Cancellation of spin-orbit effects in quantum gates based on the exchange coupling in quantum dots

The effects of the spin-orbit interaction on quantum gate operations based on the spin exchange coupling were studied. The electron spin in a quantum dot or a similar nanostruture was employed to represent the qubit. Results showed the exact cancellation of the spin-orbit effects in the sequence producing the quantum XOR gate for the ideal case where the pulse shapes of the exchange and spin-orbit interactions were identical. For the nonideal case, the gate error was suppressed by two small parameters, the deviation of the two pulse shapes and the spin-orbit constant. Small errors in the XOR gate were noticed due to the dipole-dipole interactions.