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Quantum computation requires high-fidelity single-qubit and two-qubit gateson a scalable platform. Silicon spin qubits are a promising platform towardrealization of this goal. In this paper we show how to perform single-qubit andCZ gates in a linear chain of three spin qubits with always-on exchangecoupling, which is relevant for certain dot- and donor-based silicon devices.We also show how to make the CZ gate robust against both charge noise and pulselength error using a two-tone pulse shaping method. The robust pulse maintainsa fidelity of 99.99% at 3.5% fluctuations in exchange or pulse amplitude, whichis an improvement over the uncorrected pulses where this fidelity can only bemaintained for fluctuations in exchange up to 2% or up to 0.2% in amplitude.

Single-tone pulse sequences and robust two-tone shaped pulses for three silicon spin qubits with always-on exchange