Quantum machine learning (QML) offers a powerful, flexible paradigm for programming near-term quantum computers, with applications in chemistry, metrology, materials science, data science, and mathematics. Here, one trains an ansatz, in the form of a parameterized quantum circuit, to accomplish a task of interest. However, challenges have recently emerged suggesting that deep ansatzes are difficult to train, due to flat training landscapes caused by randomness or by hardware noise. This motivates our work, where we present a variable structure approach to build ansatzes for QML. Our approach, called VAns (Variable Ansatz), applies a set of rules to both grow and (crucially) remove quantum gates in an informed manner during the optimization. Consequently, VAns is ideally suited to mitigate trainability and noise-related issues by keeping the ansatz shallow. We employ VAns in the variational quantum eigensolver for condensed matter and quantum chemistry applications, in the quantum autoencoder for data compression and in unitary compilation problems showing successful results in all cases.

翻译：量子机器学习（QML）为近期量子计算机的编程提供了一种强大且灵活的范式，在化学、计量学、材料科学、数据科学和数学等领域具有应用价值。该方法通过训练一个参数化量子电路形式的拟设（ansatz）来完成特定任务。然而，近期出现的挑战表明，由于随机性或硬件噪声导致的平坦训练景观，深度拟设难以训练。这启发了我们的工作，提出了一种构建QML拟设的可变结构方法。我们的方法名为VAns（可变拟设），在优化过程中通过一组规则，以知情的方式有策略地增加并（关键地）移除量子门。因此，VAns通过保持拟设的浅层结构，非常适合缓解可训练性和噪声相关问题。我们将VAns应用于凝聚态和量子化学领域的变分量子特征求解器、用于数据压缩的量子自编码器以及酉编译问题，在所有案例中均展现出成功的结果。