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Quantum Machines: Measurement and Control of Engineered Quantum SystemsLecture Notes of the Les Houches Summer School: Volume 96, July 2011$
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Michel Devoret, Benjamin Huard, Robert Schoelkopf, and Leticia F. Cugliandolo

Print publication date: 2014

Print ISBN-13: 9780199681181

Published to Oxford Scholarship Online: September 2014

DOI: 10.1093/acprof:oso/9780199681181.001.0001

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Quantum error correction

Quantum error correction

Chapter:
(p.273) 7 Quantum error correction
Source:
Quantum Machines: Measurement and Control of Engineered Quantum Systems
Author(s):

I. L. Chuang

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199681181.003.0007

This chapter treats the subject of quantum error correction and fault-tolerant quantum computation. In particular, it presents the various representations of open-system quantum dynamics, insisting on the indistinguishability between different unravelings. Quantum error correction with discrete gates reacting to discrete error syndromes obtained from projective measurement can be seen as a form of quantum feedback that stabilizes a whole manifold of quantum states rather than a single one. The chapter gives a useful general introduction to the theory of stabilizers, which is key to the understanding of error correcting codes. It explains in full detail the principles behind the size of the overhead needed to make the entire quantum processor fault-tolerant, not just its memory.

Keywords:   quantum error correction, fault-tolerant quantum computing, open-system quantum dynamics, quantum feedback, stabilizer

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