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

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