Constructing Optimal Contraction Trees for Tensor Network Quantum Circuit Simulation

TL;DR

This paper presents a novel polynomial-time algorithm and a high-quality linear ordering solver for constructing optimal contraction trees in tensor network quantum circuit simulation, significantly improving efficiency over existing methods.

Contribution

The paper introduces a new polynomial-time algorithm for optimal contraction tree construction and a fast linear ordering solver, enhancing quantum circuit simulation efficiency.

Findings

Our method outperforms existing approaches on most tested quantum circuits.

The linear ordering solver provides high-quality orderings for contraction trees.

Significant reduction in simulation cost for quantum approximate optimization algorithms.

Abstract

One of the key problems in tensor network based quantum circuit simulation is the construction of a contraction tree which minimizes the cost of the simulation, where the cost can be expressed in the number of operations as a proxy for the simulation running time. This same problem arises in a variety of application areas, such as combinatorial scientific computing, marginalization in probabilistic graphical models, and solving constraint satisfaction problems. In this paper, we reduce the computationally hard portion of this problem to one of graph linear ordering, and demonstrate how existing approaches in this area can be utilized to achieve results up to several orders of magnitude better than existing state of the art methods for the same running time. To do so, we introduce a novel polynomial time algorithm for constructing an optimal contraction tree from a given order. Furthermore, we introduce a fast and high quality linear ordering solver, and demonstrate its applicability as a heuristic for providing orderings for contraction trees. Finally, we compare our solver with competing methods for constructing contraction trees in quantum circuit simulation on a collection of randomly generated Quantum Approximate Optimization Algorithm Max Cut circuits and show that our method achieves superior results on a majority of tested quantum circuits. Reproducibility: Our source code and data are available at https://github.com/cameton/HPEC2022_ContractionTrees.