nLab
matrix product state

Contents

Context

Monoidal categories

monoidal categories

With symmetry

With duals for objects

With duals for morphisms

With traces

Closed structure

Special sorts of products

Semisimplicity

Morphisms

Internal monoids

Examples

Theorems

In higher category theory

Quantum Field Theory

algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)

Introduction

Concepts

field theory:

Lagrangian field theory

quantization

quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization

renormalization

Theorems

States and observables

Operator algebra

Local QFT

Perturbative QFT

Contents

Idea

What are called matrix product states (MPS) in quantum physics (specifically in solid state physics and in AdS/CFT) are those tensor network states of the form of a ring of tensors all of rank 3.

For example, given a metric Lie algebra 𝔤\mathfrak{g} (with string diagram-notation as discussed there) its Lie bracket-tensor f[,]𝔤 *𝔤 *𝔤f \coloneqq [-,-] \in \mathfrak{g}^\ast \otimes \mathfrak{g}^\ast \otimes \mathfrak{g} gives rise to matrix product states of the following form:

graphics from Sati-Schreiber 19c

quantum probability theoryobservables and states

References

For more see the references at tensor network state.

General

Review and exposition:

See also:

In quantum computation

In the context of quantum computation:

  • Yiqing Zhou, E. Miles Stoudenmire, Xavier Waintal, What limits the simulation of quantum computers? (arXiv:2002.07730)

Last revised on February 21, 2020 at 08:33:39. See the history of this page for a list of all contributions to it.