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Future Trends in Microelectronics: Up the Nano Creek by Alex Zaslavsky, Jimmy Xu, Serge Luryi

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Is Fault-Tolerant Quantum Computation Really Possible?

M. I. Dyakonov

Laboratoire de Physique Théorique et AstroparticulesUniversité Montpellier II, France

1.   Introduction

The answer that the quantum computing community currently gives to this question is a cheerful “yes”. The so-called “threshold” theorem says that, once the error rate per qubit per gate is below a certain value, estimated as 10-4−10-6, indefinitely long quantum computation becomes feasible, even if all of the 103−106 qubits involved are subject to relaxation processes, and all the manipulations with qubits are not exact. By active intervention, errors caused by decoherence can be detected and corrected during the computation. Though today we may be several orders of magnitude above the required threshold, quantum engineers may achieve it tomorrow (or in a thousand years). Anyway large-scale quantum computation is possible in principle, and we should work hard to achieve this goal.

The enormous literature devoted to this subject (Google gives 29300 hits for “fault-tolerant quantum computation”) is purely mathematical. It is mostly produced by computer scientists with a limited understanding of physics and a somewhat restricted perception of quantum mechanics as nothing more than unitary transformations in the Hilbert space plus “entanglement”. On the other hand, the heavy machinery of the theoretical quantum computation with its specific terminology, lemmas, etc., is not readily accessible to most physicists ...

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