From tensors to qubits

TL;DR

This paper reviews advances in tensor lattice field theory, focusing on quantum simulation techniques for Abelian models, including symmetry preservation, noise robustness, and novel implementations with Rydberg atoms.

Contribution

It introduces new tensor truncation methods for quantum simulations of Abelian gauge theories and explores innovative physical implementations.

Findings

Enhanced noise-robust Gauss's law implementations

Comparison of field digitizations and character expansions

Potential for Rydberg atom-based Abelian model simulations

Abstract

We discuss recent progress in Tensor Lattice Field Theory and economical, symmetry preserving, truncations suitable for quantum computations or simulations. We focus on spin and gauge models with continuous Abelian symmetries such as the Abelian Higgs model and emphasize noise-robust implementations of Gauss's law. We discuss recent progress concerning the comparison between field digitizations and character expansions, symmetry breaking in tensor language, wave-packet preparation and possible new implementations of Abelian models using Rydberg atoms.