Generalize the QML demo of "function fitting using quantum signal processing"

Demos
1

Hello!

Thank you for giving such interesting demos! I had a question about the QML demo of function fitting using quantum signal processing. I notice that the demo is just used for 1D, but are there related demos used for more dimensions that still preserve the constraint and bounding? like for 2D and 3D?

Thank you,

2

Hi @Daniel_Wang ,

Thank you for your kind words!
I don’t know if this demo will work for more dimensions but you can give it a try and let us know how it goes.

3

Ok. I would try. Another question that I want to ask is that I am not really sure what are the advantages that we can benefit from using quantum circuits for this. For example, if we can express quantum circuits as a Fourier series with exponential terms with respect to number of qubits used. However, with this quantum signal processing, it seems to me that it is picking out the terms from Chebychev polynomials of the 1st kind with different parities (even/odd). The number of polynomials grows only linearly w.r.t. circuit depth, not exponentially. And are there multi-qubit generalizations of this?

Regards,
Shuteng

4

Hi @Daniel_Wang ,

I don’t know the answers to your specific questions but the general answer is that classical solutions will work better. We’re still exploring what are the problems where could see an advantage from using quantum computers. The short answer is that we don’t know yet.
The positive side of things is that it’s up to us to discover, so if you like math and reading papers you can join the community and discuss issues and ideas :smiley: