Master thesis defense by Julius Rye Bønnelykke

Finding and Decoding Clifford Deformed Surface codes using Machine Learning

Quantum Error Correction Codes (QECCs) promise to mitigate the high error rates of physical qubits, reducing them to the levels required to achieve quantum advantage. This reduction, however, typically comes at the cost of requiring a substantial number of physical qubits per logical qubit. A recent study [Arpit Dua et al. Clifford-Deformed Surface Codes, PRX Quantum 5, 010347 (2024)] demonstrated that existing QECCs can be enhanced using Clifford deformations (modifications to the codes stabilizers), achieving lower logical error rates without increasing the physical qubit count.

This thesis investigates the potential of using Machine Learning (ML) to decode these deformed codes - specifically, Clifford Deformed Surface Codes (CDSCs) - and explores efficient methods for identifying CDSCs with exceptionally low logical error rates.

To address the decoding challenge, a novel decoder based on a Modified Convolutional Neural Network (mCNN) is introduced. This decoder incorporates information about the Clifford deformation applied to the rotated Kitaev Surface code, in addition to the syndrome data. As a result, it generalizes across all CDSCs of a given size, achieving up to two orders-of-magnitude improvement in logical error rate over the Minimum Weight Perfect Matching (MWPM) decoder on specific CDSCs.

For the second objective, several approaches were evaluated to search for high-performing CDSCs, including ML-based methods such as Reinforcement Learning (RL) and probabilistic sampling, as well as non-ML methods like random search and hill climbing. These methods are evaluated in terms of their scalability and effectiveness for identifying CDSCs with low logical error rates.