Toward bootstrapping tensor-network contractions

• URL: http://arxiv.org/abs/2603.17856v1
• Date: Wed, 18 Mar 2026 15:44:19 GMT
• Title: Toward bootstrapping tensor-network contractions
• Abstract summary: We introduce a numerical bootstrap framework which casts the problem of tensor-network contractions into a convex optimization problem.<n>We show that, assuming a canonical form, second-order relaxation-cone can provide tight bounds on the contraction result.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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