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A potential advantage of quantum machine learning stems from the ability ofencoding classical data into high dimensional complex Hilbert space usingquantum circuits. Recent studies exhibit that not all encoding methods are thesame when representing classical data since certain parameterized circuitstructures are more expressive than the others. In this study, we show thedifference in encoding techniques can be visualized by investigating thetopology of the data embedded in complex Hilbert space. The technique forvisualization is a hybrid quantum based topological analysis which uses simplediagonalization of the boundary operators to compute the persistent Bettinumbers and the persistent homology graph. To augment the computation of Bettinumbers within a NISQ framework, we suggest a simple hybrid algorithm. Througha illuminating example of a synthetic data set and the methods of angleencoding, amplitude encoding, and IQP encoding, we reveal topologicaldifferences with the encoding methods, as well as the original data.Consequently, our results suggest the encoding method needs to be consideredcarefully within different quantum machine learning models since it canstrongly affect downstream analysis like clustering or classification.

Understanding the Mapping of Encode Data Through An Implementation of Quantum Topological Analysis