# Continuous Tensor Network States for Quantum Fields

@article{Tilloy2019ContinuousTN, title={Continuous Tensor Network States for Quantum Fields}, author={Antoine Tilloy and Juan Ignacio Cirac}, journal={Physical Review X}, year={2019} }

We introduce a new class of states for bosonic quantum fields which extend tensor network states to the continuum and generalize continuous matrix product states (cMPS) to spatial dimensions $d\geq 2$. By construction, they are Euclidean invariant, and are genuine continuum limits of discrete tensor network states. Admitting both a functional integral and an operator representation, they share the important properties of their discrete counterparts: expressiveness, invariance under gauge…

## 19 Citations

Quantum Coherent States of Interacting Bose-Fermi Mixtures in One Dimension

- Physics
- 2021

We study two-component atomic gas mixtures in one dimension involving both bosons and fermions. When the inter-species interaction is attractive, we report a rich variety of coherent ground-state…

Loop-free tensor networks for high-energy physics

- Physics, MedicinePhilosophical Transactions of the Royal Society A
- 2021

This presentation focuses on the application of loop-free tensor network methods to the study of high-energy physics problems and, in particular, to theStudy of lattice gauge theories where tensor networks can be applied in regimes where Monte Carlo methods are hindered by the sign problem.

Characterizing the quantum field theory vacuum using temporal Matrix Product states

- Mathematics, Physics
- 2018

In this paper we construct the continuous Matrix Product State (MPS) representation of the vacuum of the field theory corresponding to the continuous limit of an Ising model. We do this by exploiting…

Pushing Tensor Networks to the Limit An extension of tensor networks — mathematical tools that simplify the study of complex quantum systems — could allow their application to a broad range of quantum field theory problems

- 2019

N ot long after the birth of quantum mechanics, Paul Dirac and others postulated that, in principle, quantum mechanics could predict any desired property of matter [1]. That is, provided one can…

Differentiable Programming of Isometric Tensor Networks

- Physics, Computer ScienceMachine Learning: Science and Technology
- 2022

By introducing several gradient-based optimization methods for the isometric tensor network and comparing with Evenbly-Vidal method, it is shown that auto-differentiation has a better performance for both stability and accuracy.

Gauge invariant canonical symplectic algorithms for real-time lattice strong-field quantum electrodynamics

- Physics
- 2019

A class of high-order canonical symplectic structure-preserving geometric algorithms are developed for high-quality simulations of the quantized Dirac-Maxwell theory based strong-field quantum…

Gauge and Poincaré invariant canonical symplectic algorithms for real-time lattice strong-field quantum electrodynamics

- Physics
- 2019

A class of high-order canonical symplectic structure-preserving geometric algorithms are developed for high-quality simulations of the quantized Dirac-Maxwell theory based strong-field quantum…

Pushing Tensor Networks to the Limit

- PhysicsPhysics
- 2019

This $Physics$ viewpoint considers recent work by Tilloy and Cirac [Phys. Rev. X 9, 021040 (2019), arXiv:1808.00976]; those authors overcame several past limitations in the generalization of tensor…

Intermediate symmetric construction of transformation between anyon and Gentile statistics

- Physics, Mathematics
- 2020

Gentile statistics describes fractional statistical systems in the occupation number representation. Anyon statistics researches those systems in the winding number representation. Both of them are…

Differentiable Programming Tensor Networks

- Computer Science, PhysicsPhysical Review X
- 2019

This work presents essential techniques to differentiate through the tensor networks contractions, including stable AD for tensor decomposition and efficient backpropagation through fixed point iterations, and removes laborious human efforts in deriving and implementing analytical gradients for Tensor network programs.

## References

SHOWING 1-10 OF 77 REFERENCES

Continuum tensor network field states, path integral representations and spatial symmetries

- Physics
- 2015

A natural way to generalize tensor network variational classes to quantum field systems is via a continuous tensor contraction. This approach is first illustrated for the class of quantum field…

Renormalization and tensor product states in spin chains and lattices

- Mathematics, Physics
- 2009

We review different descriptions of many-body quantum systems in terms of tensor product states. We introduce several families of such states in terms of the known renormalization procedures, and…

Tensor Networks for Lattice Gauge Theories and Atomic Quantum Simulation

- Physics
- 2014

We show that gauge invariant quantum link models, Abelian and non-Abelian, can be exactly described in terms of tensor networks states. Quantum link models represent an ideal bridge between…

Holographic quantum states.

- Physics, MedicinePhysical review letters
- 2010

We show how continuous matrix product states of quantum fields can be described in terms of the dissipative nonequilibrium dynamics of a lower-dimensional auxiliary boundary field by demonstrating…

Fermionic Projected Entangled Pair States and Local U(1) Gauge Theories

- Physics
- 2015

Tensor networks, and in particular Projected Entangled Pair States (PEPS), are a powerful tool for the study of quantum many body physics, thanks to both their built-in ability of classifying and…

Calculus of continuous matrix product states

- Physics, Mathematics
- 2013

We discuss various properties of the variational class of continuous matrix product states, a class of Ansatz states for one-dimensional quantum fields that was recently introduced as the direct…

Entanglement renormalization for weakly interacting fields

- PhysicsPhysical Review D
- 2019

We adapt the techniques of entanglement renormalization tensor networks to weakly interacting quantum field theories in the continuum. A key tool is “quantum circuit perturbation theory,” which…

Anyons and matrix product operator algebras

- Mathematics, Physics
- 2015

Quantum tensor network states and more particularly projected entangled-pair states provide a natural framework for representing ground states of gapped, topologically ordered systems. The defining…

Class of quantum many-body states that can be efficiently simulated.

- Physics, MedicinePhysical review letters
- 2008

We introduce the multiscale entanglement renormalization ansatz, a class of quantum many-body states on a D-dimensional lattice that can be efficiently simulated with a classical computer, in that…

Holographic geometry of entanglement renormalization in quantum field theories

- Physics
- 2012

A bstractWe study a conjectured connection between AdS/CFT and a real-space quantum renormalization group scheme, the multi-scale entanglement renormalization ansatz (MERA). By making a close contact…