The scaling up of semiconductor quantum dots to two-dimensional arrays is attracting considerable interest for use in large-scale spin-based quantum computation. One of the fundamental technologies to be realized in the two-dimensional arrays of quantum dots is the coherent manipulations of individual electron spins. In this work, we report on a micromagnet design that generates stray magnetic fields that can be used for spin manipulations via electric dipole spin resonance in a 2 × 2 quantum dot array. We consider a micromagnet with lower symmetry than that typically used in the case of linear dot arrays and optimize its dimensions to produce a maximum stray field gradient while maintaining Zeeman splitting differences sufficiently large among the four dots to permit qubit addressability. The optimized field gradient is around 60% smaller than that used in linear dot arrays, but it is still large enough for spin manipulation experiments. Our result represents an important step toward the experimental realization of spin-qubit operations in two-dimensional arrays of quantum dots.

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