Exponential data encoding for quantum supervised learning

TL;DR

This paper introduces exponential-data-encoding strategies for quantum supervised learning that are resource-efficient and capable of expressing complex functions with fewer gates, outperforming classical methods in certain scenarios.

Contribution

The authors propose a novel exponential-data-encoding scheme that is hardware-efficient, optimal among non-entangling schemes, and demonstrates practical resource advantages in quantum learning.

Findings

Exponential-data encoding reduces quantum resource requirements.

Such encoding can express functions beyond classical capabilities with limited training modules.

Numerical results show effective learning of molecular and housing data.

Abstract

Reliable quantum supervised learning of a multivariate function mapping depends on the expressivity of the corresponding quantum circuit and measurement resources. We introduce exponential-data-encoding strategies that are hardware-efficient and optimal amongst all non-entangling Pauli-encoded schemes, which is sufficient for a quantum circuit to express general functions having very broad Fourier frequency spectra using only exponentially few encoding gates. We show that such an encoding strategy not only reduces the quantum resources, but also exhibits practical resource advantage during training in contrast with known efficient classical strategies when polynomial-depth training circuits are also employed. When computation resources are constrained, we numerically demonstrate that even exponential-data-encoding circuits with single-layer training modules can generally express functions that lie outside the classically-expressible region, thereby supporting the practical benefits of such a resource advantage. Finally, we illustrate the performance of exponential encoding in learning the potential-energy surface of the ethanol molecule and California's housing prices