Introduction to Quantum Error Correction
arXiv:quant-ph/0207170
Abstract
In this introduction we motivate and explain the ``decoding'' and ``subsystems'' view of quantum error correction. We explain how quantum noise in QIP can be described and classified, and summarize the requirements that need to be satisfied for fault tolerance. Considering the capabilities of currently available quantum technology, the requirements appear daunting. But the idea of ``subsystems'' shows that these requirements can be met in many different, and often unexpected ways.
44 pages, to appear in LA Science. Hyperlinked PDF at http://www.c3.lanl.gov/~knill/qip/ecprhtml/ecprpdf.pdf, HTML at http://www.c3.lanl.gov/~knill/qip/ecprhtml
References in corpus (18)
- Mixed State Entanglement and Quantum Error Correction
- The Physical Implementation of Quantum Computation
- Quantum Teleportation is a Universal Computational Primitive
- Dynamical Decoupling of Open Quantum Systems
- Dynamical suppression of decoherence in two-state quantum systems
- A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
- Reliable Quantum Computers
- A Theory of Fault-Tolerant Quantum Computation
- A Theory of Quantum Error-Correcting Codes
- Quantum Error Correction and Orthogonal Geometry
- Implementation of the Five Qubit Error Correction Benchmark
- Universal quantum computation using only projective measurement, quantum memory, and preparation of the 0 state
- A Note on Linear Optics Gates by Post-Selection
- Constructing Qubits in Physical Systems
- Introduction to NMR Quantum Information Processing
- Quantum repeaters for communication
- Introduction to Quantum Information Processing
- Thresholds for Linear Optics Quantum Computation
Cited by in corpus (26)
- Quantum Error Correction for Beginners
- Scalable Noise Estimation with Random Unitary Operators
- Quantum channels and memory effects
- Quantum Stabilizer Codes for Correlated and Asymmetric Depolarizing Errors
- Quantum Stabilizer Codes Embedding Qubits Into Qudits
- Introduction to NMR Quantum Information Processing
- On Self-Dual Quantum Codes, Graphs, and Boolean Functions
- Universal programmable photonic architecture for quantum information processing
- The multiplicative domain in quantum error correction
- Introduction to Quantum Information Processing
- Generalized Multiplicative Domains and Quantum Error Correction
- Repetition Versus Noiseless Quantum Codes For Correlated Errors
- Universal collective rotation channels and quantum error correction
- A Unified Picture of Decoherence Control
- Quantum stabilizer codes and beyond
- Conserved Topological Defects in Non-Embedded Graphs in Quantum Gravity
- An Introduction to Error-Correcting Codes: From Classical to Quantum
- Quantum Goppa Codes over Hyperelliptic Curves
- Time-dependent pointer states of the quantized atom-field model in a nonresonance regime and consequences regarding the decoherence of the central system
- Remarks on the nature of quantum computation
- The Study of Entangled States in Quantum Computation and Quantum Information Science
- Time-dependent pointer states of the generalized spin-boson model and consequences regarding the decoherence of the central system
- Noiseless subsystems for collective rotation channels in quantum information theory
- Entropy of quantum channel in the theory of quantum information
- A simple comparative analysis of exact and approximate quantum error correction
- Concatenation of Error Avoiding with Error Correcting Quantum Codes for Correlated Noise Models