Anisotropic spin exchange in pulsed quantum gates

The effects of anisotropic corrections due to spin-orbit coupling on quantum gates produced by pulsing the exchange interaction between two spin-1/2 qubits were studied. These quantum gates were parametrized by an effective Hamiltonian that commutes with itself at different times and produces the same quantum gate as a given pulse. Expressions for the various parameters in this effective Hamiltonian were obtained perturbatively in powers of spin-orbit coupling and used to shape pulses that effectively eliminate first-order spin-orbit corrections to quantum gates.