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

TL;DR

This paper introduces quantum Krylov subspace algorithms for fast-forwarding quantum simulations, enabling accurate long-time dynamics prediction beyond current hardware coherence times.

Contribution

It proposes novel quantum Krylov fast-forwarding algorithms using real-time evolved basis states and multi-reference methods for improved long-time quantum dynamics simulation.

Findings

Algorithms successfully predict long-time dynamics beyond hardware coherence.

Numerical tests on quantum chemistry problems validate approach.

Trade-off between circuit depth and classical post-processing is demonstrated.

Abstract

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 the QSD algorithms have focused on solving the eigenpair problem for ground, excited-state, and thermal observable estimation, 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 (QKFF) 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 the quantum computer and a multi-reference subspace method to ensure convergence towards high-fidelity, long-time dynamics. In particular, we show that the proposed multi-reference methodology provides a systematic way of trading off circuit depth with classical post-processing complexity. We also demonstrate the efficacy of our approach through numerical implementations for several quantum chemistry problems including the calculation of the auto-correlation and dipole moment correlation functions