Quantum Error Correction

TLDR: In this article, the authors introduce the concept of quantum error correction for quantum information processing and fault tolerance for holonomic quantum computation, including quantum dynamical decoupling and quantum convolutional codes.

Abstract: Prologue Preface Part I. Background: 1. Introduction to decoherence and noise in open quantum systems Daniel Lidar and Todd Brun 2. Introduction to quantum error correction Dave Bacon 3. Introduction to decoherence-free subspaces and noiseless subsystems Daniel Lidar 4. Introduction to quantum dynamical decoupling Lorenza Viola 5. Introduction to quantum fault tolerance Panos Aliferis Part II. Generalized Approaches to Quantum Error Correction: 6. Operator quantum error correction David Kribs and David Poulin 7. Entanglement-assisted quantum error-correcting codes Todd Brun and Min-Hsiu Hsieh 8. Continuous-time quantum error correction Ognyan Oreshkov Part III. Advanced Quantum Codes: 9. Quantum convolutional codes Mark Wilde 10. Non-additive quantum codes Markus Grassl and Martin Rotteler 11. Iterative quantum coding systems David Poulin 12. Algebraic quantum coding theory Andreas Klappenecker 13. Optimization-based quantum error correction Andrew Fletcher Part IV. Advanced Dynamical Decoupling: 14. High order dynamical decoupling Zhen-Yu Wang and Ren-Bao Liu 15. Combinatorial approaches to dynamical decoupling Martin Rotteler and Pawel Wocjan Part V. Alternative Quantum Computation Approaches: 16. Holonomic quantum computation Paolo Zanardi 17. Fault tolerance for holonomic quantum computation Ognyan Oreshkov, Todd Brun and Daniel Lidar 18. Fault tolerant measurement-based quantum computing Debbie Leung Part VI. Topological Methods: 19. Topological codes Hector Bombin 20. Fault tolerant topological cluster state quantum computing Austin Fowler and Kovid Goyal Part VII. Applications and Implementations: 21. Experimental quantum error correction Dave Bacon 22. Experimental dynamical decoupling Lorenza Viola 23. Architectures Jacob Taylor 24. Error correction in quantum communication Mark Wilde Part VIII. Critical Evaluation of Fault Tolerance: 25. Hamiltonian methods in QEC and fault tolerance Eduardo Novais, Eduardo Mucciolo and Harold Baranger 26. Critique of fault-tolerant quantum information processing Robert Alicki References Index.