  Quantum computers are expected to outperform conventional computers for a
range of important problems, from molecular simulation to search algorithms,
once they can be scaled up to large numbers of quantum bits (qubits), typically
millions. For most solid-state qubit technologies, e.g. those using
superconducting circuits or semiconductor spins, scaling poses a significant
challenge as every additional qubit increases the heat generated, while the
cooling power of dilution refrigerators is severely limited at their operating
temperature below 100 mK. Here we demonstrate operation of a scalable silicon
quantum processor unit cell, comprising two qubits confined to quantum dots
(QDs) at $\sim$1.5 Kelvin. We achieve this by isolating the QDs from the
electron reservoir, initialising and reading the qubits solely via tunnelling
of electrons between the two QDs. We coherently control the qubits using
electrically-driven spin resonance (EDSR) in isotopically enriched silicon
$^{28}$Si, attaining single-qubit gate fidelities of 98.6% and coherence time
$T_2^*$ = 2$\mu$s during `hot' operation, comparable to those of spin qubits in
natural silicon at millikelvin temperatures. Furthermore, we show that the unit
cell can be operated at magnetic fields as low as 0.1 T, corresponding to a
qubit control frequency of 3.5 GHz, where the qubit energy is well below the
thermal energy. The unit cell constitutes the core building block of a
full-scale silicon quantum computer, and satisfies layout constraints required
by error correction architectures. Our work indicates that a spin-based quantum
computer could be operated at elevated temperatures in a simple pumped $^4$He
system, offering orders of magnitude higher cooling power than dilution
refrigerators, potentially enabling classical control electronics to be
integrated with the qubit array.
