Time-dependent hamiltonian simulation with L1-norm scaling

Dominic W. Berry, Andrew M. Childs, Yuan Su, Xin Wang, Nathan Wiebe

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    45 Citations (Scopus)
    13 Downloads (Pure)


    The difficulty of simulating quantum dynamics depends on the norm of the Hamiltonian. When the Hamiltonian varies with time, the simulation complexity should only depend on this quantity instantaneously. We develop quantum simulation algorithms that exploit this intuition. For sparse Hamiltonian simulation, the gate complexity scales with the L1 norm R0t dτ kH(τ)kmax, whereas the best previous results scale with tmaxτ∈[0,t] kH(τ)kmax. We also show analogous results for Hamiltonians that are linear combinations of unitaries. Our approaches thus provide an improvement over previous simulation algorithms that can be substantial when the Hamiltonian varies significantly. We introduce two new techniques: a classical sampler of time-dependent Hamiltonians and a rescaling principle for the Schrödinger equation. The rescaled Dyson-series algorithm is nearly optimal with respect to all parameters of interest, whereas the sampling-based approach is easier to realize for near-term simulation. These algorithms could potentially be applied to semi-classical simulations of scattering processes in quantum chemistry.

    Original languageEnglish
    Article number254
    Pages (from-to)1-40
    Number of pages40
    Publication statusPublished - 15 Apr 2020

    Bibliographical note

    Copyright © 2020 Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften. All right reserved. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.


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