RealTime Krylov Theory for Quantum Computing Algorithms
Abstract
Quantum computers provide new avenues to access ground and excited state properties of systems otherwise difficult to simulate on classical hardware. New approaches using subspaces generated by realtime evolution have shown efficiency in extracting eigenstate information, but the full capabilities of such approaches are still not understood. In recent work, we developed the variational quantum phase estimation (VQPE) method, a compact and efficient realtime algorithm to extract eigenvalues on quantum hardware. Here we build on that work by theoretically and numerically exploring a generalized Krylov scheme where the Krylov subspace is constructed through a parametrized realtime evolution, which applies to the VQPE algorithm as well as others. We establish an error bound that justifies the fast convergence of our spectral approximation. We also derive how the overlap with high energy eigenstates becomes suppressed from realtime subspace diagonalization and we visualize the process that shows the signature phase cancellations at specific eigenenergies. We investigate various algorithm implementations and consider performance when stochasticity is added to the target Hamiltonian in the form of spectral statistics. To demonstrate the practicality of such realtime evolution, we discuss its application to fundamental problems in quantum computation such as electronic structure predictions for strongly correlated systems.
 Publication:

Quantum
 Pub Date:
 July 2023
 DOI:
 10.22331/q202307251066
 arXiv:
 arXiv:2208.01063
 Bibcode:
 2023Quant...7.1066S
 Keywords:

 Quantum Physics
 EPrint:
 Quantum 7, 1066 (2023)