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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.

Unified Multimodal Models (UMMs) integrate visual understanding, generation, and editing within a single unified framework. However, existing unified multimodal datasets and benchmarks remain dominated by single-turn tasks. Even in recent multi-turn datasets, many turns can be solved independently without tracking information across turns. Consequently, they provide limited supervision and evaluation for multimodal stateful interaction, which requires models to understand, maintain, update, and faithfully realize evolving dialogue states across turns. To address this gap, we introduce YANAMI, the first large-scale multimodal dialogue dataset and benchmark for stateful interaction, comprising YANAMI-400K and YANAMI-Bench. YANAMI-400K contains 400K multi-turn multimodal dialogues, with more than 2M images and 2.6M dialogue turns. The dialogues span four representative scenarios: Multi-Image Fusion, Image Editing, World Modeling, and Visual Reasoning, and require models to continuously track, preserve, and revise evolving multimodal dialogue states across turns. YANAMI-Bench comprises 400 multi-turn dialogues for systematically evaluating multimodal stateful interaction. It jointly evaluates Dialogue State Understanding and Visual Realization, characterizing the gap between models' ability to understand evolving dialogue states and their ability to faithfully realize them in visual outputs. Experiments show that fine-tuning BAGEL on YANAMI-400K improves image editing, generation, and multimodal stateful interaction by 10.3%, 2.0%, and 13.23%, respectively, while preserving its general visual understanding capabilities. Evaluations on YANAMI-Bench further reveal that existing UMMs still struggle to maintain, update, and visually realize evolving multimodal dialogue states.