Error Thresholds for Arbitrary Pauli Noise

The error threshold of a one-parameter family quantum channels is defined as the largest noise level such that capacity channel remains positive. This in turn guarantees existence correction code for modeled by channel. Discretizing single-qubit errors leads to important Pauli channels; curiously, multipartite entangled states can increase these beyond so-called hashing bound, an effect termed superadditivity coherent information. In this work, we divide simplex into families and compute numerical lower bounds on their thresholds. We find substantial increases thresholds relative bound large regions corresponding biased noise, which realistic model promising computing architectures. are computed graph states, special type stabilizer state. order determine information state, devise algorithm exploits symmetries underlying graph, resulting computational speed-up. uses tools from group theory allows us consider symmetric number vertices. Our works particularly well repetition codes concatenated (or cat codes), our results provide first comprehensive study arbitrary channels. addition, identify novel based tree graphs. outperform simplex, hence form new with desirable properties.