  We design and analyze a logical qubit composed of a linear array of electron
spins in semiconductor quantum dots. To avoid the difficulty of fully
controlling a two-dimensional array of dots, we adapt spin control and error
correction to a one-dimensional line of silicon quantum dots. Control speed and
efficiency are maintained via a scheme in which electron spin states are
controlled globally using broadband microwave pulses for magnetic resonance
while two-qubit gates are provided by local electrical control of the exchange
interaction between neighboring dots. Error correction with two-, three-, and
four-qubit codes is adapted to a linear chain of qubits with nearest-neighbor
gates. We estimate an error correction threshold of 1e-4. Furthermore, we
describe a sequence of experiments to validate the methods on near-term devices
starting from four coupled dots.
