Experimental Learning of Pure Quantum States using Sequential Single-Shot Measurement Outcomes

TL;DR

This paper presents an experimental machine-learning approach called single-shot measurement learning for accurately identifying unknown pure quantum states, achieving near-optimal infidelity without complex tomography.

Contribution

It introduces a novel, experimentally validated method that uses weighted randomness to optimize quantum state learning with minimal computational effort.

Findings

Achieved infidelity of O(N^{-0.983}) in experiments

Demonstrated high accuracy in quantum state reproduction

Validated the method using linear-optics setup with single-photon qubits

Abstract

We experimentally implement a machine-learning method for accurately identifying unknown pure quantum states. The method, called single-shot measurement learning, achieves the theoretical optimal accuracy for $\epsilon = O(N^{-1})$ in state learning and reproduction, where $\epsilon$ and $N$ denote the infidelity and number of state copies, without employing computationally demanding tomographic methods. This merit results from the inclusion of weighted randomness in the learning rule governing the exploration of diverse learning routes. We experimentally verify the advantages of our scheme by using a linear-optics setup to prepare and measure single-photon polarization qubits. The experimental results show highly accurate state learning and reproduction exhibiting infidelity of $O(N^{-0.983})$ down to $10^{-5}$, without estimation of the experimental parameters.