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I am mainly talking about QSVM from Qiskit (https://qiskit.org/documentation/stubs/qiskit.aqua.algorithms.QSVM.html#qiskit.aqua.algorithms.QSVM) versus a classical SVM. Is it just a time complexity speed-up?

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The main benefit is quantum computing may enable the use of kernels which are hard to compute classically. In other words, it may be possible to separate the input data using quantum feature maps which are not available in classical calculations.

You may find this paper helpful - it discusses the issue in some detail.

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  • $\begingroup$ Great paper. Do you have any suggestions for using QSVM in a large feature set? People who have used PCA to reduce feature sets have equal to the number of QBITS at their disposal. Do we have any library that we can uses? Appreciate it. $\endgroup$ Mar 31 at 14:56
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    $\begingroup$ @ Protima Rani Paul. The paper presents two methods: a variational method and kernel estimation method. The kernel estimation method uses a short depth circuit for computing the state overlap. This method may scale up to a reasonable number of features, depending on the physical connectivity of the qubits in your hardware. If there is too much SWAPing involved, the noise will ruin the calculation. Qiskit provides some nice SVM tools (pretty well everything you need) for feature maps of the type discussed in the paper. $\endgroup$
    – John
    Apr 2 at 0:19

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