Quantum Error Correction Codes for Truncated SU(2) Lattice Gauge Theories

TL;DR

This paper develops two quantum error correction codes tailored for truncated SU(2) lattice gauge theories, enabling error correction in quantum simulations of gauge fields on various lattice geometries.

Contribution

It introduces two novel quantum error correction codes that incorporate gauge constraints and are compatible with logical gate implementations for SU(2) lattice gauge theories.

Findings

Both codes correct single-qubit errors.

The first code's logical Hamiltonian matches the spin Hamiltonian for gauge singlet states.

Codes are applicable to multiple lattice geometries.

Abstract

We construct two quantum error correction codes for pure SU(2) lattice gauge theory in the electric basis truncated at the electric flux $j_{\rm max}=1/2$, which are applicable on quasi-1D plaquette chains, 2D honeycomb and 3D triamond and hyperhoneycomb lattices. The first code converts Gauss's law at each vertex into a stabilizer while the second only uses half vertices and is locally the carbon code. Both codes are able to correct single-qubit errors. The electric and magnetic terms in the SU(2) Hamiltonian are expressed in terms of logical gates in both codes. The logical-gate Hamiltonian in the first code exactly matches the spin Hamiltonian for gauge singlet states found in previous work.