The search for an application of near-term quantum devices is widespread. Quantum Machine Learning is touted as a potential utilisation of such devices, particularly those which are out of the reach of the simulation capabilities of classical computers. In this work, we propose a generative Quantum Machine Learning Model, called the Ising Born Machine (IBM), which we show cannot, in the worst case, and up to suitable notions of error, be simulated efficiently by a classical device. We also show this holds for all the circuit families encountered during training. In particular, we explore quantum circuit learning using non-universal circuits derived from Ising Model Hamiltonians, which are implementable on near term quantum devices. We propose two novel training methods for the IBM by utilising the Stein Discrepancy and the Sinkhorn Divergence cost functions. We show numerically, both using a simulator within Rigetti's Forest platform and on the Aspen-1 16Q chip, that the cost functions we suggest outperform the more commonly used Maximum Mean Discrepancy (MMD) for differentiable training. We also propose an improvement to the MMD by proposing a novel utilisation of quantum kernels which we demonstrate provides improvements over its classical counterpart. We discuss the potential of these methods to learn `hard' quantum distributions, a feat which would demonstrate the advantage of quantum over classical computers, and provide the first formal definitions for what we call `Quantum Learning Supremacy'. Finally, we propose a novel view on the area of quantum circuit compilation by using the IBM to `mimic' target quantum circuits using classical output data only.
翻译:短期量子装置的应用是广泛的。 量子机器学习被称之为一种潜在的利用, 特别是那些古典计算机模拟能力所不具备的设备。 在这项工作中, 我们提出一种基因化量子机器学习模型, 叫做 Ising Born Machine (IBM), 在最坏的情况下, 我们无法用一个古典设备来模拟, 并且达到适当的误差概念。 我们还显示, 对所有在训练期间遇到的电路家庭来说, 都存在这种屏障。 特别是, 我们探索利用来自Ising Model Hamiltonians的非普遍电路进行量电路学习, 特别是那些在近期量子装置上无法执行的电路。 我们提出两种新型的IBM培训方法, 即使用Stechn Incredivergence和Sinkhorn Divergence 成本功能。 我们用数字显示, 在Rigettitreat Forum平台和Aspen-1 16Q 芯片上, 我们建议, 成本功能比更常用的量流流流流化, 我们用MD(MD) 表示, 我们用其直位流流流流流流流流流流流流流流流流流流流流流流流流的变, 来展示这些直径变, 我们用这些直流流流流流化的流化的方法来演示, 我们用这些直径变, 我们用这些直路路路路路路路路路路路路路路路路路路路路路路路路路, 展示了直路路路路路路路路路路, 我们用这些直路路路, 展示了。