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Quantum computing has a potential to accelerate the data processingefficiency, especially in machine learning, by exploiting special features suchas the quantum interference. The major challenge in this application is that,in general, the task of loading a classical data vector into a quantum staterequires an exponential number of quantum gates. The approximate amplitudeencoding (AAE) method, which uses a variational means to approximately load agiven real-valued data vector into the amplitude of a quantum state, wasrecently proposed as a general approach to this problem mainly for near-termdevices. However, AAE cannot load a complex-valued data vector, which narrowsits application range. In this work, we extend AAE so that it can handle acomplex-valued data vector. The key idea is to employ the fidelity distance asa cost function for optimizing a parameterized quantum circuit, where theclassical shadow technique is used to efficiently estimate the fidelity and itsgradient. We apply this algorithm to realize the complex-valued-kernel binaryclassifier called the compact Hadamard classifier, and then give a numericalexperiment showing that it enables classification of Iris dataset and creditcard fraud detection.

Approximate complex amplitude encoding algorithm and its application to data classification problems