Machine learning of quantum data using optimal similarity measurements

TL;DR

This paper presents a hardware-efficient, sample-optimal protocol for estimating quantum state similarity using bosonic interference, enabling scalable quantum data analysis and machine learning.

Contribution

The authors introduce a novel, experimentally demonstrated method for directly measuring quantum state overlap that is both sample-optimal and hardware-efficient, advancing quantum machine learning capabilities.

Findings

Sample complexity is independent of system dimension.

Experimental implementation on a photonic platform achieved high-accuracy quantum data classification.

Demonstrated practical quantum data analysis in noisy conditions.

Abstract

Quantum machine learning seeks a computational advantage in data processing by evaluating functions of quantum states, such as their similarity, that can be classically intractable to compute. For quantum advantage to be possible, however, it is essential to bypass costly characterisation of individual data instances in favour of efficient, direct similarity evaluation. Here we demonstrate a sample-optimal, hardware-efficient protocol for estimating quantum similarity -- the state overlap -- using bosonic quantum interference. The sample complexity of this approach is independent of the system dimension and is information-theoretically optimal up to a constant factor. Experimentally, we implement the scheme on \emph{Prakash-1}, a quantum computing platform based on a fully programmable integrated photonic processor. By preparing and interfering qudit states on the chip to directly extract their overlap, we demonstrate classification and online learning of quantum data with high accuracy in realistic noisy experiments. Our results establish joint overlap measurements as a scalable pathway to efficient quantum data analysis and a practical building block for network-integrated quantum machine learning.