The coherent tunnelling of Cooper pairs across Josephson junctions (JJs) generates a nonlinear inductance that is used extensively in quantum information processors based on superconducting circuits, from setting qubit transition frequencies1 and interqubit coupling strengths2 to the gain of parametric amplifiers3 for quantum-limited readout. The inductance is either set by tailoring the metal oxide dimensions of single JJs, or magnetically tuned by parallelizing multiple JJs in superconducting quantum interference devices with local current-biased flux lines. JJs based on superconductor–semiconductor hybrids represent a tantalizing all-electric alternative. The gatemon is a recently developed transmon variant that employs locally gated nanowire superconductor–semiconductor JJs for qubit control4,5. Here we go beyond proof-of-concept and demonstrate that semiconducting channels etched from a wafer-scale two-dimensional electron gas (2DEG) are a suitable platform for building a scalable gatemon-based quantum computer. We show that 2DEG gatemons meet the requirements6 by performing voltage-controlled single qubit rotations and two-qubit swap operations. We measure qubit coherence times up to ~2 μs, limited by dielectric loss in the 2DEG substrate.