School of Physical and Mathematical Sciences, Nanyang Technological University, 637371 Singapore, Singapore.
Complexity institute, Nanyang Technological University, 639798 Singapore, Singapore.
Phys Rev Lett. 2018 Dec 28;121(26):260602. doi: 10.1103/PhysRevLett.121.260602.
In stochastic modeling, there has been a significant effort towards finding predictive models that predict a stochastic process' future using minimal information from its past. Meanwhile, in condensed matter physics, matrix product states (MPS) are known as a particularly efficient representation of 1D spin chains. In this Letter, we associate each stochastic process with a suitable quantum state of a spin chain. We then show that the optimal predictive model for the process leads directly to an MPS representation of the associated quantum state. Conversely, MPS methods offer a systematic construction of the best known quantum predictive models. This connection allows an improved method for computing the quantum memory needed for generating optimal predictions. We prove that this memory coincides with the entanglement of the associated spin chain across the past-future bipartition.
在随机建模中，人们已经做出了巨大努力，旨在寻找使用过去信息的最小量来预测随机过程未来的预测模型。同时，在凝聚态物理中，矩阵乘积态（MPS）被认为是一维自旋链的一种特别有效的表示。在这封信中，我们将每个随机过程与一个合适的自旋链量子态相关联。然后我们证明，过程的最优预测模型直接导致了相关量子态的 MPS 表示。相反，MPS 方法为最佳已知的量子预测模型提供了系统的构建方法。这种联系允许改进用于计算生成最佳预测所需的量子记忆的方法。我们证明，这种记忆与相关自旋链在过去-未来二分法中的纠缠相一致。
