Quantum diagonalization methods for lattice models and chemistry beyond the reach of exact solutions

I will start by talking about two algorithms, the Krylov quantum diagonalization and the sample-based quantum diagonalization, and how they enabled ground states calculations of lattice models and chemistry at scale, on pre-fault-tolerant quantum processors. Then I will show how to combine them to obtain a sample-based algorithm for pre-fault-tolerant devices that has scaling properties similar to phase estimation.

References:

https://arxiv.org/abs/2407.14431
https://arxiv.org/abs/2405.05068
https://arxiv.org/abs/2501.09702