Quantum Computing and Error Correction
arXiv:quant-ph/0304016
Abstract
The main ideas of quantum error correction are introduced. These are encoding, extraction of syndromes, error operators, and code construction. It is shown that general noise and relaxation of a set of 2-state quantum systems can always be understood as a combination of Pauli operators acting on the system. Each quantum error correcting code allows a subset of these errors to be corrected. In many situations the noise is such that the remaining uncorrectable errors are unlikely to arise, and hence quantum error correction has a high probability of success. In order to achieve the best noise tolerance in the presence of noise and imprecision throughout the computer, a hierarchical construction of a quantum computer is proposed.
12 pages, a very simple tutorial introduction to error correction, with emphasis on avoiding misconceptions regarding the treatment of noise
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Cited by in corpus (8)
- Quantum Error Correction for Beginners
- Quantum Decoherence
- Sparse Graph Codes for Quantum Error-Correction
- Probabilistic Model--Checking of Quantum Protocols
- Is Fault-Tolerant Quantum Computation Really Possible?
- State of the art and prospects for quantum computing
- Noise resilience and entanglement evolution in two non-equivalent classes of quantum algorithms
- Optimized Aaronson-Gottesman stabilizer circuit simulation through quantum circuit transformations