Solving ground state energy of symmetric Hamiltonian by symmetric VQE
In this paper, a symmetric Variational Quantum Eigensolver (VQE) algorithm is introduced to solve the ground state energy of symmetric Hamiltonian efficiently. As the symmetry of Hamiltonian is always broken by the typical VQE, hence the symmetric VQE proposed here is to increase the efficiency of t...
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sg-ntu-dr.10356-1485702023-02-28T23:16:16Z Solving ground state energy of symmetric Hamiltonian by symmetric VQE Soo, Chee Xian Gu Mile School of Physical and Mathematical Sciences gumile@ntu.edu.sg Science::Physics In this paper, a symmetric Variational Quantum Eigensolver (VQE) algorithm is introduced to solve the ground state energy of symmetric Hamiltonian efficiently. As the symmetry of Hamiltonian is always broken by the typical VQE, hence the symmetric VQE proposed here is to increase the efficiency of the VQE when solving the symmetric Hamiltonian by preserving the symmetry. This scheme makes use of the fact that when the unitaries are commuted with the symmetry projection operator, the transformations by the unitaries are always in the symmetric subspace. This narrows down the searching space from the whole Hilbert space to the symmetric subspace. Since the searching is done within the symmetric subspace, the initial input state must also in the symmetric subspace. By using this scheme to solve the ground state energy of the symmetric ising model, the number of parameters needed for optimization is lesser when compared to a similar circuit structure which does not preserve the symmetry. Bachelor of Science in Physics 2021-05-06T05:37:35Z 2021-05-06T05:37:35Z 2021 Final Year Project (FYP) Soo, C. X. (2021). Solving ground state energy of symmetric Hamiltonian by symmetric VQE. Final Year Project (FYP), Nanyang Technological University, Singapore. https://hdl.handle.net/10356/148570 https://hdl.handle.net/10356/148570 en application/pdf Nanyang Technological University |
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Science::Physics Soo, Chee Xian Solving ground state energy of symmetric Hamiltonian by symmetric VQE |
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In this paper, a symmetric Variational Quantum Eigensolver (VQE) algorithm is introduced to solve the ground state energy of symmetric Hamiltonian efficiently. As the symmetry of Hamiltonian is always broken by the typical VQE, hence the symmetric VQE proposed here is to increase the efficiency of the VQE when solving the symmetric Hamiltonian by preserving the symmetry. This scheme makes use of the fact that when the unitaries are commuted with the symmetry projection operator, the transformations by the unitaries are always in the symmetric subspace. This narrows down the searching space from the whole Hilbert space to the symmetric subspace. Since the searching is done within the symmetric subspace, the initial input state must also in the symmetric subspace. By using this scheme to solve the ground state energy of the symmetric ising model, the number of parameters needed for optimization is lesser when compared to a similar circuit structure which does not preserve the symmetry. |
author2 |
Gu Mile |
author_facet |
Gu Mile Soo, Chee Xian |
format |
Final Year Project |
author |
Soo, Chee Xian |
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Soo, Chee Xian |
title |
Solving ground state energy of symmetric Hamiltonian by symmetric VQE |
title_short |
Solving ground state energy of symmetric Hamiltonian by symmetric VQE |
title_full |
Solving ground state energy of symmetric Hamiltonian by symmetric VQE |
title_fullStr |
Solving ground state energy of symmetric Hamiltonian by symmetric VQE |
title_full_unstemmed |
Solving ground state energy of symmetric Hamiltonian by symmetric VQE |
title_sort |
solving ground state energy of symmetric hamiltonian by symmetric vqe |
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Nanyang Technological University |
publishDate |
2021 |
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https://hdl.handle.net/10356/148570 |
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1759856365796327424 |