Tensor network methods are taking a central role in modern quantum physics and beyond.
They can provide an efficient approximation to certain classes of quantum states, and the …

We describe a graphical calculus for completely positive maps and in doing so review the
theory of open quantum systems and other fundamental primitives of quantum information …

This special volume celebrates the 40th anniversary of the discovery of the Gorini-
Kossakowski-Sudarshan-Lindblad master equation, which is widely used in quantum …

Situated as a language between computer science, quantum physics and mathematics,
tensor network theory has steadily grown in popularity and can now be found in applications …

Automated reasoning techniques have been proven of immense importance in classical
applications like formal verification, circuit design and probabilistic inference. The domain of …

We examine the use of string diagrams and the mathematics of category theory in the
description of quantum states by tensor networks. This approach lead to a unification of …

We present a 3D topological picture-language for quantum information. Our approach
combines charged excitations carried by strings, with topological properties that arise from …

We provide a graphical calculus for computing averages of tensor network diagrams with
respect to the distribution of random vectors containing independent uniform complex …

Invariant theory is concerned with functions that do not change under the action of a given
group. Here we communicate an approach based on tensor networks to represent …

We adapt the bialgebra and Hopf relations to expose internal structure in the ground state of
a Hamiltonian with Z 2 topological order. Its tensor network description allows for exact …