具有最小开销的鲁棒量子分类器
Robust quantum classifier with minimal overhead
摘要：
为了在实际环境中见证量子优势，不仅需要在硬件水平上，而且需要在理论研究上做出大量努力，以降低给定协议的计算成本。量子计算有可能显著增强现有的经典机器学习方法，并且已经提出了几种基于核方法的二进制分类量子算法。这些算法依赖于估计期望值，这又需要重复多次昂贵的量子数据编码过程。在这项工作中，我们明确地计算获得一个固定的成功概率所需的重复次数，并表明，阿达玛测试和交换测试电路达到最佳方差的量子线路参数。只有通过对数据相关参数进行优化，才能进一步减少方差，从而减少重复次数。我们还表明，基于内核的二进制分类可以用一个单量子比特的测量，无论数据的数量和维度。最后，我们表明，一些相关的噪声模型的分类可以可靠地进行没有量子纠错。我们的研究结果对于在有限资源下设计量子分类实验是有用的，这是在嘈杂的中间尺度量子时代的共同挑战。
英文摘要：
To witness quantum advantages in practical settings, substantial efforts are required not only at the hardware level but also on theoretical research to reduce the computational cost of a given protocol. Quantum computation has the potential to significantly enhance existing classical machine learning methods, and several quantum algorithms for binary classification based on the kernel method have been proposed. These algorithms rely on estimating an expectation value, which in turn requires an expensive quantum data encoding procedure to be repeated many times. In this work, we calculate explicitly the number of repetition necessary for acquiring a fixed success probability and show that the Hadamard-test and the swap-test circuits achieve the optimal variance in terms of the quantum circuit parameters. The variance, and hence the number of repetition, can be further reduced only via optimization over data-related parameters. We also show that the kernel-based binary classification can be performed with a single-qubit measurement regardless of the number and the dimension of the data. Finally, we show that for a number of relevant noise models the classification can be performed reliably without quantum error correction. Our findings are useful for designing quantum classification experiments under limited resources, which is the common challenge in the noisy intermediate-scale quantum era.
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