We present a general dilation framework that embeds a non-Hermitian dynamics in a unitary dynamics in a larger Hilbert space. We show that an exact dilation can be guaranteed by a set of simple algebraic moment-matching conditions in the ancilla space. They generate many families of dilation methods. As a specific example, we derive a tight-binding model with nearest neighbor hoppings and demonstate how the accuracy of the dilation can be quantified via a light-cone condition.
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