CHAPTER 5 - Quantum Error-Correcting Codes

Abstract

Correction of the errors caused by decoherence is one of the most challenging problems faced by quantum computing and quantum communication. Quantum systems are affected by decoherence, the alteration of the quantum state as a result of the interaction with the environment; decoherence occurs as the state of the quantum system embodying the information is affected by physical processes that cannot be reversed. It can be seen as the effect of measurements of the state of the quantum system carried out by the environment.. The description of quantum error correction suggests a close analogy with classical error correction, and, indeed, several subspace quantum codes are based on classical error correcting code. Quantum error correction requires a multi-qubit measurement that does not disturb the quantum information in the encoded state but retrieves information about the error. The measurement of the syndrome should reveal as much as possible about the error, but should not provide any information about the value that is stored in the logical qubit; otherwise, the measurement would destroy any quantum superposition of this logical qubit with other qubits in the quantum computer.