Concatenated tensor network states

TL;DR

The paper introduces concatenated tensor network states, a new framework that efficiently describes complex quantum states with long-range correlations, enabling improved simulation of quantum dynamics and variational optimization.

Contribution

It proposes concatenated tensor networks as a novel method to represent quantum states, extending tensor network capabilities to higher dimensions and complex entanglement structures.

Findings

Efficiently describes quantum states with long-range correlations.

Includes states generated by polynomial quantum circuits and time evolution.

Demonstrates improved methods for information extraction from tensor network states.

Abstract

We introduce the concept of concatenated tensor networks to efficiently describe quantum states. We show that the corresponding concatenated tensor network states can efficiently describe time evolution and possess arbitrary block-wise entanglement and long-ranged correlations. We illustrate the approach for the enhancement of matrix product states, i.e. 1D tensor networks, where we replace each of the matrices of the original matrix product state with another 1D tensor network. This procedure yields a 2D tensor network, which includes -- already for tensor dimension two -- all states that can be prepared by circuits of polynomially many (possibly non-unitary) two-qubit quantum operations, as well as states resulting from time evolution with respect to Hamiltonians with short-ranged interactions. We investigate the possibility to efficiently extract information from these states, which serves as the basic step in a variational optimization procedure. To this aim we utilize known exact and approximate methods for 2D tensor networks and demonstrate some improvements thereof, which are also applicable e.g. in the context of 2D projected entangled pair states. We generalize the approach to higher dimensional- and tree tensor networks.