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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.

Nucleus is a typical many-body quantum system. Full calculation of a nuclear system in a classical computer is far beyond the capacity of current classical computers. With fast development of hardware, the prospect of using quantum computers in nuclear physics is closing. Here, we report a full quantum package, QCSH, for solving nuclear shell-model in a quantum computer. QCSH uses the linear combination of unitaries formalism of quantum computing, and performs all calculations in a quantum computer. The complexities of qubit resource, number of basic gates of QCSH, are both polynomial to the nuclear size. QCSH can already provide meaningful results in the near term. As examples, the binding energies of twelve light nuclei, $^{2}$H, $^{3}$H, $^{3}$He, $^{4}$He, $^{6}$Li, $^{7}$Li, $^{12}$C, $^{14}$N, $^{16}$O, $^{17}$O, $^{23}$Na and $^{40}$Ca are calculated using QCSH in a classical quantum emulator. The binding energy of Deuteron has already been experimentally studied using QCSH on a superconducting quantum computing device. QCSH not only works in near-term quantum devices, but also in future large-scale quantum computers. With the development of quantum devices, nuclear system constitutes another promising area for demonstrating practical quantum advantage.