Related papers: Improved rate-distance trade-offs for quantum codes with restricted connectivity

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

URL: http://arxiv.org/abs/2307.03283v1
Date: Thu, 6 Jul 2023 20:38:34 GMT
Title: Improved rate-distance trade-offs for quantum codes with restricted connectivity
Authors: Nou\'edyn Baspin, Venkatesan Guruswami, Anirudh Krishna, Ray Li
Abstract summary: We study how the connectivity graph associated with a quantum code constrains the code parameters. We establish a tighter dimension-distance trade-off as a function of the size of separators in the connectivity graph.
Score: 34.95121779484252
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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.

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