Addressing the advancement toward large-scale quantum computers, this article presents the first four-level pulse amplitude modulation (PAM4) wireline transmitter (TX) operating at cryogenic temperatures (CTs). With quantum computers scaling up toward thousands of quantum bits (qubits), but having too limited fidelity for robust operation, continuous rounds of quantum error correction (QEC) are necessary. However, QEC requires a large amount of data to be transferred from a cryogenic controller at 4 K to a classical processor at room temperature (RT). To bridge the gap, a high-speed data link between the quantum processor at CT and the classical counterpart at RT is needed. The proposed PAM4 TX architecture integrates a low-power 64:4 serializer structure, a high-speed 4:1 currentmode logic (CML) multiplexer, and a linear 6-bit digital-to-analog converter (DAC). Considering the challenges and benefits of CMOS operating at CTs, the TX architecture and circuitry are designed to exploit the maximum speed, while maintaining sufficient linearity. The fabricated 40-nm CMOS chip achieves a data rate of 40-Gb/s (36-Gb/s), an energy efficiency of 2.46 pJ/b (2.47 pJ/b), and 97.8% (96.6%) ratio of level mismatch (RLM) at CT (RT). While demonstrating an energy efficiency comparable to prior-art TXs in more advanced CMOS nodes at RT, the broad operating temperature of the proposed TX enables the required high-speed wireline link for large-scale quantum computers.