Molecular Ground State Simulation by Subspace Restriction and Hund's Rule
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866911736952520704 |
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| author | Chiang, Tsung-Chi Ku, Calvin Chou, Jyh-Pin Hu, Alice Chen, Peng-Jen Lai, Ching-Jui |
| author_facet | Chiang, Tsung-Chi Ku, Calvin Chou, Jyh-Pin Hu, Alice Chen, Peng-Jen Lai, Ching-Jui |
| contents | Simulation of molecular ground states on near-term quantum hardware is constrained by qubit availability and the cost of variational optimization. To address these challenges, the Subspace Restriction Scheme (SRS) is introduced as a mathematical framework that projects the molecular Hamiltonian onto a selected Fock subspace prior to qubit encoding. By enforcing molecular multiplicity and a generalized Hund's rule, the Multi-Hund Subspace (MHS) is constructed. This physically motivated restriction significantly reduces the effective Fock-space dimension, asymptotically saving $N$ qubits for a Hamiltonian of $M$ spatial orbitals and $N$ electrons. As a result, we successfully overcome classical memory bottlenecks and enable simulations of large systems, such as the $H_{22}$ chain, which requires 44 qubits under standard Jordan-Wigner (JW) encoding. While the strict pairing structure may limit accuracy in strongly correlated dissociation regimes, MHS effectively captures the essential low-energy physics of closed-shell molecules near equilibrium. In Variational Quantum Eigensolver (VQE) benchmarks, MHS enhances optimization behaviour and achieves high accuracy with a shallow ansatz. These findings demonstrate that physically motivated subspace restriction offers an effective approach to more resource-efficient quantum-chemistry simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03268 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Molecular Ground State Simulation by Subspace Restriction and Hund's Rule Chiang, Tsung-Chi Ku, Calvin Chou, Jyh-Pin Hu, Alice Chen, Peng-Jen Lai, Ching-Jui Quantum Physics Simulation of molecular ground states on near-term quantum hardware is constrained by qubit availability and the cost of variational optimization. To address these challenges, the Subspace Restriction Scheme (SRS) is introduced as a mathematical framework that projects the molecular Hamiltonian onto a selected Fock subspace prior to qubit encoding. By enforcing molecular multiplicity and a generalized Hund's rule, the Multi-Hund Subspace (MHS) is constructed. This physically motivated restriction significantly reduces the effective Fock-space dimension, asymptotically saving $N$ qubits for a Hamiltonian of $M$ spatial orbitals and $N$ electrons. As a result, we successfully overcome classical memory bottlenecks and enable simulations of large systems, such as the $H_{22}$ chain, which requires 44 qubits under standard Jordan-Wigner (JW) encoding. While the strict pairing structure may limit accuracy in strongly correlated dissociation regimes, MHS effectively captures the essential low-energy physics of closed-shell molecules near equilibrium. In Variational Quantum Eigensolver (VQE) benchmarks, MHS enhances optimization behaviour and achieves high accuracy with a shallow ansatz. These findings demonstrate that physically motivated subspace restriction offers an effective approach to more resource-efficient quantum-chemistry simulations. |
| title | Molecular Ground State Simulation by Subspace Restriction and Hund's Rule |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2404.03268 |