On the Optimal Linear Contraction Order for Tree Tensor Networks

  title={On the Optimal Linear Contraction Order for Tree Tensor Networks},
  author={Mihail Stoian},
Tensor networks are nowadays the backbone of classical simulations of quantum many-body systems and quantum circuits. Most tensor methods rely on the fact that we can eventually contract the tensor network to obtain the final result. While the contraction operation itself is trivial, its execution time is highly dependent on the order in which the contractions are performed. To this end, one tries to find beforehand an optimal order in which the contractions should be performed. However, there is… 

Figures from this paper



Hyper-optimized tensor network contraction

This work implements new randomized protocols that find very high quality contraction paths for arbitrary and large tensor networks, and introduces a hyper-optimization approach, where both the method applied and its algorithmic parameters are tuned during the path finding.

Towards a polynomial algorithm for optimal contraction sequence of tensor networks from trees.

It is proved that for any tensor tree network, the proposed algorithm can achieve a sequence of contractions that guarantees the minimal time complexity and a linear space complexity simultaneously.

Faster identification of optimal contraction sequences for tensor networks.

A modified search algorithm with enhanced pruning is presented which exhibits a performance increase of several orders of magnitude while still guaranteeing identification of an optimal operation-minimizing contraction sequence for a single tensor network.

Constructing Optimal Contraction Trees for Tensor Network Quantum Circuit Simulation

This paper introduces a novel polynomial time algorithm for constructing an optimal contraction tree from a given order, and introduces a fast and high quality linear ordering solver, and demonstrates its applicability as a heuristic for providing orderings for contraction trees.

Efficient Contraction of Large Tensor Networks for Weighted Model Counting through Graph Decompositions

It is proved that finding an efficient contraction order for a tensor network is equivalent to the well-known problem of finding an optimal carving decomposition, and memory-optimal contraction orders for planar tensor networks can be found in cubic time.

Optimizing Tensor Network Contraction Using Reinforcement Learning

This work proposes a Reinforcement Learning (RL) approach combined with Graph Neural Networks (GNN) to address the contraction ordering problem and shows how a carefully implemented RL-agent that uses a GNN as the basic policy construct can address these challenges and obtain significant improve-ments over state-of-the-art techniques.

Efficient tree tensor network states (TTNS) for quantum chemistry: generalizations of the density matrix renormalization group algorithm.

The concept of half-renormalization is introduced which greatly improves the efficiency of the calculations and demonstrates the strengths and weaknesses of tree tensor network states versus matrix product states.

On Optimizing a Class of Multi-Dimensional Loops with Reductions for Parallel Execution

This paper addresses the compile-time optimization of a form of nested-loop computation that is motivated by a computational physics application and a pruning search strategy for determination of an optimal form is developed.

On the optimal nesting order for computing N-relational joins

This paper proposes a data structure whereby the number of page fetches required for query evaluation is substantially reduced and derives a formula for the expected number ofpage fetches, and presents an efficient algorithm for finding an optimal nesting order.

Adaptive Optimization of Very Large Join Queries

An adaptive optimization framework is introduced that is able to solve most common join queries exactly, while simultaneously scaling to queries with thousands of joins, and produces optimal or near-optimal solutions for most common queries.