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arXiv · 2502.19688

Infinite-dimensional Extension of the Linear Combination of Hamiltonian Simulation: Theorems and Applications

Rundi Lu·Hao-En Li·Zhengwei Liu·Jin-Peng Liu
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Abstract

We generalize the Linear Combination of Hamiltonian Simulation (LCHS) formula [An, Liu, Lin, Phys. Rev. Lett. 2023] to simulate time-evolution operators in infinite-dimensional spaces, including scenarios involving unbounded operators. This extension, named Inf-LCHS for short, bridges the gap between finite-dimensional quantum simulations and the broader class of infinite-dimensional quantum dynamics governed by partial differential equations (PDEs). Furthermore, we propose two sampling methods by integrating the infinite-dimensional LCHS with Gaussian quadrature schemes (Inf-LCHS-Gaussian) or Monte Carlo integration schemes (Inf-LCHS-MC). We demonstrate the applicability of the Inf-LCHS theorem to a wide range of non-Hermitian dynamics, including linear parabolic PDEs, queueing models (birth-or-death processes), Schr\"odinger equations with complex potentials, Lindblad equations, and black hole thermal field equations. Our analysis provides insights into simulating general linear dynamics using a finite number of quantum dynamics and includes cost estimates for the corresponding quantum algorithms.

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Rundi Lu, Hao-En Li, Zhengwei Liu, Jin-Peng Liu. 2025-02-27. Infinite-dimensional Extension of the Linear Combination of Hamiltonian Simulation: Theorems and Applications. https://arxiv.org/abs/2502.19688

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