Faster identification of optimal contraction sequences for tensor networks
Abstract
The efficient evaluation of tensor expressions involving sums over multiple indices is of significant importance to many fields of research, including quantum manybody physics, loop quantum gravity, and quantum chemistry. The computational cost of evaluating an expression may depend strongly on the order in which the index sums are evaluated, and determination of the operationminimizing contraction sequence for a single tensor network (single term, in quantum chemistry) is known to be NPhard. The current preferred solution is an exhaustive search, using either an iterative depthfirst approach with pruning or dynamic programming and memoization, but these approaches are impractical for many of the larger tensor network ansätze encountered in quantum manybody physics. We present a modified search algorithm with enhanced pruning which exhibits a performance increase of several orders of magnitude while still guaranteeing identification of an optimal operationminimizing contraction sequence for a single tensor network. A reference implementation for matlab, compatible with the ncon() and multienv() network contractors of arXiv:1402.0939 and Evenbly and Pfeifer, Phys. Rev. B 89, 245118 (2014),10.1103/PhysRevB.89.245118, respectively, is supplied.
 Publication:

Physical Review E
 Pub Date:
 September 2014
 DOI:
 10.1103/PhysRevE.90.033315
 arXiv:
 arXiv:1304.6112
 Bibcode:
 2014PhRvE..90c3315P
 Keywords:

 02.70.c;
 05.30.d;
 03.67.a;
 Computational techniques;
 simulations;
 Quantum statistical mechanics;
 Quantum information;
 Condensed Matter  Strongly Correlated Electrons;
 Physics  Computational Physics;
 Quantum Physics
 EPrint:
 25 pages, 12 figs, 2 tables, includes reference implementation of algorithm, v2.01. Update corrects the display of contraction sequences involving singletensor traces (i.e. where an index in the input appears twice on the same tensor)