Only use the specific parameters (angles) in variational quantum eigensolver

Question

I’m following the tutorial (https://qiskit.org/textbook/ch-applications/vqe-molecules.html) to construct the VQE circuit. In this tutorial, it used the classical optimizer like “COBYLA, SPSA, SLSQP” to choose the appropriate parameters. I wonder how to adjust the optimizers so the optimizers will always choose the specific parameters.

I want to choose two kinds of specific parameters:

1. The multiple of a number. For example: I want the parameters to be 2πi/2^10 ,i∈N

2. A given set. For example: I want the parameters to be chosen from a set {0.01, 0.05, 0.23, …}

How do I constraint the optimizers? Thanks for answering my questions!

Answer 1

If you make your parameter space discontinuous, then most optimisation algorithms will not work. They require a smooth continuous function to calculate gradients (gradient-free ones make similar assumptions too).

If your set is small and the total number of parameters is not too large, you can try all combinations (brute force).

You want to go into the direction of discreet optimisation, so that is the keyword you are looking for ;)