Scalable Ground-State Certification of Quantum Spin Systems via Structured Noncommutative Polynomial Optimization
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866918425294536704 |
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| author | Wang, Jie Jansen, David Frerot, Irénée Renou, Marc-Olivier Magron, Victor Acín, Antonio |
| author_facet | Wang, Jie Jansen, David Frerot, Irénée Renou, Marc-Olivier Magron, Victor Acín, Antonio |
| contents | A fundamental challenge in quantum physics is determining the ground-state properties of many-body systems. Whereas standard approaches, such as variational calculations, consist of writing down a wave function ansatz and minimizing over the possible states expressible by this ansatz, one can alternatively formulate the problem as a noncommutative polynomial optimization problem. This optimization problem can then be addressed using a hierarchy of semidefinite programming relaxations. In contrast to variational calculations, the semidefinite program can provide lower bounds for ground state energies and upper and lower bounds on observable expectation values. However, this approach typically suffers from severe scalability issues, limiting its applicability to small-to-medium-scale systems. In this article, we demonstrate that leveraging the inherent structures of the system can significantly mitigate these scalability challenges and thus allows us to compute meaningful bounds for quantum spin systems on up to $16\times16$ square lattices. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_01555 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Scalable Ground-State Certification of Quantum Spin Systems via Structured Noncommutative Polynomial Optimization Wang, Jie Jansen, David Frerot, Irénée Renou, Marc-Olivier Magron, Victor Acín, Antonio Quantum Physics Optimization and Control 90C23, 81-08, 47N10 A fundamental challenge in quantum physics is determining the ground-state properties of many-body systems. Whereas standard approaches, such as variational calculations, consist of writing down a wave function ansatz and minimizing over the possible states expressible by this ansatz, one can alternatively formulate the problem as a noncommutative polynomial optimization problem. This optimization problem can then be addressed using a hierarchy of semidefinite programming relaxations. In contrast to variational calculations, the semidefinite program can provide lower bounds for ground state energies and upper and lower bounds on observable expectation values. However, this approach typically suffers from severe scalability issues, limiting its applicability to small-to-medium-scale systems. In this article, we demonstrate that leveraging the inherent structures of the system can significantly mitigate these scalability challenges and thus allows us to compute meaningful bounds for quantum spin systems on up to $16\times16$ square lattices. |
| title | Scalable Ground-State Certification of Quantum Spin Systems via Structured Noncommutative Polynomial Optimization |
| topic | Quantum Physics Optimization and Control 90C23, 81-08, 47N10 |
| url | https://arxiv.org/abs/2604.01555 |