# Conversion of projected entangled pair states into a canonical form

## TL;DR

This paper introduces an algorithm to convert PEPS into a canonical form using a variational gauging approach, enhancing stability and efficiency for tensor network calculations in quantum many-body physics.

## Contribution

It presents a novel variational gauging algorithm for PEPS canonicalization, improving convergence and stability in tensor network computations.

## Key findings

- Effective in norm calculations for quantum models
- Enables energy optimization within PEPS canonical form
- Demonstrates rapid convergence with a new initialization scheme

## Abstract

We propose an algorithm to convert a projected entangled pair state (PEPS) into a canonical form, analogous to the well-known canonical form of a matrix product state. Our approach is based on a variational gauging ansatz for the QR tensor decomposition of PEPS columns into a matrix product operator and a finite depth circuit of unitaries and isometries. We describe a practical initialization scheme that leads to rapid convergence in the QR optimization. We explore the performance and stability of the variational gauging algorithm in norm calculations for the transverse-field Ising and Heisenberg models on a square lattice. We also demonstrate energy optimization within the PEPS canonical form for the transverse-field Ising and Heisenberg models. We expect this canonical form to open up improved analytical and numerical approaches for PEPS.