The theory of entanglement provides a fundamentally new language for describing
interactions and correlations in many-body systems. Its vocabulary consists of qubits and …

Originally developed in the context of condensed-matter physics and based on
renormalization group ideas, tensor networks have been revived thanks to quantum …

The preparation of long-range entangled states using unitary circuits is limited by Lieb-
Robinson bounds, but circuits with projective measurements and feedback (“adaptive …

Modern applications in engineering and data science are increasingly based on
multidimensional data of exceedingly high volume, variety, and structural richness …

We introduce protocols to prepare many-body quantum states with quantum circuits assisted
by local operations and classical communication. We show that by lifting the requirement of …

The curse of dimensionality associated with the Hilbert space of spin systems provides a
significant obstruction to the study of condensed matter systems. Tensor networks have …

Part 2 of this monograph builds on the introduction to tensor networks and their operations
presented in Part 1. It focuses on tensor network models for super-compressed higher-order …

Finite-depth quantum circuits preserve the long-range entanglement structure in quantum
states and map between states within a gapped phase. To map between states of different …

The discussions in § 2 and § 3 make it rather clear that while we have to evaluate a
sequence of functional integrals to compute the Rényi entropies, these are rather complex …

We present a variational renormalization group (RG) approach based on a reversible
generative model with hierarchical architecture. The model performs hierarchical change-of …