Algorithms for Tensor Network Contraction Ordering
This addresses computational bottlenecks in tensor network calculations for physics and quantum computing, though it's incremental as it applies existing optimization methods to this problem.
The paper tackles the problem of finding efficient contraction sequences for tensor networks, showing that simulated annealing and genetic algorithms consistently outperform greedy search with advantages scaling with network size.
Contracting tensor networks is often computationally demanding. Well-designed contraction sequences can dramatically reduce the contraction cost. We explore the performance of simulated annealing and genetic algorithms, two common discrete optimization techniques, to this ordering problem. We benchmark their performance as well as that of the commonly-used greedy search on physically relevant tensor networks. Where computationally feasible, we also compare them with the optimal contraction sequence obtained by an exhaustive search. We find that the algorithms we consider consistently outperform a greedy search given equal computational resources, with an advantage that scales with tensor network size. We compare the obtained contraction sequences and identify signs of highly non-local optimization, with the more sophisticated algorithms sacrificing run-time early in the contraction for better overall performance.