I am trying to implement QAOA for graph coloring with hard constraints. In this paper, eq. 9 a custom mixer is proposed, is looks like this:

$B_{ui} = \frac{1}{2^{l + 1}}(X_{u0}X_{u1} + Y_{u0}Y_{u1}) \prod_{j=1}^l(I + Z_{v_ji})$.

$l$ is the number of neighboring nodes, u - the node, i - the color. And I think, there is a mistake, and $i$ should be instead of ones. As I understand, new mixer unitary is this:

$\hat{U}_M = \prod_{u, i} e^{-i\frac{a}{2^{l+1}}X_{u0}X_{u1}\prod_{j=1}^l(I + Z_{v_ji})}e^{-i\frac{a}{2^{l+1}}Y_{u0}Y_{u1}\prod_{j=1}^l(I + Z_{v_ji})}$

How to implement this on qiskit? Are there any tips, examples or advice?

I know how to implement terms which are products of Pauli gates such as $Z_iZ_kY_j$ or something like it, but I have no idea, how to write product in general, especially when $I$ is involved.

I have found a question, which shed light on how to implement custom mixers, but I still don't quite understand.

A blog post could be helpful, investigating. Not exactly, there are solutions for exact number of nodes, which I might try.



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.