Block-Encoding Tensor Networks and QUBO Embeddings
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912816475144192 |
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| author | Issel, Sebastian |
| author_facet | Issel, Sebastian |
| contents | We give an algorithm that converts any tensor network (TN) into a sequence of local unitaries whose composition block-encodes the network contraction, suitable for Quantum Eigenvalue / Singular Value Transformation (QET/QSVT). The construction embeds each TN as a local isometry and dilates it to a unitary. Performing this step for every site of the tensor, allows the full network to be block-encoded. The theory is agnostic to virtual-bond sizes; for qubit resource counts and examples we assume global power-of-two padding. Further, we present a deterministic sweep that maps Quadratic Unconstrained Binary Optimization (QUBO) / Ising Hamiltonians into Matrix Product Operators (MPOs) and general TN. We provide formal statements, pseudo-code, resource formulae, and a discussion of the use for state preparation and learning of general quantum operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_00935 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Block-Encoding Tensor Networks and QUBO Embeddings Issel, Sebastian Quantum Physics We give an algorithm that converts any tensor network (TN) into a sequence of local unitaries whose composition block-encodes the network contraction, suitable for Quantum Eigenvalue / Singular Value Transformation (QET/QSVT). The construction embeds each TN as a local isometry and dilates it to a unitary. Performing this step for every site of the tensor, allows the full network to be block-encoded. The theory is agnostic to virtual-bond sizes; for qubit resource counts and examples we assume global power-of-two padding. Further, we present a deterministic sweep that maps Quadratic Unconstrained Binary Optimization (QUBO) / Ising Hamiltonians into Matrix Product Operators (MPOs) and general TN. We provide formal statements, pseudo-code, resource formulae, and a discussion of the use for state preparation and learning of general quantum operators. |
| title | Block-Encoding Tensor Networks and QUBO Embeddings |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2510.00935 |