Parallel decoding of multiple logical qubits in tensor-network codes

Understand

We consider tensor-network stabilizer codes and show that their tensor-network decoder has the property that independent logical qubits can be decoded in parallel.

• As long as the error rate is below threshold, we show that this parallel decoder is essentially optimal.
• As an application, we verify this for the max-rate holographic Steane (heptagon) code.
• For holographic codes this tensor-network decoder was shown to be efficient with complexity polynomial in n, the number of physical qubits.