Product-State Approximation Algorithms for the Transverse Field Ising Model
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| author | Lipardi, Vincenzo Mestel, David Stamoulis, Georgios |
| author_facet | Lipardi, Vincenzo Mestel, David Stamoulis, Georgios |
| contents | We study classical polynomial-time approximation algorithms for the transverse-field Ising model (TFIM) Hamiltonian, allowing a mixture of ferromagnetic and anti-ferromagnetic interactions between pairs of qbits, alongside transverse field terms with arbitrary non-negative weights.
Our main results are a series of approximation algorithms (all approximation ratios with respect to the true quantum optimum): (i) a simple maximum of two product state rounding algorithm achieving an approximation ratio $γ\approx 0.71$ , (ii) a strengthened rounding, inspired by the anticommutation property of the two $X_i, Z_iZ_j$ observables achieving ratio $γ\approx 0.7860$, and (iii) a further improvement by interpolation achieving ratio $γ\approx 0.8156$. We also give an explicit (purely ferromagnetic) TFIM instance on three qbits for which every product state achieves at most $169/180\approx 0.9389$ of the true optimum, yielding an upper bound for all algorithms producing product state approximations, even in the purely ferromagnetic case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_13106 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Product-State Approximation Algorithms for the Transverse Field Ising Model Lipardi, Vincenzo Mestel, David Stamoulis, Georgios Quantum Physics Data Structures and Algorithms We study classical polynomial-time approximation algorithms for the transverse-field Ising model (TFIM) Hamiltonian, allowing a mixture of ferromagnetic and anti-ferromagnetic interactions between pairs of qbits, alongside transverse field terms with arbitrary non-negative weights. Our main results are a series of approximation algorithms (all approximation ratios with respect to the true quantum optimum): (i) a simple maximum of two product state rounding algorithm achieving an approximation ratio $γ\approx 0.71$ , (ii) a strengthened rounding, inspired by the anticommutation property of the two $X_i, Z_iZ_j$ observables achieving ratio $γ\approx 0.7860$, and (iii) a further improvement by interpolation achieving ratio $γ\approx 0.8156$. We also give an explicit (purely ferromagnetic) TFIM instance on three qbits for which every product state achieves at most $169/180\approx 0.9389$ of the true optimum, yielding an upper bound for all algorithms producing product state approximations, even in the purely ferromagnetic case. |
| title | Product-State Approximation Algorithms for the Transverse Field Ising Model |
| topic | Quantum Physics Data Structures and Algorithms |
| url | https://arxiv.org/abs/2601.13106 |