  Electronic systems for qubit control and measurement serve as a bridge
between quantum programming language and quantum information processors. With
the rapid development of superconducting quantum circuit (SQC) technology,
synchronization in a large-scale system, low-latency execution, and low noise
are required for electronic systems. Here, we present a field-programmable gate
array (FPGA)-based electronic system with a distributed synchronous clock and
trigger architecture. The system supports synchronous control of qubits with
jitters of approximately 5 ps. We implement a real-time digital signal
processing system in the FPGA, enabling precise timing control, arbitrary
waveform generation, IQ demodulation for qubit state discrimination, and the
generation of real-time qubit-state-dependent trigger signals for
feedback/feedforward control. The hardware and firmware low-latency design
reduces the feedback/feedforward latency of the electronic system to 125 ns,
significantly less than the decoherence times of the qubit. Finally, we
demonstrate the functionalities and low-noise performance of this system using
a fluxonium quantum processor.
