  Quantum computers promise a highly efficient approach to investigate quantum
phase transitions, which describe abrupt changes between different ground
states of many-body systems. At quantum critical points, the divergent
correlation length and entanglement entropy render the ground state preparation
difficult. In this work, we explore the imaginary-time evolution for probing
the universal critical behavior as the universal information of the ground
state can be extracted in the early-time relaxation process. We propose a
systematic and scalable scheme to probe the universal behaviors via
imaginary-time critical dynamics on quantum computers and demonstrate the
validness of our approach by both numerical simulation and quantum hardware
experiments. With the full form of the universal scaling function in terms of
imaginary time, system size, and circuit depth, we successfully probe the
universality by scaling analysis of the critical dynamics at an early time and
with shallower quantum circuit depth. Equipped with quantum error mitigation,
we also confirm the expected scaling behavior from experimental results on a
superconducting quantum processor which stands as the first experimental
demonstration on universal imaginary-time quantum critical dynamics.
