Native linear-optical protocol for efficient multivariate trace estimation

TL;DR

This paper introduces a photon-native linear-optical protocol for efficiently estimating multivariate traces of quantum states, with applications in quantum information processing and machine learning.

Contribution

It presents a novel, sample-efficient linear-optical protocol for multivariate trace estimation, extending the capabilities of quantum state analysis.

Findings

Protocol is sample-efficient.

Applicable to quantum kernel estimation.

Useful for characterizing multiphoton indistinguishability.

Abstract

The Hong-Ou-Mandel test estimates the overlap between spectral functions characterizing the internal degrees of freedom of two single photons. It can be viewed as a photon-native protocol that implements the well-known quantum SWAP test. Here, we propose a native linear-optical protocol that efficiently estimates multivariate traces of quantum states called Bargmann invariants, which are ubiquitous in quantum mechanics. Our protocol may be understood as a photon-native version of the cycle test in the circuit model, which encompasses many-photon multimode quantum states. We show the protocol is sample-efficient and discuss applications, such as generalized suppression laws, efficient quantum kernel estimation for quantum machine learning, eigenspectrum estimation, and the characterization of multiphoton indistinguishability.