2007/08/31 by Gregory M. Crosswhite, Dave Bacon · 10 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Quantum many-body systems #Tensor decomposition and applications #quant-ph
paper · pdf · doi:10.1103/physreva.78.012356
published as Phys. Rev. A 78, 012356 (2008) · 18 pages, 19 figures, LaTeX; numerous improvements have been made to the manuscript in response to referee feedback
arxiv created 2008/07/07 · openalex publication_date 2008/07/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A diagram is introduced for visualizing matrix product states which makes transparent a connection between matrix product factorizations of states and operators, and complex weighted finite state automata. It is then shown how one can proceed in the opposite direction: writing an automaton that ``generates'' an operator gives one an immediate matrix product factorization of it. Matrix product factorizations have the advantage of reducing the cost of computing expectation values by facilitating caching of intermediate calculations. Thus our connection to complex weighted finite state automata yields insight into what allows for efficient caching in matrix product algorithms. Finally, these techniques are generalized to the case of multiple dimensions.