Drastic Circuit Depth Reductions with Preserved Adversarial Robustness by Approximate Encoding for Quantum Machine Learning

Abstract

Quantum machine learning (QML) is emerging as an application of quantum computing with the potential to deliver quantum advantage, but its realization for practical applications remains impeded by challenges. Among these, a key barrier is the computationally expensive task of encoding classical data into a quantum state, which could erase any prospective speedups over classical algorithms. In this study, we implement methods for the efficient preparation of quantum states representing encoded image data using variational, genetic, and matrix product state algorithms. Our results show that these methods can approximately prepare states to a level suitable for QML using circuits 2 orders of magnitude shallower than a standard state preparation implementation, thus drastically reducing circuit depth and gate count without unduly sacrificing classification accuracy. Additionally, the QML models trained and evaluated on approximately encoded data displayed an increased robustness to adversarially generated input data perturbations. This partial alleviation of adversarial vulnerability, made possible by the retention of the meaningful large-scale features of the data despite the “drowning out” of adversarial perturbations, constitutes a considerable benefit for approximate state preparation in addition to lessening the requirements of the quantum hardware. Our results, based on simulations and experiments on IBM quantum devices, highlight a promising pathway for the future implementation of accurate and robust QML models on complex datasets relevant for practical applications, bringing the possibility of NISQ-era QML advantage closer to reality.