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We design and analyze a logical qubit composed of a linear array of electronspins in semiconductor quantum dots. To avoid the difficulty of fullycontrolling a two-dimensional array of dots, we adapt spin control and errorcorrection to a one-dimensional line of silicon quantum dots. Control speed andefficiency are maintained via a scheme in which electron spin states arecontrolled globally using broadband microwave pulses for magnetic resonancewhile two-qubit gates are provided by local electrical control of the exchangeinteraction between neighboring dots. Error correction with two-, three-, andfour-qubit codes is adapted to a linear chain of qubits with nearest-neighborgates. We estimate an error correction threshold of 1e-4. Furthermore, wedescribe a sequence of experiments to validate the methods on near-term devicesstarting from four coupled dots.

A logical qubit in a linear array of semiconductor quantum dots