Quantum Error Correction and Fault Tolerant Computing
This work fills the gap in quantum computing literature by treating error handling and fault-tolerant computing.
Quantum information has become a field of intense research. While most titles focus on theory and application of quantum computing, the market does lack a book on the error treatment. This book fills this gap. Professor Frank Gaitan is an experienced researcher who has been the first to derive relevant results in the community. He now has compiled his knowledge into this monograph.
Aus dem Inhalt:
1. Introduction A. Encoding and processing information B. Protecting information from noise---classical error correcting codes C. Pros and cons of storage and processing of information using quantum systems D. Quantum error correcting codes---first pass 2. General Properties of Quantum Error Correcting Codes A. Quantum channel---quantum system subject to environmental noise B. Quantum operations---formal description of noise C. Quantum error correction---necessary and sufficient conditions D. First example---either 9-qubit Shor code or [5,1,3] perfect code 3. Quantum Stabilizer Codes (QSC) A. General framework B. Examples C. Alternate description of QSC D. Concatenated codes 4. Encoding and Decoding QSC A. Standard form of QSC B. Quantum Circuit Model (a.k.a. quantum networks) C. Network for encoding QSC D. Different approaches to decoding QSC 5. Fault Tolerant Quantum Computation A. Quantum computing in presence of noise B. Error detection and recovery C. Fault tolerant encoded operations---generators of N(G) D. Fault tolerant encoded operations using measurement E. Fault tolerant operators on QSCs with multiple encoded qubits F. Fault tolerant operations not belonging to N(G) G. Extension to fault tolerant encoded operations on N-encoded qubits 6. Performance Threshold for Reliable Quantum Computing A. Concatenated codes and fault-tolerant encoded operations B. Threshold calculations 7. Bounds on Quantum Error Correcting Codes A. General bounds B. Bounds on degenerate codes C. Error correction and entanglement purification D. Channel capacity Appendix A: Finite Group Theory 1. definitions 2. stabilizer, centralizer, and normalizer of a group 3. homomorphism theorems Appendix B: Quantum Circuit Model 1. Gottesman-Knill theorem 2. universality of Hadamard, phase, and CNOT gates 3. universality of Barenco 2-qubit gate 4. universality of Toffoli gate