CaltechTHESIS (California Institute of Technology) · 2004 · 54 citations · 0 references
EngineeringPhysicsFault-tolerant ComputingFault-tolerant SystemsQuantum ComputingCoding TheoryError Control CodingError CorrectionError-correcting CodesQuantum ComputationQuantum DecoherenceEntangled StatesFault-tolerant Quantum ComputationQuantum Channel CapacityQuantum Channel CodingQuantum Error CorrectionQuantum Error-correcting CodesQuantum Fault ToleranceStabilizer Codes
Quantum computation faces operational errors and decoherence, prompting the development of quantum error correction, especially stabilizer codes that provide a powerful group‑theoretical framework for constructing and analyzing such codes. This review surveys the field of quantum error correction and introduces the stabilizer code formalism. It examines known stabilizer codes, quantum channel capacities, coding bounds, and fault‑tolerant computation strategies.
Controlling operational errors and decoherence is one of the major challenges facing the field of quantum computation and other attempts to create specified many-particle entangled states. The field of quantum error correction has developed to meet this challenge. A group-theoretical structure and associated subclass of quantum codes, the stabilizer codes, has proved particularly fruitful in producing codes and in understanding the structure of both specific codes and classes of codes. I will give an overview of the field of quantum error correction and the formalism of stabilizer codes. In the context of stabilizer codes, I will discuss a number of known codes, the capacity of a quantum channel, bounds on quantum codes, and fault-tolerant quantum computation.