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A quantum hardware-induced graph kernel based on Gaussian Boson Sampling
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A device called a 'Gaussian Boson Sampler' has initially been proposed as a near-term demonstration of classically intractable quantum computation. As recently shown, it can also be used to decide whether two graphs are isomorphic. Based on these results we construct a feature map and graph similarity measure or 'graph kernel' using samples from the device. We show that the kernel performs well compared to standard graph kernels on typical benchmark datasets, and provide a theoretical motivation for this success, linking the distribution of a Gaussian Boson Sampler to the number of matchings in subgraphs. Our results contribute to a new way of thinking about kernels as a (quantum) hardware-efficient feature mapping, and lead to an interesting application for near-term quantum computing.
Forward citations
Cited by 2 Pith papers
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Exact simulation of Gaussian Boson Sampling in polynomial space and exponential time
A chain-rule algorithm samples each mode of a Gaussian Boson Sampler sequentially, giving exact simulation in polynomial space and time exponential in the detected photon number.
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The Capacity of Quantum Neural Networks
The memory capacity of any quantum neural network is at most the information content of its trainable parameters, so classically-parameterized QNNs lack capacity advantage over classical NNs.
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