Fig. 2
From: A generative modeling approach for benchmarking and training shallow quantum circuits
DDQCL on the BAS data set. The top left panel shows patterns that belong to BAS(2, 2) our quantum circuit is to generate. The top central panel shows undesired patterns. On the top right panel, we show a possible mapping of the 4 pixels to N = 4 qubits, and we show some of the qubit-to-qubit connectivity topologies that can be set up in entangling layer and natively implemented by the ion trap quantum computer (e.g chain, star, and all). The bottom left panel shows the results of DDQCL simulations of shallow circuits with different topologies. We show the bootstrapped median and 90% confidence interval over the distribution of medians of the KL divergence as learning progresses for 100 iterations. The mean-field-like circuit L = 1 (green crosses) severely underperforms. A significant improvement is obtained with L = 2, where most of the parameters for XX gates have been learned to their maximum entangling value. These observations indicate that entanglement is a key resource for learning the BAS data set. Note that for L = 2 the choice of topology becomes a key factor for improving the performance. The chain topology (purple squares) performs slightly better than the star topology (red stars) even though they have the same number of parameters. The all-to-all topology (orange circles) significantly outperform all the others as it has more expressive power. The bottom central image extends the previous analysis to deeper circuits with L = 4 and approximatively twice the number of parameters. All the topologies achieve a lower median KL divergence and the confidence intervals shrink. The bottom right panel shows the bootstrapped mean qBAS(2, 2) score and 95% confidence interval for simulations (green bars) and experiments on the ion trap quantum computer hosted at University of Maryland (pink bars)
