Interference Engineering for Quantum Imaginary-Time Evolution through Multiple Energy Shifts

Abstract

Energy shifting is usually trivial in imaginary-time evolution because it changes only the normalization of the evolved state. On a quantum computer, however, imaginary-time evolution can be implemented as a coherent or sampled superposition of real-time evolutions, in which energy shifts generate relative phases that can interfere. Here we introduce multi-shift quantum imaginary-time evolution (MS-QITE), which uses a distribution of energy shifts to engineer this interference and optimize different implementations. In a Monte Carlo realization, multi-shift reshapes the normalized sampling distribution and concentrates it within a shorter real-time window, thereby reducing the typical Hamiltonian-evolution time and improving the stability of ground-state-energy estimation. In a continuous-variable-assisted realization, it enables projection onto a state supported over a finite quadrature interval, substantially reducing the required squeezing over an intermediate temperature range while retaining accurate thermal-state preparation. Numerical results for transverse-field Ising models demonstrate that energy shifts provide an interference-based degree of freedom for optimizing quantum imaginary-time evolution.