Simuleringar av mångpartikelsystem på en emulerad kvantdator
Simuleringar av mångpartikelsystem på en emulerad kvantdator
Typ
Examensarbete för kandidatexamen
Program
Publicerad
2019
Författare
Holmin, Sebastian
Eklind, Carl
Karlsson, Joel
Nathanson, Axel
Nilsson, Eric
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
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.
Beskrivning
Ämne/nyckelord
Quantum Computing, VQE, Lipkin Model, Nelder-Mead, Bayesian optimization, UCC, many-body theory, Rigetti Computing