Theory of decoherence-free fault-tolerant universal quantum computation

Julia Kempe, D. Bacon, D. A. Lidar, K. B. Whaley

Research output: Contribution to journalArticle

Abstract

Universal quantum computation on decoherence-free subspaces and subsystems (DFSs) is examined with particular emphasis on using only physically relevant interactions. A necessary and sufficient condition for the existence of decoherence-free (noiseless) subsystems in the Markovian regime is derived here for the first time. A stabilizer formalism for DFSs is then developed which allows for the explicit understanding of these in their dual role as quantum error correcting codes. Conditions for the existence of Hamiltonians whose induced evolution always preserves a DFS are derived within this stabilizer formalism. Two possible collective decoherence mechanisms arising from permutation symmetries of the system-bath coupling are examined within this framework. It is shown that in both cases universal quantum computation which always preserves the DFS (natural fault-tolerant computation) can be performed using only two-body interactions. This is in marked contrast to standard error correcting codes, where all known constructions using one- or two-body interactions must leave the code space during the on-time of the fault-tolerant gates. A further consequence of our universality construction is that a single exchange Hamiltonian can be used to perform universal quantum computation on an encoded space whose asymptotic coding efficiency is unity. The exchange Hamiltonian, which is naturally present in many quantum systems, is thus asymptotically universal.

Original languageEnglish (US)
Article number042307
Pages (from-to)1-29
Number of pages29
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume63
Issue number4
DOIs
StatePublished - Jan 1 2001

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quantum computation
error correcting codes
formalism
permutations
interactions
unity
baths
coding
symmetry

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

Theory of decoherence-free fault-tolerant universal quantum computation. / Kempe, Julia; Bacon, D.; Lidar, D. A.; Whaley, K. B.

In: Physical Review A - Atomic, Molecular, and Optical Physics, Vol. 63, No. 4, 042307, 01.01.2001, p. 1-29.

Research output: Contribution to journalArticle

Kempe, Julia ; Bacon, D. ; Lidar, D. A. ; Whaley, K. B. / Theory of decoherence-free fault-tolerant universal quantum computation. In: Physical Review A - Atomic, Molecular, and Optical Physics. 2001 ; Vol. 63, No. 4. pp. 1-29.
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