A Probabilistic Imaginary Time Evolution Algorithm Based on Non-unitary Quantum Circuit

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.