Time Evolution of Schrödinger’s Equation Using Quantum Phase Estimation and Non-Self-Adjoint Hamiltonian

Quantum computing, leveraging the principles of superposition and entanglement, speeds up the computational process in dynamical systems. Quantum Phase Estimation (QPE) which is a core of many quantum algorithms is an oracle to determine a significant invariant of systems, namely the eigenvalues of the state transition matrix. In addition to showing the scalability of QPE, this paper illustrates the time evolution of phase in the Schrödinger’s equation through Python Code executed in the Qiskit/Aer simulator. In addition, this paper proposes an efficient method for phase estimation of a non-self-adjoint Hamiltonian, which offers great potential in solving complex quantum systems.