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Space, Time, Parallelism and Noise Requirements for Reliable Quantum Computing
Author(s) -
Steane A.M.
Publication year - 1998
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/(sici)1521-3978(199806)46:4/5<443::aid-prop443>3.0.co;2-8
Subject(s) - computer science , quantum computer , error detection and correction , block (permutation group theory) , block code , noise (video) , algorithm , parallel computing , fault tolerance , qubit , coding (social sciences) , computer engineering , theoretical computer science , quantum , distributed computing , mathematics , decoding methods , physics , geometry , quantum mechanics , artificial intelligence , image (mathematics) , statistics
Quantum error correction methods use processing power to combat noise. The noise level which can be tolerated in a fault‐tolerant method is therefore a function of the computational resources available, especially the size of computer and degree of parallelism. I present an analysis of error correction with block codes, made fault‐tolerant through the use of prepared ancilla blocks. The preparation and verification of the ancillas is described in detail. It is shown that the ancillas need only be verified against a small set of errors. This, combined with previously known advantages, makes this ’ancilla factory‚ the best method to apply error correction, whether in concatenated or block coding. I then consider the resources required to achieve 2 · 10 10 computational steps reliably in a computer of 2150 logical qubits, finding that the simplest [[ n , 1, d ]] block codes can tolerate more noise with smaller overheads than the 7 L ‐bit concatenated code. The scaling is such that block codes remain the better choice for all computations one is likely to contemplate.