A general scheme to perform universal, fault-tolerant quantum computation within decoherence-free subspaces (DFSs) is presented. At most two-qubit interactions are required, and 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 spatially symmetric (collective) decoherence. Our results have immediate relevance to quantum computer implementations in which quantum logic is implemented through exchange interactions, such as the recently proposed spin-spin coupled quantum dot arrays and donor-atom arrays.
Physical Review Letters
- Pub Date:
- August 2000
- Quantum Physics
- 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