  Single flux quantum (SFQ) circuitry is a promising candidate for a scalable
and integratable cryogenic quantum control system. However, the operation of
SFQ circuits introduces non-equilibrium quasiparticles (QPs), which are a
significant source of qubit decoherence. In this study, we investigate QP
behavior in a superconducting quantum-classical hybrid chip that comprises an
SFQ circuit and a qubit circuit. By monitoring qubit relaxation time, we
explore the dynamics of SFQ-circuit-induced QPs. Our findings reveal that the
QP density near the qubit reaches its peak after several microseconds of SFQ
circuit operation, which corresponds to the phonon-mediated propagation time of
QPs in the hybrid circuits. This suggests that phonon-mediated propagation
dominates the spreading of QPs in the hybrid circuits. Our results lay the
foundation to suppress QP poisoning in quantum-classical hybrid systems.
