Quantum computations: algorithms and error correction

Abstract

Contents §0. Introduction §1. Abelian problem on the stabilizer §2. Classical models of computations 2.1. Boolean schemes and sequences of operations 2.2. Reversible computations §3. Quantum formalism 3.1. Basic notions and notation 3.2. Transformations of mixed states 3.3. Accuracy §4. Quantum models of computations 4.1. Definitions and basic properties 4.2. Construction of various operators from the elements of a basis 4.3. Generalized quantum control and universal schemes §5. Measurement operators §6. Polynomial quantum algorithm for the stabilizer problem §7. Computations with perturbations: the choice of a model §8. Quantum codes (definitions and general properties) 8.1. Basic notions and ideas 8.2. One-to-one codes 8.3. Many-to-one codes §9. Symplectic (additive) codes 9.1. Algebraic preparation 9.2. The basic construction 9.3. Error correction procedure 9.4. Torus codes §10. Error correction in the computation process: general principles 10.1. Definitions and results 10.2. Proofs §11. Error correction: concrete procedures 11.1. The symplecto-classical case 11.2. The case of a complete basis

Keywords

MathematicsComputationQuantum computerQuantum algorithmQuantum error correctionQuantumAlgorithmAlgebra over a fieldDiscrete mathematicsPure mathematicsQuantum mechanics

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Publication Info

Year: 1997
Type: article
Volume: 52
Issue: 6
Pages: 1191-1249
Citations: 1347
Access: Closed

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APA Style

                            
                                    Alexei Kitaev
                                
                            (1997). 
                            Quantum computations: algorithms and error correction. 
                            Russian Mathematical Surveys
                            , 52
                            (6)
                            , 1191-1249.
                            https://doi.org/10.1070/rm1997v052n06abeh002155

Identifiers

DOI: 10.1070/rm1997v052n06abeh002155

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