Imaginary time evolution of a quantum system through analytic continuation from real-time quantum simulation

How can quantum computers perform imaginary-time evolution (ITE), which is crucial for preparing eigenstates and avoiding classical sign problems, without directly implementing difficult nonunitary operations?

The authors derive an analytic continuation formula that expresses the nonunitary ITE operator as an integral over real-time evolution operators weighted by a spectral filter. This approach relies on knowing a lower bound on the ground state energy of a Hermitian Hamiltonian. By evaluating real-time matrix elements at discrete time points and applying integration techniques such as gaussian quadrature, the desired ITE matrix elements are approximated. The method is tested on classical diffusion processes via 1D Fokker-Planck equations and 1D quantum mechanical scattering, with small-scale hardware demonstrations executed on IBM quantum processors.

Analytic continuation successfully reproduces exact imaginary-time evolution results across the studied 1D physical systems. Numerical simulations and quantum hardware tests demonstrate that real-time correlation functions can be reliably transformed to yield accurate imaginary-time observables and probability distributions. Although finite integration cutoffs introduce systematic errors, increasing the cutoff and tightening the ground state energy bound systematically improves the convergence toward exact solutions.

This technique bridges real-time quantum simulations and imaginary-time calculations, offering a practical pathway for quantum hardware to tackle tasks like ground-state preparation and thermal or diffusive statistical mechanics without requiring complex nonunitary gate constructions.