Helium States in a CAS(2,2) Subspace Inspired by Quantum Photonics
Abstract
We present a four-mode Fock-state photonics implementation of the variational quantum deflation (VQD) algorithm to calculate the ground-state and excited-state energies for the neutral helium atom in a CAS(2,2) Subspace. Its CAS(2,2) electronic Hilbert space is encoded into a bosonic Fock-space representation and subsequently optimized using a continuous-variable quantum circuit. The circuit architecture under study is constructed of single-mode phase shifts, beam splitters, and cross-Kerr interactions. The variational circuit is initialized in the Fock state ket1100 and its performance is benchmarked against exact diagonalization of the active-space configuration-interaction (CASCI) Hamiltonian. We also extend the method to optimize from the first to three excited states of the helium atom with the aid of the variational quantum deflation (VQD) method in a CAS(2,2). We then investigate the performance of this circuit architecture as a basis for implementing the VQD method. In the ideal noiseless simulation setting, we see that the survival probability of the ground and the excited states within the target CAS subspace is unity, because the total photon number and the photon number in the two spin sectors α and β are preserved. We demonstrate that the proposed approach enables the determination of the ground and excited-state energies within the CAS(2,2) electronic Hilbert space using a continuous-variable quantum circuit and the variational quantum deflation (VQD) algorithm, while satisfying the orthogonality conditions with negligible errors.
Related
- Optical Schrödinger cat states generated using cavity Rydberg quantum photonics
- Quantum Chaos and Spread of States in Krylov Subspace: A Topical Review
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- Asymptotics of Ground States for Helium-Like and Bosonic Atoms in a Two-Cluster Region
BibTeX
@misc{mirmasoudi2026helium,
title = {{Helium States in a CAS(2,2) Subspace Inspired by Quantum Photonics}},
author = {Forouzan Mirmasoudi and Badie Ghavami},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06448},
eprint = {2611.06448},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06448},
}
RIS
TY - UNPB
TI - Helium States in a CAS(2,2) Subspace Inspired by Quantum Photonics
AU - Forouzan Mirmasoudi
AU - Badie Ghavami
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06448
UR - https://arxiv.org/abs/2611.06448
AB - We present a four-mode Fock-state photonics implementation of the variational quantum deflation (VQD) algorithm to calculate the ground-state and excited-state energies for the neutral helium atom in a CAS(2,2) Subspace. Its CAS(2,2) electronic Hilbert space is encoded into a bosonic Fock-space representation and subsequently optimized using a continuous-variable quantum circuit. The circuit architecture under study is constructed of single-mode phase shifts, beam splitters, and cross-Kerr interactions. The variational circuit is initialized in the Fock state ket1100 and its performance is benchmarked against exact diagonalization of the active-space configuration-interaction (CASCI) Hamiltonian. We also extend the method to optimize from the first to three excited states of the helium atom with the aid of the variational quantum deflation (VQD) method in a CAS(2,2). We then investigate the performance of this circuit architecture as a basis for implementing the VQD method. In the ideal noiseless simulation setting, we see that the survival probability of the ground and the excited states within the target CAS subspace is unity, because the total photon number and the photon number in the two spin sectors α and β are preserved. We demonstrate that the proposed approach enables the determination of the ground and excited-state energies within the CAS(2,2) electronic Hilbert space using a continuous-variable quantum circuit and the variational quantum deflation (VQD) algorithm, while satisfying the orthogonality conditions with negligible errors.
ER -