Toric codes and quantum doubles from two-body Hamiltonians

TL;DR

This paper introduces a method to realize toric code and quantum double models as low-energy limits of two-body Hamiltonians using a novel perturbation gadget based on error-detecting subsystem codes, preserving symmetries.

Contribution

It provides a new construction for simulating complex topological models with simple two-body interactions, leveraging PEPS descriptions and error-detecting codes.

Findings

Successfully reproduces toric code and quantum double models from two-body Hamiltonians.

Maintains the symmetries of the original models in the low-energy limit.

Uses natural couplings aligned with the original Hamiltonians.

Abstract

We present a procedure to obtain the Hamiltonians of the toric code and Kitaev quantum double models as the low-energy limits of entirely two-body Hamiltonians. Our construction makes use of a new type of perturbation gadget based on error-detecting subsystem codes. The procedure is motivated by a PEPS description of the target models, and reproduces the target models' behavior using only couplings which are natural in terms of the original Hamiltonians. This allows our construction to exactly capture the symmetries of the target models.