qTorch: The Quantum Tensor Contraction Handler

TL;DR

This paper presents qTorch, a tensor network contraction tool for simulating quantum circuits, demonstrating its efficiency on Max-Cut problems with up to 100 qubits and analyzing the impact of graph structure on simulation performance.

Contribution

The study introduces a tensor contraction program for quantum circuit simulation, compares two contraction ordering methods, and provides insights into when tensor contraction outperforms full Hilbert space simulation.

Findings

Tensor contraction is more efficient for graphs with low treewidth.

qTorch successfully simulates up to 100 qubits for Max-Cut problems.

The stochastic contraction method is advantageous when tree decomposition is costly.

Abstract

Classical simulation of quantum computation is necessary for studying the numerical behavior of quantum algorithms, as there does not yet exist a large viable quantum computer on which to perform numerical tests. Tensor network (TN) contraction is an algorithmic method that can efficiently simulate some quantum circuits, often greatly reducing the computational cost over methods that simulate the full Hilbert space. In this study we implement a tensor network contraction program for simulating quantum circuits using multi-core compute nodes. We show simulation results for the Max-Cut problem on 3- through 7-regular graphs using the quantum approximate optimization algorithm (QAOA), successfully simulating up to 100 qubits. We test two different methods for generating the ordering of tensor index contractions: one is based on the tree decomposition of the line graph, while the other generates ordering using a straight-forward stochastic scheme. Through studying instances of QAOA circuits, we show the expected result that as the treewidth of the quantum circuit's line graph decreases, TN contraction becomes significantly more efficient than simulating the whole Hilbert space. The results in this work suggest that tensor contraction methods are superior only when simulating Max-Cut/QAOA with graphs of regularities approximately five and below. Insight into this point of equal computational cost helps one determine which simulation method will be more efficient for a given quantum circuit. The stochastic contraction method outperforms the line graph based method only when the time to calculate a reasonable tree decomposition is prohibitively expensive. Finally, we release our software package, qTorch (Quantum TensOR Contraction Handler), intended for general quantum circuit simulation.