Can small quantum systems learn?

TL;DR

This paper investigates the limitations and possibilities of small quantum systems in learning tasks, especially Bayesian inference, showing that while some methods are impossible, new adaptive quantum approaches can outperform classical ones under certain conditions.

Contribution

The paper introduces a novel adaptive approximate quantum Bayesian inference method that is polynomially faster than classical methods and explores its relation to fault tolerance.

Findings

Lower bounds from Grover's search limit efficient blackbox updates.

The proposed quantum inference method is polynomially faster than classical counterparts.

Quantum systems with classical memory or error correction can effectively learn from their environment.

Abstract

We examine the question of whether quantum mechanics places limitations on the ability of small quantum devices to learn. We specifically examine the question in the context of Bayesian inference, wherein the prior and posterior distributions are encoded in the quantum state vector. We conclude based on lower bounds from Grover's search that an efficient blackbox method for updating the distribution is impossible. We then address this by providing a new adaptive form of approximate quantum Bayesian inference that is polynomially faster than its classical analogue and tractable if the quantum system is augmented with classical memory or if the low-order moments of the distribution are protected using a repetition code. This work suggests that there may be a connection between fault tolerance and the capacity of a quantum system to learn from its surroundings.