qTorch: The Quantum Tensor Contraction Handler

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 may be used for such simulations, often greatly reducing the computational cost over methods that simulate the full Hilbert space. In this study we implement a parallel tensor network contraction program for simulating a variety of quantum circuits, including the quantum approximate optimization algorithm (QAOA) applied to Max-Cut and quantum circuits for quantum chemistry simulations. We show simulation results for 3through 7-regular MaxCut/QAOA circuits, even successfully simulating up to 100 qubits for some of the 3-regular circuits. 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. This tradeoff occurs when the Max-Cut problem’s graph regularity is five or six, suggesting that tensor contraction methods are superior for simulating Max-Cut/QAOA with graphs of regularities approximately five and below. 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 (The Quantum TensOR Contraction Handler), intended for general quantum circuit simulation. The software may be used to more quickly study the numerical behavior of arbitrary quantum algorithms. For a nontrivial subset of these quantum circuits, 50 to 100 qubits can easily be simulated on a single compute node, an ability that is beyond of reach of other modern software packages.