Hamiltonian Simulation in the Interaction Picture

2018/05/02 by Guang Hao Low, Nathan Wiebe, Low, Guang Hao +1 · 23 citations
Computer Science · Decision Sciences · #Advanced Data Storage Technologies #Advanced Database Systems and Queries #FOS: Physical sciences #Quantum Physics (quant-ph) #Scientific Computing and Data Management

paper · pdf · doi:10.48550/arxiv.1805.00675

openalex publication_date 2018/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a low-space overhead simulation algorithm based on the truncated Dyson series for time-dependent quantum dynamics. This algorithm is applied to simulating time-independent Hamiltonians by transitioning to the interaction picture, where some portions are made time-dependent. This can provide a favorable complexity trade-off as the algorithm scales exponentially better with derivatives of the time-dependent component than the original Hamiltonian. We show that this leads to an exponential improvement in gate complexity for simulating some classes of diagonally dominant Hamiltonian. Additionally we show that this can reduce the gate-complexity scaling for simulating N-site Hubbard models for time t with arbitrary long-range interactions as well as reduce the cost of quantum chemistry simulations within a similar-sized plane-wave basis to \widetildeO(N²t) from \widetildeO(N^11/3t). We also show a quadratic improvement in query complexity for simulating sparse time-dependent Hamiltonians, which may be of independent interest.

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