Simuleringar av mångpartikelsystem på en emulerad kvantdator

Abstract

In this study we apply the Variational Quantum Eigensoler (VQE) algorithm on an emulated quantum computer to solve for the ground state energy in the Lipkin model, using software developed by Rigetti Computing. The variational parameters are optimized with the Nelder- Mead algorithm as well as a Bayesian optimization algorithm. By exploiting the quasi-spinn symmetry of the Hamiltonian, we reduce the dimension of the Hamiltonian matrix, and subsequently apply the VQE algorithm on up to 4 × 4-matrices, corresponding to a seven-particle Lipkin model. Furthermore, we construct tailored ansätze and compare them to the established Unitary Coupled-Cluster ansatz. Using the best found combination of optimization algorithm, ansatz and number of samples on the Quantum Virtual Machine (QVM) per function evaluation, we determine the ground state energy given a total amount of 3 million measurements on the QVM for different values of the interaction parameter V/ . We conclude that both the Nelder-Mead and Bayesian optimization algorithm are able to calculate the ground state energy for the seven-particle Lipkin model within 1.2% and 0.7% of the analytical energy, respectively. Furthermore, the Bayesian optimization algorithm performs much better for a lower number of total measurements on the QVM while for a higher number the Nelder-Mead algorithm exhibits a more stable behaviour. Therefore we predict that a combination of the two optimization algorithms might be more efficient than using each on their own.