A family of [[6k, 2k, 2]] codes for practical, scalable adiabatic quantum computation

TL;DR

This paper introduces a new family of [[6k, 2k, 2]] quantum error-correcting codes optimized for adiabatic quantum computation, enabling universal logical operations and efficient error suppression while preserving planarity.

Contribution

The authors present the first codes that support universal weight-two logical operators and maintain planarity with minimal graph degree increase.

Findings

Supports universal weight-two logical operators

Maintains planarity with only a two-degree increase

Facilitates dynamical decoupling error suppression

Abstract

In this work, we introduce a new family of [[6k, 2k, 2]] codes designed specifically to be compatible with adiabatic quantum computation. These codes support computationally universal sets of weight-two logical operators and are particularly well-suited for implementing dynamical decoupling error suppression. For Hamiltonians embeddable on a planar graph of fixed degree, our encoding maintains a planar connectivity graph and increase the graph degree by only two. These codes are the first known to possess these features.