Solving Eigenvalue Problem with Analog Quantum Phase Estimation

Determining eigenvalues is a central challenge in quantum mechanics, crucial for understanding the behavior of quantum many-body systems. Classical methods for calculating the eigenenergies of a Hamiltonian are computationally intensive, while quantum computers offer a more efficient alternative through Quantum Phase Estimation (QPE). However, implementing QPE on digital quantum computers often requires Trotterization, a process made impractical by the noise and hardware limitations of current quantum devices, which restrict the number of viable Trotter steps. In this work, we propose an analog approach to simulating QPE that bypasses the need for Trotterization and can be implemented using circuit Quantum Electrodynamics (cQED) systems. This method not only enhances the practical potential of quantum computing but also introduces a novel framework for solving eigenvalue problems in quantum many-body systems, opening new pathways for advancements in quantum mechanics.