A prototypical experiment is shown with a four-qubit nuclear magnetic resonance quantum processor, which demonstrates the iterative optimization process. Here, we develop this protocol and implement it on a quantum processor with limited resources. Since for high-dimensional problems the required computational resources can be prohibitive, it is desirable to investigate quantum versions of the gradient descent, such as the recently proposed (Rebentrost et al. It promises to find a local minimum of a function by iteratively moving along the direction of the steepest descent. The gradient descent method is central to numerical optimization and is the key ingredient in many machine learning algorithms.
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