Decoding Holographic Codes with an Integer Optimisation Decoder

TL;DR

This paper introduces an integer optimisation-based decoder for stabiliser codes, demonstrating thresholds against Pauli errors in holographic codes and analyzing their error correction performance.

Contribution

It presents a novel integer optimisation decoder for stabiliser codes and provides numerical analysis of holographic code thresholds and scaling properties.

Findings

Thresholds against Pauli errors range from 7% to 16%.

Holographic codes show polynomial scaling of distance measures.

Decoder performance varies with code rate.

Abstract

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.