[ICQ] Anirudh Krishna (IBM) Tradeoffs between connectivity and codes

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 kd2/(D−1)≤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.

This talk is based on the following papers:

1. https://arxiv.org/abs/2106.00765
2. https://arxiv.org/abs/2109.10982
3. https://arxiv.org/abs/2307.03283


Room 178