Fault-tolerant simulation of Lattice Gauge Theories with gauge covariant codes

TL;DR

This paper establishes a novel connection between quantum error correction and Lattice Gauge Theories, enabling fault-tolerant simulation of LGTs using gauge covariant codes that preserve locality and facilitate efficient quantum computations.

Contribution

It introduces a gauge covariant error-correcting code for Abelian LGTs, linking logical operations to Hamiltonian dynamics and enabling fault-tolerant time evolution.

Findings

Error correction enhances LGT simulation robustness

Hamiltonian expressed via logical operations preserves locality

Fault-tolerant evolution achieved with product formulas and qubitization

Abstract

We show in this paper that a strong and easy connection exists between quantum error correction and Lattice Gauge Theories (LGT) by using the Gauge symmetry to construct an efficient error-correcting code for Abelian LGTs. We identify the logical operations on this gauge covariant code and show that the corresponding Hamiltonian can be expressed in terms of these logical operations while preserving the locality of the interactions. Furthermore, we demonstrate that these substitutions actually give a new way of writing the LGT as an equivalent hardcore boson model. Finally we demonstrate a method to perform fault-tolerant time evolution of the Hamiltonian within the gauge covariant code using both product formulas and qubitization approaches. This opens up the possibility of inexpensive end to end dynamical simulations that save physical qubits by blurring the lines between simulation algorithms and quantum error correcting codes.