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

TL;DR

This paper extends the approximate amplitude encoding method to handle complex-valued data vectors using a fidelity-based optimization approach, enabling quantum data classification tasks on near-term devices.

Contribution

It introduces a novel extension of AAE for complex data, utilizing fidelity as a cost function and classical shadow techniques for efficient optimization.

Findings

Successfully applied to Iris dataset classification

Enabled credit card fraud detection with quantum classifier

Demonstrated feasibility on near-term quantum devices

Abstract

Quantum computing has a potential to accelerate the data processing efficiency, especially in machine learning, by exploiting special features such as the quantum interference. The major challenge in this application is that, in general, the task of loading a classical data vector into a quantum state requires an exponential number of quantum gates. The approximate amplitude encoding (AAE) method, which uses a variational means to approximately load a given real-valued data vector into the amplitude of a quantum state, was recently proposed as a general approach to this problem mainly for near-term devices. However, AAE cannot load a complex-valued data vector, which narrows its application range. In this work, we extend AAE so that it can handle a complex-valued data vector. The key idea is to employ the fidelity distance as a cost function for optimizing a parameterized quantum circuit, where the classical shadow technique is used to efficiently estimate the fidelity and its gradient. We apply this algorithm to realize the complex-valued-kernel binary classifier called the compact Hadamard classifier, and then give a numerical experiment showing that it enables classification of Iris dataset and credit card fraud detection.