Phase cancellation diagonalization method: A general approach to non-orthogonal basis sets for quantum devices*

Here we examine a family of algorithms that use real time Hamiltonian dynamics for quantum subspace diagonalization. The algorithm we focus on generates a series of time evolved states, resulting in a generalized eigenvalue equation that can be solved for ground and excited eigenstates. This method requires a surprisingly small number of basis states generated by real time evolution to compute chemically accurate results, making it particularly attractive for the NISQ era. We examine the theoretical underpinnings of the method, which involves the cancellation of phases with time evolution, and also systematically examine the role of noise in solving the generalized eigenvalue equation. We demonstrate our approach numerically over a range of systems, both in classical simulations (for LiH and Cr2) and on quantum hardware (for the transverse field Ising model).