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Infinite-dimensional Extension of the Linear Combination of Hamiltonian Simulation: Theorems and Applications
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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.
Forward citations
Cited by 6 Pith papers
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Presents structure-preserving quantum method-of-lines algorithms for parabolic and hyperbolic PDEs with mixed BCs, using Coons interpolation, similarity transforms, and explicit quantum circuit constructions with comp...
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Quantum circuit framework for advection-diffusion PDEs with Robin and periodic boundary conditions via LCHS, including LCU error analysis and gate complexity showing potential quantum advantage in high dimensions.
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Quantum Simulation of Non-Hermitian Special Functions and Dynamics via Contour-based Matrix Decomposition
CBMD decomposes non-Hermitian operators via contour residues to enable optimal-query quantum simulation of first-order dynamics and special functions such as Bessel and Airy evolutions without requiring diagonalizability.
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Quantum Simulation of Non-Hermitian Special Functions and Dynamics via Contour-based Matrix Decomposition
CBMD decomposes non-Hermitian evolution operators into Hermitian LCU terms via a matrix residue theorem, matching known optimal query bounds and offering a route to polynomial matrix functions.
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Circuit-Efficient Randomized Quantum Simulation of Non-Unitary Dynamics with Observable-Driven and Symmetry-Aware Designs
A randomized compilation of LCHS for non-unitary dynamics, with an observable-driven variant and a symmetry-aware sampler, claims reduced ancilla and circuit depth at the cost of more repetitions.
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