Benhemou, Asmae; (2025) Progress in quantum error correction and simulation, a many-body physics approach. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

Quantum computers can perform computational tasks in an exponentially large state space, provided the system maintains high fidelity. However, quantum systems are highly susceptible to errors arising from environmental coupling and intrinsic quantum processes. Building and operating a quantum processor therefore requires a robust strategy to protect the encoded information from errors. This challenge gave rise to the field of quantum error correction, which employs redundancy to encode quantum information using sophisticated protocols. In parallel, topological phases of matter have emerged as exciting platforms for achieving fault- tolerant and scalable quantum computation. These states exhibit intrinsic error resistance due to their topological nature, making them ideal candidates for encoding and manipulating quantum information. A symbiotic relationship has developed between these research areas, inspiring the study of topological quantum error-correcting codes. This thesis explores four themes: candidate logical encodings for topological quantum computing systems using the braiding and interaction of quasi-particle defects, including the surface code and a chain of parafermions; improved decoding for topological quantum codes; and proposals for quantum simulation leveraging the power of neutral atoms for braiding qudit topological states, and simulating quantum effects in black holes.

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