2018/04/30 by Andrey Kardashin, Alexey Uvarov, Jacob Biamonte
Computer Science · Mathematics · Physics and Astronomy · #Cartesian tensor #Computer science #Eigenvalues and eigenvectors #Exact solutions in general relativity #Mathematical analysis #Mathematics #Physics #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum computer #Quantum many-body systems #Quantum mechanics #Quantum network #Quantum state #Tensor (intrinsic definition) #Tensor contraction #Tensor density #Tensor field #Tensor product #Theoretical computer science #Unitary state #cond-mat.dis-nn #cond-mat.str-el #cs.LG #quant-ph
paper · pdf · doi:10.3389/fphy.2020.586374
published as Frontiers in Physics 8: 586374 (2021) · 6 pages, 2 figures, numerics added
arxiv created 2020/09/12 · openalex publication_date 2021/03/01 · arxiv updated 2021/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Tensor network algorithms seek to minimize correlations to compress the classical data representing quantum states. Tensor network algorithms and similar tools—called tensor network methods—form the backbone of modern numerical methods used to simulate many-body physics and have a further range of applications in machine learning. Finding and contracting tensor network states is a computational task, which may be accelerated by quantum computing. We present a quantum algorithm that returns a classical description of a rank- r tensor network state satisfying an area law and approximating an eigenvector given black-box access to a unitary matrix. Our work creates a bridge between several contemporary approaches, including tensor networks, the variational quantum eigensolver (VQE), quantum approximate optimization algorithm (QAOA), and quantum computation.