论文标题
噪声存在的量子内核法
Quantum Kernel Method in the Presence of Noise
论文作者
论文摘要
机器学习中的内核方法包括将输入数据编码为“特征空间”的希尔伯特空间中的向量，并将目标函数建模为特征空间上的线性映射。在给定成本函数的情况下，计算这样的最佳线性图需要计算核矩阵，其条目等于特征向量的内部产物。在量子内核法中，假定特征向量是量子状态，在这种情况下，量子内核矩阵是根据量子状态的重叠来给出的。实际上，为了估计应应用量子内核矩阵的条目，例如，掉期检验和此类交换测试的数量是评估量子内核方法性能的相关参数。此外，量子系统会受到噪声的影响，因此不能精确准备量子状态作为特征向量，这是量子内核矩阵计算的另一个错误来源。考虑到以上两个考虑因素，我们证明了量子内核方法的性能（概括误差）的束缚。
Kernel method in machine learning consists of encoding input data into a vector in a Hilbert space called the feature space and modeling the target function as a linear map on the feature space. Given a cost function, computing such an optimal linear map requires computation of a kernel matrix whose entries equal the inner products of feature vectors. In the quantum kernel method it is assumed that the feature vectors are quantum states in which case the quantum kernel matrix is given in terms of the overlap of quantum states. In practice, to estimate entries of the quantum kernel matrix one should apply, e.g., the SWAP-test and the number of such SWAP-tests is a relevant parameter in evaluating the performance of the quantum kernel method. Moreover, quantum systems are subject to noise, so the quantum states as feature vectors cannot be prepared exactly and this is another source of error in the computation of the quantum kernel matrix. Taking both the above considerations into account, we prove a bound on the performance (generalization error) of the quantum kernel method.
