  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.
