Decoding holographic codes with an integer optimization decoder
Robert Harris, Elliot Coupe, Nathan A. McMahon, Gavin K. Brennen, Thomas M. Stace
Abstract
We develop a most likely error Pauli error decoding algorithm for stabilizer codes based on general purpose integer optimization. Using this decoder we analyze 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 scale polynomially with number of physical qubits.
Topics & Concepts
Pauli exclusion principleDecoding methodsCode (set theory)QubitComputer scienceAlgorithmMathematicsPhysicsQuantum mechanicsQuantumProgramming languageSet (abstract data type)Quantum Computing Algorithms and ArchitectureCoding theory and cryptographyQuantum Information and Cryptography