Waveform-Memory-Free Polynomial I/Q Envelope Generator for Superconducting Qubit Control

This paper presents a polynomial I/Q envelope generator for superconducting qubit control that requires no waveform lookup table. The architecture computes DRAG-like in-phase and quadrature envelopes from a compact support polynomial, without storing pulse samples. Programmable parameters control pulse duration, in-phase amplitude, and quadrature strength. A 16-bit VHDL implementation on a Zynq UltraScale+ FPGA meets a 500 MHz timing constraint after placement and routing, using 57 LUTs, 20 flip-flops, and 5 DSP blocks. The generated pulse family is compared with Gaussian-DRAG through normalized spectral analysis and closed-system simulations of a three-level transmon. These results characterize the hardware cost and simulated quantum control performance of the proposed generator.