Quantum simulation of molecular excited-state manifolds and energies using the TEPID-ADAPT-VQE algorithm

• URL: http://arxiv.org/abs/2606.29547v1
• Date: Sun, 28 Jun 2026 18:21:45 GMT
• Title: Quantum simulation of molecular excited-state manifolds and energies using the TEPID-ADAPT-VQE algorithm
• Abstract summary: Simulation of molecular excited states is a key challenge in quantum chemistry and a promising application for quantum computing.<n>In this work, we investigate the efficacy of the truncated eigenvalue parametrized initial density adaptive variational algorithm (TEPID-ADAPT-VQE) for computing low-lying excited states and potential energy surfaces.<n>We find that both algorithms accurately reproduce excited-state geometries and potential energy curves within chemical accuracy for all the molecules and studied.
• Score: 0.7466390172678973
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The simulation of molecular excited states is a key challenge in quantum chemistry and a promising application for quantum computing. In this work, we investigate the efficacy of the truncated eigenvalue parametrized initial density adaptive variational algorithm (TEPID-ADAPT-VQE) for computing low-lying excited states and potential energy surfaces. TEPID-ADAPT variationally diagonalizes a truncated low-temperature Gibbs state, enabling the simultaneous preparation of multiple excited states within a single optimization. We apply the method to H$_2$, LiH, and linear H$_4$ across bond lengths spanning weakly and strongly correlated regimes. The adaptive derivative-assembled problem-tailored (ADAPT) ansatz construction yields compact circuits suitable for near-term hardware. We also implement a modified version of the MORE-ADAPT-VQE algorithm for comparison with TEPID-ADAPT. We find that both algorithms accurately reproduce excited-state spectra and potential energy curves within chemical accuracy for all the molecules and geometries studied. However, TEPID-ADAPT has the advantage of utilizing only a single, physically motivated hyperparameter (temperature) that controls the energy scale at which excited states are targeted, while MORE-ADAPT utilizes multiple hyperparameters whose optimal values depend sensitively on the target problem. These results demonstrate that combining adaptive ansatz construction with density-matrix-based formulations provides an efficient framework for excited-state quantum chemistry on near-term devices.

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