A superconducting waveform synthesizer produces an arbitrary waveform and includes an encoder that produces a bitstream; a pattern generator that produces a current bias pulse from the bitstream; a Josephson junction that produces a quantized output pulse from the current bias pulse; and a converter that produces an arbitrary waveform from the quantized output pulse. A process for producing an arbitrary waveform includes producing a bitstream; producing a current bias pulse from the bitstream; communicating the current bias pulse to a Josephson junction; producing, by the Josephson junction, a quantized output pulse from the current bias pulse; producing a quantized output pulse from the current bias pulse; and producing an arbitrary waveform from the quantized output pulse.