Entanglement regularization in the quantum dynamics of tensor network states*

A well-known computational challenge in quantum many-body dynamics is the exponential scaling of the system degrees of freedom with its size. This so-called "course of dimensionality" renders the full description of an arbitrary quantum state virtually intractable due to the enormous dimension of the Hilbert space. In an effort to tackle this issue, tensor networks (TN) have emerged as a general data compression scheme which allow the truncation of the Hilbert space, by exploiting the intrinsic entanglement structure of quantum states. Moreover, with the emergent interest in quantum information, a demand for hybrid algorithms that are suitable for current and future NISQ devices is on the rise, and TN methods are considered to be compelling candidates.

Using a TN approach, we present a mechanism for the controlled time-evolution of the nuclear degrees of freedom of multi-configurational chemical systems at a reduced storage and computational complexity. The procedure, which is rooted in the matrix product decompositions of both the Trotterized time-evolution operator and the wave function, aims to suppress the potentially exponential growth of non-physical entanglement that could render simulations intractable, a well-known issue in TN methods. Our algorithm is probed using a symmetric hydrogen-bonded system, namely, the protonated 2,2'-bipyridine, and its results are compared to those obtained via direct diagonalization.