Fig. 6: Comparison between EQC and two non-equivariant hardware-efficient ansatzes.
From: Equivariant quantum circuits for learning on weighted graphs
We show results for TSP instances with five (TSP5) and ten (TSP10) cities in a and b, and c and d, respectively. Models were trained on 10 and 100 instances, and with one and four layers. The boxes show the upper quartile, median and lower quartile for each model configuration, the whiskers of the boxes extend to 1.5 times the interquartile range, and the black diamonds denote outliers. Each box is computed over results for ten agents. The hardware-efficient ansatz with trainable embedding (HWETE) consists of trainable graph encoding layers as those in the EQC, with an additional variational part in each layer that consists of parametrized single-qubit Y-gates and a ladder of CZ-gates. The HWE ansatz is the same as the HWETE, but where the graph-embedding part is not trainable and only the Y-gates in each layer are trained. We also show approximation ratios of a random algorithm, where a random tour is picked as the solution to each instance. The dotted, black lines denote the upper bound of the Christofides algorithm. We see that the HWE ansatzes perform extremely badly and barely outperform picking random tours only in some cases.
