Biased-Noise Thresholds of Zero-Rate Holographic Codes with Tensor-Network Decoding

Understand

A crucial insight for practical quantum error correction is that different types of errors, such as single-qubit Pauli operators, typically occur with different probabilities.

• Finding an optimal quantum code under such biased noise is a challenging problem, related to the (generally unknown) maximum capacity of the corresponding noisy channel.
• A benchmark for this capacity is given by the hashing bound, which describes the performance of random stabilizer codes and leads to the matter of identifying codes that come close to the bound while also being efficiently decodable.
• In this work, we perform the first comprehensive analysis of asymptotically zero-rate holographic codes under biased noise.