithms, showcasing their potential applications in quantum material design.