Described is an apparatus which comprises: a 4-state input magnet; a first spin channel region adjacent to the 4-state input magnet; a 4-state output magnet; a second spin channel region adjacent to the 4-state input and output magnets; and a third spin channel region adjacent to the 4-state output magnet. Described in an apparatus which comprises: a 4-state input magnet; a first filter layer adjacent to the 4-state input magnet; a first spin channel region adjacent to the first filter layer; a 4-state output magnet; a second filter layer adjacent to the 4-state output magnet; a second spin channel region adjacent to the first and second filter layers; and a third spin channel region adjacent to the second filter layer.