This article presents the first cryogenic phase-locked loop (PLL) operating at 4.2 K. The PLL is designed for the control system of scalable quantum computers. The specifications of PLL are derived from the required control fidelity for a single-qubit operation. By considering the benefits and challenges of cryogenic operation, a dedicated analog PLL structure is used so as to maintain high performance from 300 to 4.2 K. The PLL incorporates a dynamic-amplifier-based charge-domain sub-sampling phase detector (PD), which simultaneously achieves low phase noise (PN) and low reference spur, thanks to its high phase-detection gain and minimized periodic disturbances on the voltage-controlled oscillator (VCO) control. Fabricated in a 40-nm CMOS process, the PLL achieves -78.4-dBc reference spur, 75-fs rms jitter, and 4-mW power consumption at 300 K when generating a 10-GHz carrier, leading to a -256.5-dB jitter-power FOM. At 4.2 K, the PLL synthesizes 9.4-to 11.6-GHz tones with an rms jitter of 37 fs and a reference spur of -69 dBc while consuming 2.7 mW at 10 GHz.