Figure 2: A linear array of three equally spaced quantum dots with nearest neighbor exchange interaction implements a NAND gate when placed in a global magnetic field. Spin polarization parallel to the field “upspin” encodes bit 1 and spin polarization antiparallel to the field “downspin” encodes bit 0. The following conditions must be satisfied: (i) the exchange interaction strength must exceed one-half of the Zeeman splitting caused by the global magnetic field and (ii) the local magnetic field used to align input spins must cause a Zeeman splitting in the input dot far greater than the Zeeman splitting due to the global magnetic field.