Huang Hsin-Yuan, Broughton Michael, Mohseni Masoud, Babbush Ryan, Boixo Sergio, Neven Hartmut, McClean Jarrod R
Google Quantum AI, Venice, CA, USA.
Institute for Quantum Information and Matter, Caltech, Pasadena, CA, USA.
Nat Commun. 2021 May 11;12(1):2631. doi: 10.1038/s41467-021-22539-9.
The use of quantum computing for machine learning is among the most exciting prospective applications of quantum technologies. However, machine learning tasks where data is provided can be considerably different than commonly studied computational tasks. In this work, we show that some problems that are classically hard to compute can be easily predicted by classical machines learning from data. Using rigorous prediction error bounds as a foundation, we develop a methodology for assessing potential quantum advantage in learning tasks. The bounds are tight asymptotically and empirically predictive for a wide range of learning models. These constructions explain numerical results showing that with the help of data, classical machine learning models can be competitive with quantum models even if they are tailored to quantum problems. We then propose a projected quantum model that provides a simple and rigorous quantum speed-up for a learning problem in the fault-tolerant regime. For near-term implementations, we demonstrate a significant prediction advantage over some classical models on engineered data sets designed to demonstrate a maximal quantum advantage in one of the largest numerical tests for gate-based quantum machine learning to date, up to 30 qubits.
将量子计算用于机器学习是量子技术最令人兴奋的潜在应用之一。然而，提供数据的机器学习任务可能与通常研究的计算任务有很大不同。在这项工作中，我们表明，一些传统上难以计算的问题可以通过从数据中进行经典机器学习来轻松预测。以严格的预测误差界限为基础，我们开发了一种用于评估学习任务中潜在量子优势的方法。这些界限在渐近意义上是紧密的，并且对于广泛的学习模型在经验上具有预测性。这些构造解释了数值结果，表明借助数据，经典机器学习模型即使针对量子问题进行了定制，也可以与量子模型竞争。然后，我们提出了一种投影量子模型，该模型为容错机制下的一个学习问题提供了简单而严格的量子加速。对于近期实现，在迄今为止针对基于门的量子机器学习的最大数值测试之一（多达30个量子比特）中，我们在为展示最大量子优势而设计的工程数据集上展示了相对于一些经典模型的显著预测优势。
