Extended Quantum Computing Patterns

How to obtain a problem-aware parameter initialization for Variational Quantum Algorithms (VQAs) that reduces the optimization runtime?

A VQA needs to be executed on a quantum device, which encompasses the optimization of its variational parameters. Parameter optimization requires repeated access to the quantum device, typically starting with random initial parameter values [Kulshrestha and Safro 2022], to sample solutions and determine a direction for their optimization, e.g., through gradient descent.

Obtaining viable parameter initializations for VQAs is challenging due to large parameter spaces and effects, such as barren plateaus [Cerezo et al. 2021] and non-convex optimization landscapes [Huembeli and Dauphin 2021]. Barren plateaus are areas with vanishing gradients in a cost function's parameter space that must be avoided, whereas local minima in non-convex optimization landscapes pose an additional challenge to efficient parameter initialization as they disturb the search for a global optimum.

Transfer viable variational parameter values from related problem instances. As shown in the solution sketch below, optimized parameter values may be stored or directly reused for new problem instances. In many cases, it can be expected that optimized parameter values for a solved problem instance are in proximity of viable parameter values for a related or similar new problem instance. Therefore, optimized parameter values from earlier executions may be utilized for a problem-aware parameter initialization instead of a random initialization. Appropriate databases, toolkits, and provenance systems for quantum computing [Shaydulin et al. 2021] [Weder et al. 2021] facilitate the optional storage of optimized parameter values for their utilization in later executions.

Parameter transfers can reduce the number of iterations of the optimization loop. A favorable parameter initialization can also increase the likelihood of finding globally optimal parameter values and thus increase the solution quality.

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This pattern is a refinement of the Warm-Start pattern and can be applied in conjunction with VQA, including its refinements like QAOA, [Weigold et al. 2021a].

Variational Parameter Transfer has been frequently proposed and applied for QAOA and MaxCut [Brandao et al. 2018] [Wurtz and Lykov 2021] [Galda et al. 2021] [Shaydulin et al. 2023]. Moreover, Shaydulin et al.'s repository of preoptimized parameters implements the storage option [Shaydulin et al. 2021]. Beisel et al. propose a modeling construct for workflows to integrate warm-starts via parameter initialization in VQAs [Beisel et al. 2023].