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Learn about a general dilation framework for embedding non-Hermitian dynamics within unitary dynamics in larger Hilbert spaces through this 48-minute conference presentation. Discover how exact dilation can be guaranteed using simple algebraic moment-matching conditions in the ancilla space, which generate multiple families of dilation methods. Explore a specific tight-binding model example with nearest neighbor hoppings and understand how to quantify dilation accuracy through light-cone conditions. Gain insights into advanced quantum simulation techniques for open quantum systems from this technical presentation delivered at IPAM's New Frontiers in Quantum Algorithms for Open Quantum Systems Workshop.