Classical probability distributions on sets of sequences can be modeled using quantum states. Here, we do so with a quantum state that is pure and entangled. Because it is entangled, the reduced densities that describe subsystems also carry information about the complementary subsystem. This is in contrast to the classical marginal distributions on a subsystem in which information about the complementary system has been integrated out and lost. A training algorithm based on the density matrix renormalization group (DMRG) procedure uses the extra information contained in the reduced densities and organizes it into a tensor network model. An understanding of the extra information contained in the reduced densities allow us to examine the mechanics of this DMRG algorithm and study the generalization error of the resulting model. As an illustration, we work with the even-parity dataset and produce an estimate for the generalization error as a function of the fraction of the dataset ...

中文翻译：

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用量子态对序列进行建模：深入了解

可以使用量子状态对序列集上的经典概率分布进行建模。在这里，我们使用纯净且纠缠的量子态来实现。因为它是纠缠的，所以描述子系统的密度降低了，也携带了有关互补子系统的信息。这与子系统上的经典边际分布形成对比，在子系统中，有关补充系统的信息已被整合并丢失。基于密度矩阵重归一化组（DMRG）过程的训练算法使用降低的密度中包含的额外信息，并将其组织为张量网络模型。对降低密度中包含的额外信息的理解使我们能够研究此DMRG算法的机制并研究所得模型的泛化误差。举例来说，