English

Block-Encoding Tensor Networks and QUBO Embeddings

Quantum Physics 2026-01-13 v2

Abstract

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.

Keywords

Cite

@article{arxiv.2510.00935,
  title  = {Block-Encoding Tensor Networks and QUBO Embeddings},
  author = {Sebastian Issel},
  journal= {arXiv preprint arXiv:2510.00935},
  year   = {2026}
}
R2 v1 2026-07-01T06:10:47.039Z