Excited States from ADAPT-VQE convergence path in Many-Body Problems: application to nuclear pairing problem and $H_4$ molecule dissociation

• URL: http://arxiv.org/abs/2506.22275v1
• Date: Fri, 27 Jun 2025 14:45:01 GMT
• Title: Excited States from ADAPT-VQE convergence path in Many-Body Problems: application to nuclear pairing problem and $H_4$ molecule dissociation
• Authors: Jing Zhang, Denis Lacroix,
• Abstract summary: A quantum computing algorithm is proposed to obtain low-lying excited states in many-body interacting systems.<n>The approximate eigenstates are obtained by using a quantum space diagonalization method in a subspace of states selected from the convergence path of the ADAPT-VQE.
• Score: 6.5877766193350675
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A quantum computing algorithm is proposed to obtain low-lying excited states in many-body interacting systems. The approximate eigenstates are obtained by using a quantum space diagonalization method in a subspace of states selected from the convergence path of the ADAPT-VQE (adaptive derivative-assembled pseudo-Trotter Ansatz variational quantum eigensolver) towards the ground state of the many-body problem. This method is shown to be accurate with only a small overhead in terms of quantum resources required to get the ground state. We also show that the quantum algorithm might be used to facilitate the convergence of the ADAPT-VQE method itself. Successful applications of the technique are made to like-particle pairing as well as neutron-proton pairing. Finally, the $H_4$ molecule's dissociation also illustrates the technique, demonstrating its accuracy and versatility.

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