Resolving low energy spectra with tensor hyper-contractions and quantum filter diagonalization

Quantum computers are a strong candidate for calculating the low energy spectra in complex electronic structure systems. While variational algorithms havehave had some initial success in this area, there is a large overhead in the numberof circuits it takes to perform noisy optimization. Here, we exploit the use oftensor hyper-contractions (THC) within the framework of quantum filter diag-onalization which is an approximate sub-space diagonalization. This allows usto achieve a direct non-variational approach to calculating the spectra with farfewer circuits run on the hardware. We also demonstrate error mitigation andpost-selection strategies which are tailored specifically for this approach and boost the quality of results. Finally, it is shown how this technique bescaled to larger systems