Finite automata for caching in matrix product algorithms

Details Finite automata for caching in matrix product algorithms Finite automata for caching in matrix product algorithms

2007-08-09

arxiv.org/abs/0708.1221v3

Phys. Rev. A 78, 012356 (2008)

Physics

Quantum Physics

18 pages, 19 figures, LaTeX; numerous improvements have been made to the manuscript in response to referee feedback

Scientific paper

10.1103/PhysRevA.78.012356

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.

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