Implementation of an error-corrected quantum computer is believed to require a quantum processor with a million or more physical qubits, and, in order to run such a processor, a quantum control system of similar scale will be required. Such a controller will need to be integrated within the cryogenic system and in close proximity with the quantum processor in order to make such a system practical. Here, we present a prototype cryogenic CMOS quantum controller designed in a 28-nm bulk CMOS process and optimized to implement a 16-word (4-bit) XY gate instruction set for controlling transmon qubits. After introducing the transmon qubit, including a discussion of how it is controlled, design considerations are discussed, with an emphasis on error rates and scalability. The circuit design is then discussed. Cryogenic performance of the underlying technology is presented, and the results of several quantum control experiments carried out using the integrated controller are described. This article ends with a comparison to the state of the art and a discussion of further research to be carried out. It has been shown that the quantum control IC achieves promising performance while dissipating less than 2 mW of total ac and dc power and requiring a digital data stream of less than 500 Mb/s.