Nonlocal approximation toward implementation of quantum imaginary-time evolution method on NISQ devices

In quantum many-body problems, the imaginary-time evolution method is a well known approach to obtain the ground state on classical computers. A recent proposed imaginary-time evolution (QITE) method on quantum computers is expected to solve problems faster than classical computers [1], however, its implementation on noisy intermediate-scale quantum (NISQ) devices is difficult due to the depth of the circuits. We propose two methods to overcome this problem [2]: the first is a nonlocal approximation method removing the locality condition imposed when transforming the imaginary-time evolution operator into a unitary operator in the QITE method; the second is a compression method of the quantum circuit for imaginary-time steps. We show that the introducing the nonlocal approximation and compression methods can significantly reduce the accumulation of errors attributed to deep circuit depth, paving the way for the implementation of the QITE method on NISQ devices.

[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, Nature Physics, 16, 205, (2020).
[2] H. Nishi, T. Kosugi, and Y-i. Matsushita, arXiv2005.12715 (2020).