{"ID":22952698,"CreatedAt":"2026-09-17T02:12:05.498442134Z","UpdatedAt":"2026-09-20T18:11:56.143995915Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.18757","arxiv_id":"2609.18757","title":"Query-Optimal and Gate-Efficient Lindbladian Simulation","abstract":"We give a quantum algorithm for Lindbladian simulation given a block encoding of the Hamiltonian $H$ and a projected unitary encoding of the stacked jump operator $B=\\sum_{k=1}^m \\lvert k\\rangle\\otimes L_k$, with normalization factors $α_H$ and $α_B$, respectively. For evolution time $t$, set $τ=(α_H+α_B^2)t$. The algorithm approximates the evolution channel to diamond-norm error $\\varepsilon$ using $O\\!\\left(τ+\\frac{\\log(1/\\varepsilon)}{\\log\\!\\left(e+\\log(1/\\varepsilon)/τ\\right)}\\right)$ oracle queries, matching the query lower bound for Hamiltonian simulation. The number of additional one- and two-qubit gates is linear in the query complexity up to polylogarithmic factors. The query- and gate-complexity bounds extend to Lipschitz-continuous time-dependent Lindbladians under coherent time-indexed oracle access. Our construction uses a one-query transducer that implements a product of rational approximations to short-time evolution when supplied with a catalyst. We bound the error from omitting the catalyst by exploiting orthogonality between different sequences of Kraus labels. The gate implementation combines a compressed Kraus-label representation, which stores only the positions and values of the nonzero labels, with the rotation factorization of Chen et al.","short_abstract":"We give a quantum algorithm for Lindbladian simulation given a block encoding of the Hamiltonian $H$ and a projected unitary encoding of the stacked jump operator $B=\\sum_{k=1}^m \\lvert k\\rangle\\otimes L_k$, with normalization factors $α_H$ and $α_B$, respectively. For evolution time $t$, set $τ=(α_H+α_B^2)t$. The algo...","url_abs":"https://arxiv.org/abs/2609.18757","url_pdf":"https://arxiv.org/pdf/2609.18757v1","authors":"[\"Boyang Chen\",\"Minbo Gao\",\"Xinzhao Wang\",\"Shuo Zhou\"]","published":"2026-09-16T14:44:42Z","proceeding":"quant-ph","tasks":"[\"quant-ph\",\"cs.DS\"]","methods":"[]","has_code":false}