  Imaginary time evolution is a powerful tool applied in quantum physics, while
existing classical algorithms for simulating imaginary time evolution suffer
high computational complexity as the quantum systems become larger and more
complex. In this work, we propose a probabilistic algorithm for implementing
imaginary time evolution based on non-unitary quantum circuit. We demonstrate
the feasibility of this method by solving the ground state energy of several
quantum many-body systems, including H2, LiH molecules and the quantum Ising
chain. Moreover, we perform experiments on superconducting and trapped ion
cloud platforms respectively to find the ground state energy of H2 and its most
stable molecular structure. We also analyze the successful probability of the
algorithm, which is a polynomial of the output error and introduce an approach
to increase the success probability by rearranging the terms of Hamiltonian.
