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.
@article{arxiv.1608.06335,
title = {A logical qubit in a linear array of semiconductor quantum dots},
author = {Cody Jones and Michael A. Fogarty and Andrea Morello and Mark F. Gyure and Andrew S. Dzurak and Thaddeus D. Ladd},
journal= {arXiv preprint arXiv:1608.06335},
year = {2018}
}