Weighted Subspace Search VQE to find Kth excited-state energies
Generally, The variational quantum eigensolver (VQE) is used for finding the ground state energy for a given hamiltonian. To find the kth excited state energy of the hamiltonian we would need to run the VQE optimization process for atleast k+1 time. Not to mention each time we 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.
This is where the idea of Subspace Search VQE (SSVQE) comes in. The algorithm is used to find kth excited-state energy of a hamiltonian in just two subsequent optimization processes. The original research about the development of SSVQE is given in this paper. But, can we do better? Yes, the research shows that using the weights as hyperparameters we can find the kth excited-state energy in just a single optimization process. This is a more generalised version of SSVQE namely, Weighted SSVQE and it will be the centre of our focus in this project. There are two variants of this algorithm:
1) Weighted SSVQE to find kth excited state energy.
2) Weighted SSVQE to find all energies up to the kth excited state.
Team Name:
Parmanu
Project Description:
Weighted Subspace Search VQE to find Kth excited-state energies
Generally, The variational quantum eigensolver (VQE) is used for finding the ground state energy for a given hamiltonian. To find the kth excited state energy of the hamiltonian we would need to run the VQE optimization process for atleast k+1 time. Not to mention each time we 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.
This is where the idea of Subspace Search VQE (SSVQE) comes in. The algorithm is used to find kth excited-state energy of a hamiltonian in just two subsequent optimization processes. The original research about the development of SSVQE is given in this paper. But, can we do better? Yes, the research shows that using the weights as hyperparameters we can find the kth excited-state energy in just a single optimization process. This is a more generalised version of SSVQE namely, Weighted SSVQE and it will be the centre of our focus in this project. There are two variants of this algorithm:
1) Weighted SSVQE to find kth excited state energy.
2) Weighted SSVQE to find all energies up to the kth excited state.
Presentation:
Presentation Video
Source code:
Github Repository
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