Decoherence and fidelity of single-electron spin states in quantum dots: effects of nuclearhyperfine coupling and double occupancy

Abstract

The decoherence and fidelity of spin states in a localized single-electron quantum dot in thepresence of a dc magnetic field, arising either from the nuclear hyperfine interaction withinthe dot or due to its coupling with another localized quantum dot, are examined in detail.A general framework for determining the time evolution of the reduced density matrixρ for a single dot is presented, which is exact up to the second order in interaction with anyreservoir. In particular, it is applied to the problem of nuclear hyperfine coupling, andapproximate estimates of coherence decay time are made when the nuclear spins are eitherpolarized or unpolarized and the internal dynamics of nuclear spins is determinedmainly by the nuclear magnetic dipole–dipole interaction. The fidelity of a pureunperturbed electronic one-qubit spin state is obtained as a function of time,which is exact even on a very short timescale of logic gate operations. The timevariation of the fidelity of the same one-qubit state on the localized dot as a part ofthe direct product with another one-qubit state on another localized dot arisingbecause of coupling between these quantum dots is also calculated in this paper.In this case, we include both the single-particle tunnelling between the dots aswell as the direct and exchange Coulomb interactions, including on-site Coulombrepulsion. This allows for the double occupation of a single dot. It is found that theloss of fidelity of such two-qubit states due to double occupancy and additionalphase errors in the presence of appreciable dot–dot coupling can become a moresevere limiting factor than that due to the hyperfine interaction in individual dots.