Universal Fault-Tolerant Computation on Decoherence-Free Subspaces

Abstract

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.

5 pages, no figures. Many small changes and clarifications. Expanded discussion of relevance to solid-state implementations. This version to appear in Phys. Rev. Lett

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• Hilbert space structure of a solid state quantum computer: two-electron states of a double quantum dot artificial molecule
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