Universal Fault-Tolerant Quantum Computation with the Exchange Interaction
by
Masoud Mohseni
Department of Physics, University of Toronto, 60 St. George St., Toronto, Ontario, Canada, M5S 1A7
Coauthors: Daniel. A. Lidar

The ability of a quantum system to perform arbitrary or "universal" computation is restricted to its naturally available/controllable interactions. It has been shown that quantum systems with controllable exchange interactions can be made computationally universal by encoding the information within a subspace of the full Hilbert space: "encoded universality". However, there has not been any success on development of a general theory to make this encoded universal computation also resilient against decoherence. In this work, we introduce a class of hybrid encoded-universality stabilizer quantum error correcting codes, and demonstrate that quantum error-correction can be performed in systems with controllable exchange interactions. Specifically, we present an analytical method for leakage-correction using only unitary operations generated by exchange interactions. Furthermore, we demonstrate that any arbitrary quantum operation can be performed on these codes without accumulation or propagation of logical or leakage errors. In other words, universal fault-tolerant quantum computation is possible from the exchange interaction.

Date received: April 29, 2004