Jay-Patel-257/Qhack-2022

The variational quantum eigensolver (VQE) is generally used for finding the ground state energy of a given hamiltonian. To find the kth excited state energy of the hamiltonian we need to run the VQE optimization process at least k+1 times. Each time we also need to calculate the hamiltonian again, taking into account the state of the previous iteration. Even after that, the accuracy decreases as the value of k increases. The Subspace Search VQE (SSVQE) algorithm is used to find the kth excited-state energy of a hamiltonian in two subsequent optimization processes. Research on a more generalized version of SSVQE, namely Weighted SSVQE, shows that by using the weights as hyperparameters we can find the kth excited-state energy in just a single optimization process. There are two variants of this algorithm: Weighted SSVQE to find kth excited state energy, and weighted SSVQE to find all energies up to the kth excited state.

Jupyter NotebookMIT