Zoom-talk: Optimal mixers restricted to subspaces and the stabilizer formalism

Speaker: Franz G. Fuchs, SINTEF

Title: Optimal mixers restricted to subspaces and the stabilizer formalism

Abstract: We present a recent work (https://arxiv.org/abs/2306.17083) on mixers constrained to a given subspace. The method connects and utilizes the stabilizer formalism that is used in error correcting codes. This can be useful in the setting when the quantum approximate optimization algorithm (QAOA), a popular meta-heuristic for solving combinatorial optimization problems, is applied in the setting where the constraints of the problem lead to a feasible subspace that is large but easy to specify. The proposed method gives a systematic way to construct mixers that are resource efficient in the number of controlled not gates and can be understood as a generalization of the well-known X and XY mixers. The numerical examples provided show a dramatic reduction of CX gates when compared to previous results. Overall, we hope that this new perspective can lead to further insight into the development of quantum algorithms.

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