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

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

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Cited by in corpus (6)

• A stochastic quantum Krylov protocol with double factorized Hamiltonians
• Sampling Error Analysis in Quantum Krylov Subspace Diagonalization
• Quantum subspace expansion in the presence of hardware noise
• Subspace-Based Local Compilation of Variational Quantum Circuits for Large-Scale Quantum Many-Body Simulation
• Correcting and extending Trotterized quantum many-body dynamics
• Cheaper and more noise-resilient quantum state preparation using eigenvector continuation