Toward bootstrapping tensor-network contractions
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910058215899136 |
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| author | Ono, Seishiro Zhang, Yanbai Po, Hoi Chun |
| author_facet | Ono, Seishiro Zhang, Yanbai Po, Hoi Chun |
| contents | Accurate contraction of tensor networks beyond one dimension is essential in various fields including quantum many-body physics. Existing approaches typically rely on approximate contraction schemes and do not provide certified error bars. We introduce a numerical bootstrap framework which casts the problem of tensor-network contractions into a convex optimization problem, thereby yielding certified lower and upper bounds on expectation values of physical observables. As a proof-of-principle, we construct such constraints explicitly for translationally invariant matrix product states and demonstrate that, assuming a canonical form, second-order-cone relaxation can provide tight bounds on the contraction result. We further demonstrate that when the requirement on canonical form is lifted, a more general semidefinite-programming approach could yield similar tight bounds at higher but still polynomial computational cost. Our work suggests numerical bootstrap could be a possible way forward for the rigorous contractions of tensor networks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_17856 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Toward bootstrapping tensor-network contractions Ono, Seishiro Zhang, Yanbai Po, Hoi Chun Strongly Correlated Electrons Quantum Physics Accurate contraction of tensor networks beyond one dimension is essential in various fields including quantum many-body physics. Existing approaches typically rely on approximate contraction schemes and do not provide certified error bars. We introduce a numerical bootstrap framework which casts the problem of tensor-network contractions into a convex optimization problem, thereby yielding certified lower and upper bounds on expectation values of physical observables. As a proof-of-principle, we construct such constraints explicitly for translationally invariant matrix product states and demonstrate that, assuming a canonical form, second-order-cone relaxation can provide tight bounds on the contraction result. We further demonstrate that when the requirement on canonical form is lifted, a more general semidefinite-programming approach could yield similar tight bounds at higher but still polynomial computational cost. Our work suggests numerical bootstrap could be a possible way forward for the rigorous contractions of tensor networks. |
| title | Toward bootstrapping tensor-network contractions |
| topic | Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2603.17856 |