A unifying framework for quantum algorithms for time-dependent non-unitary dynamics
Abstract
We present an improved autonomization method for quantum simulation of time-dependent homogeneous dissipative linear systems, combining a clock-variable reformulation with Schrödingerization to obtain a time-independent Hamiltonian system. To control both discretization error and recovery probability, we construct the clock profile from a compactly supported window function and a normalized Dirichlet kernel: the former imposes endpoint regularity, while the latter concentrates the sampled mass and keeps the discrete normalization bounded. For the subsequent Schrödingerization step, we use an exactly periodic version of an error-function initial profile, whose explicit Fourier coefficients allow direct error estimates and simplify the analysis of smooth initialization. By combining Fourier projection with weighted recovery, we retain a single logarithmic precision factor in the full algorithm. Under finite-order derivative bounds, sampled matrix access, and exact state-preparation access, we prepare the normalized solution at time T to accuracy ε with success probability Θ(1) using 𝒪 (gαATlog(gαAT/ε)) matrix queries and 𝒪(g) queries to each state-preparation oracle, where g=|x0|/|x(T)| and αA is the matrix-oracle normalization. We illustrate the construction and its recovery probabilities through a numerical experiment on a time-dependent two-cavity system.
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BibTeX
@misc{dong2026unifying,
title = {{A unifying framework for quantum algorithms for time-dependent non-unitary dynamics}},
author = {Xiaojing Dong and Chuwen Ma and Yizhe Peng and Yue Yu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.07133},
eprint = {2608.07133},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.07133},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - A unifying framework for quantum algorithms for time-dependent non-unitary dynamics
AU - Xiaojing Dong
AU - Chuwen Ma
AU - Yizhe Peng
AU - Yue Yu
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2608.07133
UR - https://arxiv.org/abs/2608.07133
AB - We present an improved autonomization method for quantum simulation of time-dependent homogeneous dissipative linear systems, combining a clock-variable reformulation with Schrödingerization to obtain a time-independent Hamiltonian system. To control both discretization error and recovery probability, we construct the clock profile from a compactly supported window function and a normalized Dirichlet kernel: the former imposes endpoint regularity, while the latter concentrates the sampled mass and keeps the discrete normalization bounded. For the subsequent Schrödingerization step, we use an exactly periodic version of an error-function initial profile, whose explicit Fourier coefficients allow direct error estimates and simplify the analysis of smooth initialization. By combining Fourier projection with weighted recovery, we retain a single logarithmic precision factor in the full algorithm. Under finite-order derivative bounds, sampled matrix access, and exact state-preparation access, we prepare the normalized solution at time T to accuracy ε with success probability Θ(1) using 𝒪 (gα_ATlog(gα_AT/ε)) matrix queries and 𝒪(g) queries to each state-preparation oracle, where g=|x_0|/|x(T)| and α_A is the matrix-oracle normalization. We illustrate the construction and its recovery probabilities through a numerical experiment on a time-dependent two-cavity system.
ER -