Quantum kernel methods are a proposal for achieving quantum computational advantage in machine learning. They are based on a hybrid classical-quantum computation where a function called the quantum kernel is estimated by a quantum device while the rest of computation is performed classically. Quantum advantages may be achieved through this method only if the quantum kernel function cannot be estimated efficiently on a classical computer. In this paper, we provide sufficient conditions for the efficient classical estimation of quantum kernel functions for bosonic systems. These conditions are based on phase-space properties of data-encoding quantum states associated with the quantum kernels: negative volume, non-classical depth, and excess range, which are shown to be three signatures of phase-space negativity. We consider quantum optical examples involving linear-optical networks with and without adaptive non-Gaussian measurements, and investigate the effects of loss on the efficiency of the classical simulation. Our results underpin the role of the negativity in phase-space quasi-probability distributions as an essential resource in quantum machine learning based on kernel methods.

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相空间负性作为量子核方法的计算资源


量子核方法是在机器学习中实现量子计算优势的提议。它们基于混合经典量子计算，其中称为量子内核的函数由量子设备估计，而其余计算则以经典方式执行。只有当量子核函数无法在经典计算机上有效估计时，才能通过这种方法实现量子优势。在本文中，我们为玻色子系统量子核函数的高效经典估计提供了足够的条件。这些条件基于与量子内核相关的数据编码量子态的相空间属性：负体积、非经典深度和超距离，这被证明是相空间负性的三个特征。我们考虑了涉及线性光网络的量子光学示例，有和没有自适应非高斯测量，并研究了损耗对经典模拟效率的影响。我们的结果支持了负性在相空间准概率分布中的作用，它是基于核方法的量子机器学习中的重要资源。