1304.6112 (Robert N. C. Pfeifer)

Identification of optimal contraction sequences for tensor networks    [PDF]

Robert N. C. Pfeifer

Tensor network Ansatze provide powerful tools for the study of quantum many-body systems on a lattice in the low-energy regime, representing the state of a system as an efficiently-contractible network of multi-index tensors optimised numerically by means of a variational algorithm. The efficient contraction of tensor networks is vital to both the development and the implementation of tensor network algorithms, but determination of optimal contraction sequences is presently performed by human operators in a process which is both tedious and prone to error. This paper presents an algorithm for exhaustively searching the space of contraction sequences on a practical timescale, automating the determination of both the optimal contraction sequence and the cost function associated with the contraction of a given tensor network. By removing the burden of computing these contraction sequences from the researcher, this tool both facilitates the development of novel efficiently-contractible tensor network Ansatze and assists in the optimal implementation of existing tensor network algorithms.

View original: http://arxiv.org/abs/1304.6112