Related papers: Efficient Tree Tensor Network States (TTNS) for Qu…
In the tensor-network framework, the expectation values of two-dimensional quantum states are evaluated by contracting a double-layer tensor network constructed from initial and final tensor-network states. The computational cost of…
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…
Exact many-body quantum problems are known to be computationally hard due to the exponential scaling of the numerical resources required. Since the advent of the Density Matrix Renormalization Group, it became clear that a successful…
Tensor networks developed in the context of condensed matter physics try to approximate order-$N$ tensors with a reduced number of degrees of freedom that is only polynomial in $N$ and arranged as a network of partially contracted smaller…
Understanding entanglement remains one of the most intriguing problems in physics. While particle and site entanglement have been studied extensively, the investigation of length or energy scale entanglement, quantifying the information…
We develop and employ general Tree Tensor Networks (TTNs) to compute the vibrational spectra for two model systems: a set of 64-dimensional coupled oscillators and acetonitrile. We explore various tree architectures, ranging from the simple…
Novel randomness-induced disordered ground states in two-dimensional (2D) quantum spin systems have been attracting much interest. For quantitative analysis of such random quantum spin systems, one of the most promising numerical approaches…
Tree tensor network states (TTNS) generalize the notion of having low Schmidt-rank to multipartite quantum states, through a parameter known as the bond dimension. This leads to succinct representations of quantum many-body systems with a…
Hybrid Tensor Networks (hTN) offer a promising solution for encoding variational quantum states beyond the capabilities of efficient classical methods or noisy quantum computers alone. However, their practical usefulness and many…
This work is concerned with tree tensor network operators (TTNOs) for representing quantum Hamiltonians. We first establish a mathematical framework connecting tree topologies with state diagrams. Based on these, we devise an algorithm for…
A tensor network renormalization algorithm with global optimization based on the corner transfer matrix is proposed. Since the environment is updated by the corner transfer matrix renormalization group method, the forward-backward iteration…
This book serves as an introductory yet thorough guide to tensor networks and their applications in quantum computation and quantum information, designed for advanced undergraduate and graduate-level readers. In Part I, foundational topics…
Tree tensor networks (TTNs) are widely used in low-rank approximation and quantum many-body simulation. In this work, we present a formal analysis of the differential geometry underlying TTNs. Building on this foundation, we develop…
The resemblance between the methods used in quantum-many body physics and in machine learning has drawn considerable attention. In particular, tensor networks (TNs) and deep learning architectures bear striking similarities to the extent…
The fields of entanglement theory and tensor networks have recently emerged as central tools for characterising quantum phases of matter. In this article, we determine the entanglement structure of ground states of gapped symmetric quantum…
Tensor network algorithms have been remarkably successful solving a variety of problems in quantum many-body physics. However, algorithms to optimize two-dimensional tensor networks known as PEPS lack many of the aspects that make the…
Tensor networks provide succinct representations of quantum many-body states and are an important computational tool for strongly correlated quantum systems. Their expressive and computational power is characterized by an underlying…
Tensor network states provide successful descriptions of strongly correlated quantum systems with applications ranging from condensed matter physics to cosmology. Any family of tensor network states possesses an underlying entanglement…
Tensor network contractions are widely used in statistical physics, quantum computing, and computer science. We introduce a method to efficiently approximate tensor network contractions using low-rank approximations, where each intermediate…
Tensor product state (TPS) based methods are powerful tools to efficiently simulate quantum many-body systems in and out of equilibrium. In particular, the one-dimensional matrix-product (MPS) formalism is by now an established tool in…