Accelerating Quantum Dense-Output Simulation through Locality
Abstract
Estimating time-accumulated observables, or dense outputs, is central to extracting classical information from quantum simulations. Whereas most quantum-simulation algorithms aim to reproduce a final state or a single-time expectation value, many applications require the integrated signal JH(O)=∫0T ⟨ ψ(t)|O(t)|ψ(t)⟩ dt. Previous Hamiltonian-simulation-based dense-output algorithms have query costs that depend on the norm of the full Hamiltonian, which can grow with system size. However, one can naturally optimize the simulation algorithm when the system structure is known. Consequently, we develop a locality-based truncation framework for the dense-output problem on lattice Hamiltonians. By truncating the Hamiltonian and tightening the resulting error with Lieb-Robinson bounds, we show that a local simulation can recover the dense output. We bound the quantum simulation error from spatial truncation and translate it into local-simulation query bounds. Our analysis includes free and interacting systems for both fermions and bosons, as well as open quantum systems governed by Lindbladians. The improvement from our truncation algorithm varies from constant to unbounded as the system size grows. We also give example applications and conduct relevant numerical experiments to support our findings.
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BibTeX
@misc{yang2026accelerating,
title = {{Accelerating Quantum Dense-Output Simulation through Locality}},
author = {Songqinghao Yang and Chang Liu and Junkai Wang and Jingxuan Zhang and Jin-Peng Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.40094},
eprint = {2609.40094},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.40094},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Accelerating Quantum Dense-Output Simulation through Locality
AU - Songqinghao Yang
AU - Chang Liu
AU - Junkai Wang
AU - Jingxuan Zhang
AU - Jin-Peng Liu
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.40094
UR - https://arxiv.org/abs/2609.40094
AB - Estimating time-accumulated observables, or dense outputs, is central to extracting classical information from quantum simulations. Whereas most quantum-simulation algorithms aim to reproduce a final state or a single-time expectation value, many applications require the integrated signal J_H(O)=∫_0^T ⟨ ψ(t)|O(t)|ψ(t)⟩ dt. Previous Hamiltonian-simulation-based dense-output algorithms have query costs that depend on the norm of the full Hamiltonian, which can grow with system size. However, one can naturally optimize the simulation algorithm when the system structure is known. Consequently, we develop a locality-based truncation framework for the dense-output problem on lattice Hamiltonians. By truncating the Hamiltonian and tightening the resulting error with Lieb-Robinson bounds, we show that a local simulation can recover the dense output. We bound the quantum simulation error from spatial truncation and translate it into local-simulation query bounds. Our analysis includes free and interacting systems for both fermions and bosons, as well as open quantum systems governed by Lindbladians. The improvement from our truncation algorithm varies from constant to unbounded as the system size grows. We also give example applications and conduct relevant numerical experiments to support our findings.
ER -