# Improved rate-distance trade-offs for quantum codes with restricted connectivity

**Authors:** Nouédyn Baspin, Venkatesan Guruswami, Anirudh Krishna, Ray Li  
**arXiv:** [2307.03283](https://arxiv.org/abs/2307.03283)  
**Date:** 2023-07-06  
**Summary page:** https://www.summarizepaper.com/fr/arxiv-id/2307.03283v1/

## Abstract

For quantum error-correcting codes to be realizable, it is important that the qubits subject to the code constraints exhibit some form of limited connectivity. The works of Bravyi & Terhal (BT) and Bravyi, Poulin & Terhal (BPT) established that geometric locality constrains code properties -- for instance $[[n,k,d]]$ quantum codes defined by local checks on the $D$-dimensional lattice must obey $k d^{2/(D-1)} \le O(n)$. Baspin and Krishna studied the more general question of how the connectivity graph associated with a quantum code constrains the code parameters. These trade-offs apply to a richer class of codes compared to the BPT and BT bounds, which only capture geometrically-local codes. We extend and improve this work, establishing a tighter dimension-distance trade-off as a function of the size of separators in the connectivity graph. We also obtain a distance bound that covers all stabilizer codes with a particular separation profile, rather than only LDPC codes.