Tensor-network codes

TL;DR

This paper introduces tensor-network stabilizer codes with a natural decoder, generalizing holographic codes beyond previous constructions, and demonstrates their effectiveness with a notable noise threshold and efficient decoding.

Contribution

It presents a new class of tensor-network stabilizer codes, extending holographic code constructions, and provides an efficient tensor-network decoder with practical noise threshold results.

Findings

Achieved an 18.8% noise threshold under depolarizing noise.

Demonstrated polynomial complexity of the tensor-network decoder for holographic codes.

Generalized holographic codes beyond perfect isometries.

Abstract

Inspired by holographic codes and tensor-network decoders, we introduce tensor-network stabilizer codes which come with a natural tensor-network decoder. These codes can correspond to any geometry, but, as a special case, we generalize holographic codes beyond those constructed from perfect or block-perfect isometries, and we give an example that corresponds to neither. Using the tensor-network decoder, we find a threshold of 18.8% for this code under depolarizing noise. We also show that for holographic codes the exact tensor-network decoder (with no bond-dimension truncation) is efficient with a complexity that is polynomial in the number of physical qubits, even for locally correlated noise.