Related papers: Categorical Tensor Network States
Correlator product states (CPS) are a powerful and very broad class of states for quantum lattice systems whose amplitudes can be sampled exactly and efficiently. They work by gluing together states of overlapping clusters of sites on the…
We analyze few-body quantum states with particular correlation properties imposed by the requirement of maximal bipartite entanglement for selected partitions of the system into two complementary parts. A novel framework to treat this…
With the rapid progress in quantum hardware and software, the need for verification of quantum systems becomes increasingly crucial. While model checking is a dominant and very successful technique for verifying classical systems, its…
Large-scale quantum networks have been employed to overcome practical constraints of transmissions and storage for single entangled systems. Our goal in this article is to explore the strong entanglement distribution of quantum networks. We…
Tensor networks provide a powerful new framework for classifying and simulating correlated and topological phases of quantum matter. Their central premise is that strongly correlated matter can only be understood by studying the underlying…
The theory of entanglement provides a fundamentally new language for describing interactions and correlations in many body systems. Its vocabulary consists of qubits and entangled pairs, and the syntax is provided by tensor networks. We…
Many topologically nontrivial states of matter possess gapless degrees of freedom on the boundary, and when these boundary states delocalize into the bulk, a phase transition occurs and the system becomes topologically trivial. We show that…
The rank of a tensor is analyzed in context of quantum entanglement. A pure quantum state $\bf v$ of a composite system consisting of $d$ subsystems with $n$ levels each is viewed as a vector in the $d$-fold tensor product of…
These are exciting times for quantum physics as new quantum technologies are expected to soon transform computing at an unprecedented level. Simultaneously network science is flourishing proving an ideal mathematical and computational…
The string-net condensate is a new class of materials which exhibits the quantum topological order. In order to answer the important question, "how useful is the string-net condensate in quantum information processing?", we consider the…
The classification of quantum states into distinct classes poses a significant challenge. In this study, we address this problem using quantum neural networks in combination with a problem-inspired circuit and customised as well as…
We formalize and generalize the concept of a topological state-sum construction using the language of tensor networks. We give examples for constructions that are possibly more general than all state-sum constructions in the literature that…
Efficient simulation of quantum computers relies on understanding and exploiting the properties of quantum states. This is the case for methods such as tensor networks, based on entanglement, and the tableau formalism, which represents…
Despite the fundamental importance of quantum entanglement in many-body systems, our understanding is mostly limited to bipartite situations. Indeed, even defining appropriate notions of multipartite entanglement is a significant challenge…
We propose the entanglement bipartitioning approach to design an optimal network structure of the tree-tensor-network (TTN) for quantum many-body systems. Given an exact ground-state wavefunction, we perform sequential bipartitioning of…
Neural-Network Quantum States have been recently introduced as an Ansatz for describing the wave function of quantum many-body systems. We show that there are strong connections between Neural-Network Quantum States in the form of…
We introduce an entanglement branching operator to split a composite entanglement flow in a tensor network which is a promising theoretical tool for many-body systems. We can optimize an entanglement branching operator by solving a…
In this paper, we construct a tensor network representation of quantum causal histories, as a step towards directly representing states in quantum gravity via bulk tensor networks. Quantum causal histories are quantum extensions of causal…
We present a quantum algorithm that additively approximates the value of a tensor network to a certain scale. When combined with existing results, this provides a complete problem for quantum computation. The result is a simple new way of…
Tensor network formalisms have emerged as powerful tools for simulating quantum state evolution. While widely applied in the study of optical quantum circuits, such as Boson Sampling, existing tensor network approaches fail to address the…