Efficient Quantum Imaginary Time Evolution by Drifting Real-Time Evolution: An Approach with Low Gate and Measurement Complexity

Abstract

Quantum imaginary time evolution (QITE) is one of the promising candidates for finding the eigenvalues and eigenstates of a Hamiltonian on a quantum computer. However, the original proposal suffers from large circuit depth and measurements due to the size of the Pauli operator pool and Trotterization. To alleviate the requirement for deep circuits, we propose a time-dependent drifting scheme inspired by the qDRIFT algorithm [Campbell, E. Phys. Rev. Lett. 2019, 123, 070503]. We show that this drifting scheme removes the depth dependency on the size of the operator pool and converges inversely with respect to the number of steps. We further propose a deterministic algorithm that selects the dominant Pauli term to reduce the fluctuation for the ground state preparation. We also introduce an efficient measurement reduction scheme across Trotter steps that removes its cost dependence on the number of iterations. We analyze the main source of error for our scheme both theoretically and numerically. We numerically test the validity of depth reduction, convergence performance of our algorithms, and the faithfulness of the approximation for our measurement reduction scheme on several benchmark molecules. In particular, the results on the LiH molecule give circuit depths comparable to that of the advanced adaptive variational quantum eigensolver (VQE) methods while requiring much fewer measurements.