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arXiv:2006.12025 · Quantum Machine Intelligence

Quantum computing methods for supervised learning

Viraj Kulkarni, Milind Kulkarni, Aniruddha Pant

Published Sep 6, 2021• 38 citations
arXivHTMLPDF
DOI
10.1007/s42484-021-00050-0

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An overarching milestone of quantum machine learning (QML) is to demonstrate the advantage of QML over all possible classical learning methods in accelerating a common type of learning task, as represented by supervised learning from classical data. However, the provable advantages of QML in supervised learning have been known so far only for the learning tasks designed for using the advantage of specific quantum algorithms, i.e., Shor’s algorithms. Here, we explicitly construct an unprecedentedly broader family of supervised learning tasks with classical data to offer the provable advantage of QML based on general quantum computational advantages, progressing beyond Shor’s algorithms. Our learning task is feasibly achievable by executing a general class of functions that can be computed efficiently in polynomial time for a large fraction of inputs by arbitrary quantum algorithms, but not by any classical algorithm. We prove the hardness of achieving this learning task for any possible polynomial-time classical learning method. We also clarify protocols for preparing the classical data to demonstrate this learning task in experiments. These results provide a way to exploit a variety of quantum advantages in computing functions for the realization of provably advantageous QML.
Abstract Quantum machine learning has the potential to improve traditional machine learning methods and overcome some of the main limitations imposed by the classical computing paradigm. However, the practical advantages of using quantum resources to solve pattern recognition tasks are still to be demonstrated. This work proposes a universal, efficient framework that can reproduce the output of a plethora of classical supervised machine learning algorithms exploiting quantum computation’s advantages. The proposed framework is namedMultiple Aggregator Quantum Algorithm(MAQA) due to its capability to combine multiple and diverse functions to solve typical supervised learning problems. In its general formulation, MAQA can be potentially adopted as the quantum counterpart of all those models falling into the scheme of aggregation of multiple functions, such as ensemble algorithms and neural networks. From a computational point of view, the proposed framework allows generating an exponentially large number of different transformations of the input at the cost of increasing the depth of the corresponding quantum circuit linearly. Thus, MAQA produces a model with substantial descriptive power to broaden the horizon of possible applications of quantum machine learning with a computational advantage over classical methods. As a second meaningful addition, we discuss the adoption of the proposed framework as hybrid quantum–classical and fault-tolerant quantum algorithm.