Fast high-fidelity entangling gates for spin qubits in Si double quantum dots

Implementing high-fidelity two-qubit gates in single-electron spin qubits in silicon double quantum dots is still a major challenge. In this work, we employ analytical methods to design control pulses that generate high-fidelity entangling gates for quantum computers based on this platform. Using realistic parameters and initially assuming a noise-free environment, we present simple control pulses that generate CNOT, CPHASE, and CZ gates with average fidelities greater than 99.99\% and gate times as short as 45 ns. Moreover, using the local invariants of the system's evolution operator, we show that a simple square pulse generates a CNOT gate in less than 27 ns and with a fidelity greater than 99.99\%. Last, we use the same analytical methods to generate two-qubit gates locally equivalent to $\sqrt{\mathrm{CNOT}}$ and $\sqrt{\mathrm{CZ}}$ that are used to implement simple two-piece pulse sequences that produce high-fidelity CNOT and CZ gates in the presence of low-frequency noise.