Fast-forwarding quantum simulation with real-time quantum Krylov subspace algorithms

Quantum subspace diagonalization (QSD) algorithms have emerged as a competitive family of algorithms that avoid many of the optimization pitfalls associated with parameterized quantum circuit algorithms. While the vast majority of QSD algorithms have focused on solving the eigenpair problem for ground-state, excited-state, and thermal observable estimations, there has been a lot less work in considering QSD algorithms for the problem of quantum dynamical simulation. In this work, we propose several quantum Krylov fast-forwarding algorithms capable of predicting long-time dynamics well beyond the coherence time of current quantum hardware. Our algorithms use real-time evolved Krylov basis states prepared on a quantum computer and a multireference subspace method to ensure convergence towards high-fidelity, long-time dynamics. In particular, we show that the proposed multireference methodology provides a systematic way of trading off circuit depth with classical postprocessing complexity. We also demonstrate the efficacy of our approach through numerical implementations for several quantum chemistry problems, including the calculation of the autocorrelation and dipole moment correlation functions.

Automated summary

This research introduces several quantum Krylov fast-forwarding algorithms that accurately predict long-time dynamics, and demonstrates the effectiveness of the proposed multireference method in balancing circuit depth and classical postprocessing complexity.