Thanks, those works are aimed at retrieving ensemble properties of RCS and also are not very practical. I was wondering if there was anything else besides that

Great work, congrats. Do you think it’s possible to use the framework to simulate sampling from noisy circuits? Would that be harder?

I believe this kind of algorithm will shepherd the transition of quantum applications from pre-fault-tolerant to early-fault-tolerant quantum architectures, operating within quantum-centric supercomputing environments.

We prove efficient convergence given a polynomially overlapping reference state, a well-behaved Hamiltonian spectrum and polynomial support of the ground state. We show the effectiveness of the method experimentally against an Anderson impurity model on 85 qubits on our IBM quantum processors.

With this work in collaboration with Oak Ridge National Laboratory, we develop an algorithm that does exactly that. We call it sample-based Krylov quantum diagonalization (SKQD). The idea is to draw samples from a Krylov basis and use those to project and diagonalize the target Hamiltonian itself.