Quantum Unsupervised and Supervised Learning on Superconducting Processors

TL;DR

The algorithm's accuracy is found comparable to the classical K-means algorithm for clustering and classification problems, and it is found that it becomes less computationally expensive to implement for large datasets as compared to its classical counterpart.

Abstract

Machine learning algorithms perform well on identifying patterns in many different datasets due to their versatility. However, as one increases the size of the dataset, the computation time for training and using these statistical models grows quickly. Quantum computing offers a new paradigm which may have the ability to overcome these computational difficulties. Here, we propose a quantum analogue to K-means clustering, implement it on simulated superconducting qubits, and compare it to a previously developed quantum support vector machine. We find the algorithm's accuracy comparable to the classical K-means algorithm for clustering and classification problems, and find that it has asymptotic complexity $O(N^{3/2}K^{1/2}\log{P})$, where $N$ is the number of data points, $K$ is the number of clusters, and $P$ is the dimension of the data points, giving a significant speedup over the classical analogue.

Figures (5)

• Figure 1: Identified clusters (red, green, blue) by both algorithms in a Gaussian dataset. The dataset was constructed by randomly assigning three cluster centroids with means ranging from [-10, 10]. The datapoints were then randomly generated using a standard deviation of 3.0 away from the cluster centroid, corresponding to a moderately noisy model. Note that the data contains 5 feature dimensions, while only 3 are pictured. Both classical and quantum algorithms perfectly cluster the data, as shown above.
• Figure 2: Cluster accuracy vs. standard deviation of data. As the standard deviation of each generated datapoint from its cluster centroid increases, the data becomes more and more noisy. Each algorithm was executed on four datasets of standard deviations ranging from 1.0 to 4.0. Both algorithms perform well below standard deviations of 3.0, and begin to suffer a performance dropoff above that.
• Figure 3: Wine dataset - True and predicted classifications (red, green, blue) with Quantum K-means algorithm. Predicted clusters exactly reflect true boundaries in the data. The natural clustering in the Wine dataset is accurately detected by our algorithm, showing that it tends to detect clustering at a level comparable to similar classical algorithms.
• Figure 4: Iris dataset - True and predicted classifications (red, green, blue) with Quantum K-means algorithm. Two of the three predicted classes stray from the true data boundaries. This is because there is little natural separation between the two classes represented on the right side of the graphs, and as such, clustering algorithms do not always perform well at classifying the data.
• Figure 5: HTRU_2 dataset - True and predicted classifications (green, blue) with Quantum K-means algorithm. Predicted clusters closely reflect true boundaries in the data. Like in Wine, the natural clustering in the HTRU_2 dataset is accurately detected by our algorithm.