论文标题
使用SU（$ d $）对称性的量子量算法的超级量子量子加速
Towards Super-polynomial Quantum Speedup of Equivariant Quantum Algorithms with SU($d$) Symmetry
论文作者
论文摘要
我们介绍了一个模棱两可的卷积量子算法的框架，该算法是针对具有任意SU $（D）$对称性的物理系统上的许多机器学习任务量身定制的。它使我们能够增强量子计算的自然模型 - 排列量子计算（PQC）[量子INF。 Comput。，10，470-497（2010）] - 定义一个更强大的模型：PQC+。虽然显示PQC在经典上是有效的，但我们表现出一个可以在PQC+机器上有效解决的问题，而不知道经典的多项式时间算法。因此提供了反对PQC+经典模拟的证据。我们进一步讨论可以在PQC+范式中执行的实用量子机学习算法。
We introduce a framework of the equivariant convolutional quantum algorithms which is tailored for a number of machine-learning tasks on physical systems with arbitrary SU$(d)$ symmetries. It allows us to enhance a natural model of quantum computation -- permutational quantum computing (PQC) [Quantum Inf. Comput., 10, 470-497 (2010)] -- and define a more powerful model: PQC+. While PQC was shown to be efficiently classically simulatable, we exhibit a problem which can be efficiently solved on PQC+ machine, whereas no classical polynomial time algorithm is known; thus providing evidence against PQC+ being classically simulatable. We further discuss practical quantum machine learning algorithms which can be carried out in the paradigm of PQC+.
