Quantum machine learning with adaptive linear optics

TL;DR

This paper explores the potential of adaptive linear optics in quantum machine learning, analyzing classical simulation limits and identifying conditions under which quantum advantage may be achievable.

Contribution

It introduces quantum subroutines using Boson Sampling with adaptive measurements and derives classical simulation regimes, clarifying the parameters needed for quantum advantage.

Findings

Classical simulability depends on the number of adaptive measurements and input photons.

Explicit limits are set on parameters for quantum advantage with adaptive linear optics.

Potential for near-term quantum advantage with a single adaptive measurement remains open.

Abstract

We study supervised learning algorithms in which a quantum device is used to perform a computational subroutine - either for prediction via probability estimation, or to compute a kernel via estimation of quantum states overlap. We design implementations of these quantum subroutines using Boson Sampling architectures in linear optics, supplemented by adaptive measurements. We then challenge these quantum algorithms by deriving classical simulation algorithms for the tasks of output probability estimation and overlap estimation. We obtain different classical simulability regimes for these two computational tasks in terms of the number of adaptive measurements and input photons. In both cases, our results set explicit limits to the range of parameters for which a quantum advantage can be envisaged with adaptive linear optics compared to classical machine learning algorithms: we show that the number of input photons and the number of adaptive measurements cannot be simultaneously small compared to the number of modes. Interestingly, our analysis leaves open the possibility of a near-term quantum advantage with a single adaptive measurement.