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I have essentially developed a Quantum Support Vector Machine to classify some data I have successfully. I wanted to know if it is possible to quantify the speed-up and time difference between this algorithm and a classical Support Vector Machine doing the exact same task. Also is it possible to somewhat estimate how this speed-up will be for larger datasets and scaling?
Thanks a lot!
The paper published in Science: "Defining and Detecting Quantum Speed-up" tells you to measure quantum speed-up with the following formula (... ready for it?!):
$$\tag{1} \textrm{speed-up} = \frac{Q}{C}, $$
where $Q$ is the runtime on a quantum computer, and $C$ is the runtime on a classical computer. Believe it or not, this is Eq. 1 in that paper.
In reality it's much more complicated than that that, because different classical hardware will have a different $C$ value.
"Also is it possible to somewhat estimate how this speed-up will be for larger datasets and scaling?"
Without knowing the specific details of your algorithm, which might provide some insight into how the scaling can be measured, you would have to do experiments on larger and larger inputs and empirically guess the asymptotic scaling based on that (which is hard to do properly right now because quantum devices are limited in the number of qubits they offer).
