Tensor networks are powerful tools to simulate quantum circuits, and have therefore been used for the experimental verification of quantum supremacy on very complicated problems. A hybrid Schr¨odinger-Feynman contraction approach has proven to be extremely efficient when simulating the Sycamore circuit, i.e., Google’s quantum supremacy circuit. However, precise heuristics to choose between multiple possible solutions are still undefined. In this work, we first go through Schr¨odinger, Feynman and hybrid contraction methods, explain the software to implement them, and estimate their complexity in terms of both time and memory consumption. Then, we define the heuristics we used to determine the best solution and compare time and memory reductions. We show that it is not worth using a hybrid approach on matrix product states due to the dominance of memory complexity. We illustrate unexpected behavior of hybrid complexity curves as functions of the number of partitions K when simulating the Sycamore circuit. Finally, we show the effect of randomness of gate positions in the complexities for a random quantum circuit designed by us.     «

Tensor networks are powerful tools to simulate quantum circuits, and have therefore been used for the experimental verification of quantum supremacy on very complicated problems. A hybrid Schr¨odinger-Feynman contraction approach has proven to be extremely efficient when simulating the Sycamore circuit, i.e., Google’s quantum supremacy circuit. However, precise heuristics to choose between multiple possible solutions are still undefined. In this work, we first go through Schr¨odinger, Feynm...     »