Universal Fault-Tolerant Computation on Decoherence-Free Subspaces

Details Universal Fault-Tolerant Computation on Decoherence-Free Subspaces Universal Fault-Tolerant Computation on Decoherence-Free Subspaces

1999-09-18

arxiv.org/abs/quant-ph/9909058v2

Phys. Rev. Lett. Vol 85 (8), p. 1758-61 (2000)

Physics

Quantum Physics

5 pages, no figures. Many small changes and clarifications. Expanded discussion of relevance to solid-state implementations. T

Scientific paper

10.1103/PhysRevLett.85.1758

A general scheme to perform universal quantum computation within decoherence-free subspaces (DFSs) of a system's Hilbert space is presented. This scheme leads to the first fault-tolerant realization of universal quantum computation on DFSs with the properties that (i) only one- and two-qubit interactions are required, and (ii) the system remains within the DFS throughout the entire implementation of a quantum gate. We show explicitly how to perform universal computation on clusters of the four-qubit DFS encoding one logical qubit each under "collective decoherence" (qubit-permutation-invariant system-bath coupling). Our results have immediate relevance to a number of solid-state quantum computer implementations, in particular those in which quantum logic is implemented through exchange interactions, such as the recently proposed spin-spin coupled GaAs quantum dot arrays and the Si:$^{31}$P nuclear spin arrays.

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