Comparison of Probabilistic Imaginary-Time Evolution Methods on Quantum and Classical Devices

Imaginary-time evolution is an important technique in tensor network methods and quantum Monte Carlo methods on classical computers, and in recent years its application to quantum computers has also been progressing. In this work, we focus particularly on the Probabilistic Imaginary-Time Evolution (PITE) method. We first derive its formulation within the framework of state-vector-based simulations, compute physical quantities directly from quantum state vectors without statistical errors, and compare the results with those obtained from shot-based simulations. Next, we apply the PITE method to the Heisenberg chain and investigate the optimal initial state for convergence. We also apply it to the transverse-field Ising model on a state-of-the-art ion-trap quantum device to confirm its effectiveness. Finally, we examine the possibility of error mitigation in this model and explore its applicability to NISQ devices.