Problem-dependent Quantum Circuit Design Based on Entropy Matching
Keywords: Quantum computing, Expressibility, Ansatz design, Linear entropy.
TL;DR: We propose an entropy-based framework for designing quantum circuits in quantum machine learning, optimizing circuit depth to avoid barren plateaus while maintaining high performance on tasks like binary classification.
Abstract: Variational quantum machine learning (QML) have shown great promise for harnessing quantum advantage in machine learning tasks. However, architecture design of quantum circuits employed in these QML algorithms has been poorly explored for practical problems. Specifically, quantum circuits should have sufficient expressibility for modeling complex functions considering the inherent structures of real-world data. Naively increasing the circuit depth could enhance the expressibility of quantum circuits, which also induce the barren plateau problem as a by-product. In this work, we develop an architecture design framework to solve this problem. We use a simple yet effective metric of quantum entanglement, i.e. the linear entropy, to guide the circuit design from the perspective of the input data. First, we quantify the entanglement of input data by calculating the 1-qubit linear entropy of their amplitude encoding states. Then we implement an entropy matching approach to identify the optimal circuit depth that lead to the linear entropy being close the entropy of input data. The effectiveness of circuit designs based on entropy is verified by extensive experimental results. Specifically, we demonstrate that real-world datasets like MNIST images has limited quantum entanglement. Therefore, circuits designed with entropy matching exhibit relatively small depths being free from the barren plateau issue while maintaining benign performances in binary classification tasks. This work not only advances the efficiency of quantum circuit design but also sets the stage for further refinement of QML performance, with broad implications for practical quantum computing applications.
Primary Area: other topics in machine learning (i.e., none of the above)
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Submission Number: 9369
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