Quantum simulation through variational approach involving linear combination of unitary operators

Classical computers face difficulties in simulating any quantum system due to the exponential growth in resource requirements with the increase of particles in the problem. We can overcome this difficulty through quantum computers, which have become a reality in the current Noisy Intermediate Scale Quantum Computers (NISQ) era. With the advancement of qubit technology, significant progress has been made in quantum chemistry and recently in nuclear physics. Researchers have started to examine various quantum algorithms such as Quantum Phase estimation (QPE), Variational Quantum Eigensolver (VQE), and Linear Combination of Unitaries (LCU). Among all these, VQE is most popularly used for approximate state preparation and energy calculation which is based on the variational principle. We have used two methods for our work. First, we have used VQE for the ground state energy calculation. Second, we implement the variational approach through LCU to calculate the ground state energy. The expectation value of non-unitary operator is calculated as proposed in herein