Decoding Holographic Codes with an Integer Optimisation Decoder

Understand

We develop a most likely error Pauli error decoding algorithm for stabiliser codes based on general purpose integer optimisation.

• Using this decoder we analyse the performance of holographic codes against Pauli errors and find numerical evidence for thresholds against Pauli errors for bulk qubits.
• We compare the performance of holographic code families of various code rates and find phenomenological Pauli error thresholds ranging from $7\%$ to $16\%$, depending on the code rate.
• Additionally we give numerical evidence that specific distance measures of the codes we consider scales polynomially with number of physical qubits.