Double-occupation errors induced by orbital dephasing in exchange-interaction quantum gates
S. D. Barrett, C. H. W. Barnes · Physical review. B, Condensed matter · 2002
We describe an error mechanism that affects the operation of an exchange interaction based two-qubit quantum gate. The error mechanism is due to dephasing of the orbital degrees of freedom of the electrons in the gate. We examine this mechanism using a Markovian master equation for a two-electron, two-site system with its charge degrees of freedom weakly coupled to a bosonic environment. We find that dephasing leads to a finite probability of finding two electrons on one site at the end of a gate operation. The resulting error probability P depends on the ratio of the orbital dephasing rate $\ensuremath{\Gamma}$ and the on-site Coulomb repulsion energy U as $P\ensuremath{\sim}\ensuremath{\Gamma}/U$ and is approximately independent of the total gate pulse duration. Typical values for these parameters in various semiconductor systems suggest that the resulting error rate is of order ${10}^{\ensuremath{-}2}--{10}^{\ensuremath{-}3}$ per gate operation. This is significantly larger than present estimates for the error threshold required for fault tolerant quantum computation. We discuss the implications for the implementation of scalable quantum information processing using the exchange interaction.