We demonstrate how gradient ascent pulse engineering optimal control methods can be implemented ondonor-electron-spin qubits in Si semiconductors with an architecture complementary to the original Kane'sproposal. We focus on the high-fidelity-controlled-NOT (cNoT) gate and explicitly find its digitized controlsequences by optimizing its fidelity over the external controls of the hyperfine A and exchange J interactions.This high-fidelity-cNoT gate has an error of about 10-6, below the error threshold required for fault-tolerantquantum computation, and its operation time of 100 ns is about three times faster than 297 ns of theproposed global control scheme. It also relaxes significantly the stringent distance constraint of twoneighboring donor atoms of 10-20 nm as reported in the original Kane's proposal to about 30 nm in whichsurface A and J gates may be built with current fabrication technology. The effects of the control voltagefluctuations, the dipole-dipole interaction, and the electron-spin decoherence on the CNOT gate fidelity are alsodiscussed.
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