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- W4294783118 abstract "The QAOA is a variational quantum algorithm, where a quantum computer implements a variational ansatz consisting of p layers of alternating unitary operators and a classical computer is used to optimize the variational parameters. For a random initialization the optimization typically leads to local minima with poor performance, motivating the search for initialization strategies of QAOA variational parameters. Although numerous heuristic intializations were shown to have a good numerical performance, an analytical understanding remains evasive. Inspired by the study of energy landscapes, in this work we focus on so-called transition states (TS) that are saddle points with a unique negative curvature direction that connects to local minima. Starting from a local minimum of QAOA with p layers, we analytically construct 2p + 1 TS for QAOA with p + 1 layers. These TS connect to new local minima, all of which are guaranteed to lower the energy compared to the minimum found for p layers. We introduce a Greedy procedure to effectively maneuver the exponentially increasing number of TS and corresponding local minima. The performance of our procedure matches the best available initialization strategy, and in addition provides a guarantee for the minimal energy to decrease with an increasing number of layers p. Generalization of analytic TS and the Greedy approach to other ansatze may provide a universal framework for initialization of variational quantum algorithms." @default.
- W4294783118 created "2022-09-06" @default.
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- W4294783118 date "2022-09-02" @default.
- W4294783118 modified "2023-09-25" @default.
- W4294783118 title "Transition states and greedy exploration of the QAOA optimization landscape" @default.
- W4294783118 doi "https://doi.org/10.48550/arxiv.2209.01159" @default.
- W4294783118 hasPublicationYear "2022" @default.
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