On the energy barrier of hypergraph product codes

TL;DR

This paper establishes tight bounds on the energy barrier of quantum codes derived from hypergraph products of classical codes, crucial for understanding their potential as self-correcting quantum memories.

Contribution

It provides the first rigorous bounds on the energy barrier for hypergraph product quantum codes, linking it to the classical codes' energy barriers, especially for LDPC codes.

Findings

Energy barrier bounds are tight and depend on classical code properties.

For LDPC codes, the quantum energy barrier matches the classical energy barrier up to a constant.

The results inform the design of quantum codes with desirable self-correcting properties.

Abstract

A macroscopic energy barrier is a necessary condition for self-correcting quantum memory. In this paper, we prove tight bounds on the energy barrier applicable to any quantum code obtained from the hypergraph product of two classical codes. If the underlying classical codes are low-density parity-check codes (LDPC), the energy barrier of the quantum code is shown to be the minimum energy barrier of the underlying classical codes (and their transposes) up to an additive $O(1)$ constant.