Quantum feature maps for graph machine learning on a neutral atom quantum processor

Using a quantum processor to embed and process classical data enables the generation of correlations between variables that are inefficient to represent through classical computation. A fundamental question is whether these correlations could be harnessed to enhance learning performances on real data sets. Here we report the use of a neutral atom quantum processor comprising up to 32 qubits to implement machine learning tasks on graph -structured data. To that end, we introduce a quantum feature map to encode the information about graphs in the parameters of a tunable Hamiltonian acting on an array of qubits. Using this tool, we first show that interactions in the quantum system can be used to distinguish nonisomorphic graphs that are locally equivalent. We then realize a toxicity screening experiment, consisting of a binary classification protocol on a biochemistry data set comprising 286 molecules of sizes ranging from 2 to 32 nodes, and obtain results which are comparable to the implementation of the best classical kernels on the same data set. Using techniques to compare the geometry of the feature spaces associated with kernel methods, we then show evidence that the quantum feature map perceives data in an original way, which is hard to replicate using classical kernels.