Year: 2026
Type: preprint
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 $\varepsilon$ with success probability $Θ(1)$ using $\mathcal O\!\bigl(gα_AT\log(gα_AT/\varepsilon)\bigr)$ matrix queries and $\mathcal O(g)$ queries to each state-preparation oracle, where $g=\|\boldsymbol{x}_0\|/\|\boldsymbol{x}(T)\|$ 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.
Source: arXiv (Cornell University)
Authors: Dong, Xiaojing, Ma, Chuwen, Peng, Yizhe, Yu, Yue
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funders: National Natural Science Foundation of China, Science and Technology Commission of Shanghai Municipality, Natural Science Foundation of Hunan Province, Shanghai Jiao Tong University, Higher Education Discipline Innovation Project, Fundamental Research Funds for the Central Universities, Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province
OpenAlex ID: W7202117232
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