Variational Quantum Subspace Construction via Symmetry-Preserving Cost Functions
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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_ | 1866909866502651904 |
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| author | Akande, Hamzat A. Perrin, Alexandre Senjean, Bruno Saubanere, Matthieu |
| author_facet | Akande, Hamzat A. Perrin, Alexandre Senjean, Bruno Saubanere, Matthieu |
| contents | Determining low-energy eigenstates in electronic many-body quantum systems is a key challenge in computational chemistry and condensed-matter physics. Hybrid quantum-classical approaches, such as the Variational Quantum Eigensolver and Quantum Subspace Methods, offer practical solutions but face limitations in circuit depth and measurement overhead. In this article, we propose a variational strategy based on symmetry-preserving cost functions to iteratively construct a reduced subspace for the extraction of low-lying energy states. We show that, under certain conditions, our approach leads to a tridiagonal representation similar to that obtained with the Lanczos algorithm. The iterative process allows control over the trade-off between circuit depth, the number of variational parameters, and the number of measurements required to achieve the desired accuracy, making it suitable for current quantum hardware. As a proof of concept, we test the proposed algorithms on H4 chain and ring, targeting both the ground-state energy and the charge gap. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_16915 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Variational Quantum Subspace Construction via Symmetry-Preserving Cost Functions Akande, Hamzat A. Perrin, Alexandre Senjean, Bruno Saubanere, Matthieu Quantum Physics Determining low-energy eigenstates in electronic many-body quantum systems is a key challenge in computational chemistry and condensed-matter physics. Hybrid quantum-classical approaches, such as the Variational Quantum Eigensolver and Quantum Subspace Methods, offer practical solutions but face limitations in circuit depth and measurement overhead. In this article, we propose a variational strategy based on symmetry-preserving cost functions to iteratively construct a reduced subspace for the extraction of low-lying energy states. We show that, under certain conditions, our approach leads to a tridiagonal representation similar to that obtained with the Lanczos algorithm. The iterative process allows control over the trade-off between circuit depth, the number of variational parameters, and the number of measurements required to achieve the desired accuracy, making it suitable for current quantum hardware. As a proof of concept, we test the proposed algorithms on H4 chain and ring, targeting both the ground-state energy and the charge gap. |
| title | Variational Quantum Subspace Construction via Symmetry-Preserving Cost Functions |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2411.16915 |