Determining Hamiltonian eigenstates on a quantum computer using quantum imaginary time evolution

The accurate computation of Hamiltonian ground and excited states on quantum computers stands to impact many problems in the physical and computer sciences, from quantum simulation to machine learning. Given the challenges posed in constructing large-scale quantum computers, these tasks should be carried out in a resource-efficient way. We recently introduced [1] the quantum imaginary time evolution and quantum Lanczos algorithms, which are analogues of classical algorithms for finding ground and excited states. Compared with their classical counterparts, they require exponentially less space and time per iteration, and can be implemented without deep circuits and ancillae, or high-dimensional optimizations. We discuss applications to spins and fermions.

[1] M. Motta, C. Sun, A. T. K. Tan, M. J. O'Rourke, E. Ye, A. J. Minnich, F. G. S. L. Brandao and G. K.-L. Chan, arXiv:1901.07653