Quantum machine learning -- and specifically Variational Quantum Algorithms (VQAs) -- 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 VQAs. 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——特别是变分量子算法（VQAs）——为编程近期量子计算机提供了强大而灵活的范式，在化学、计量学、材料科学、数据科学和数学中均有应用。在此范式中，通过训练一个参数化量子电路形式的拟设（ansatz）来完成目标任务。然而，近期出现了一些挑战，表明深层拟设因随机性或硬件噪声导致的平坦训练景观而难以训练。这促使我们提出了一种构建VQAs拟设的变结构方法。该方法名为VAns（变分拟设），在优化过程中通过一套规则，以基于信息的方式既扩展（关键性地）又移除量子门。因此，VAns通过保持拟设的浅层结构，能理想地缓解与可训练性和噪声相关的问题。我们将VAns应用于凝聚态与量子化学领域的变分量子本征求解器、数据压缩的量子自编码器以及酉编译问题中，在所有案例中均取得了成功的结果。