  The encoding of qubits in semiconductor spin carriers has been recognised as
a promising approach to a commercial quantum computer that can be
lithographically produced and integrated at scale. However, the operation of
the large number of qubits required for advantageous quantum applications will
produce a thermal load exceeding the available cooling power of cryostats at
millikelvin temperatures. As the scale-up accelerates, it becomes imperative to
establish fault-tolerant operation above 1 kelvin, where the cooling power is
orders of magnitude higher. Here, we tune up and operate spin qubits in silicon
above 1 kelvin, with fidelities in the range required for fault-tolerant
operation at such temperatures. We design an algorithmic initialisation
protocol to prepare a pure two-qubit state even when the thermal energy is
substantially above the qubit energies, and incorporate radio-frequency readout
to achieve fidelities up to 99.34 per cent for both readout and initialisation.
Importantly, we demonstrate a single-qubit Clifford gate fidelity of 99.85 per
cent, and a two-qubit gate fidelity of 98.92 per cent. These advances overcome
the fundamental limitation that the thermal energy must be well below the qubit
energies for high-fidelity operation to be possible, surmounting a major
obstacle in the pathway to scalable and fault-tolerant quantum computation.
