Symmetric spin–orbit interaction in triple quantum dot and minimisation of spin–orbit leakage in CNOT gate

Abstract

We analyse spin–orbit interaction in triple quantum dots and show that a symmetric spin–orbit Hamiltonian does not follow the standard form used in double quantum dots, as a consequence of the presence of the third dot in the setup. Furthermore, CNOT implementation schemes based on the exchange interaction were studied. It was shown that an antisymmetric Dzyaloshinsky–Moriya term is the dominant source of spin–orbit leakage from the computational space. We present a simple scheme for the minimisation of leakage that can be implemented in cases where interacting spins enclose parallelogram or equilateral triangle loops.