The curse of random quantum data

TL;DR

This paper investigates how random quantum data negatively impact quantum machine learning performance, revealing an exponential suppression in efficiency and generalization, and suggests that careful data design can mitigate these issues.

Contribution

It introduces the concept of the 'curse of random quantum data' and demonstrates how data randomness hampers quantum ML, providing insights for dataset design to improve performance.

Findings

Random quantum data exponentially suppresses training efficiency.

Generalization capabilities are hindered by data randomness.

Careful dataset design can overcome these limitations.

Abstract

Quantum machine learning, which involves running machine learning algorithms on quantum devices, may be one of the most significant flagship applications for these devices. Unlike its classical counterparts, the role of data in quantum machine learning has not been fully understood. In this work, we quantify the performances of quantum machine learning in the landscape of quantum data. Provided that the encoding of quantum data is sufficiently random, the performance, we find that the training efficiency and generalization capabilities in quantum machine learning will be exponentially suppressed with the increase in the number of qubits, which we call "the curse of random quantum data". Our findings apply to both the quantum kernel method and the large-width limit of quantum neural networks. Conversely, we highlight that through meticulous design of quantum datasets, it is possible to avoid these curses, thereby achieving efficient convergence and robust generalization. Our conclusions are corroborated by extensive numerical simulations.