Robust optimal quantum learning without quantum memory

TL;DR

This paper introduces a quantum learning machine for binary classification of qubit states that operates without quantum memory, achieving optimal error rates, robustness to noise, and efficient classical memory usage, outperforming traditional estimate-and-discriminate methods.

Contribution

It presents a novel quantum learning machine that does not require quantum memory and maintains optimal performance under noise and data variations.

Findings

Achieves minimum error rate for any training set size.

Robust against noise and training set variations.

Uses only logarithmic classical memory relative to training qubits.

Abstract

A quantum learning machine for binary classification of qubit states that does not require quantum memory is introduced and shown to perform with the minimum error rate allowed by quantum mechanics for any size of the training set. This result is shown to be robust under (an arbitrary amount of) noise and under (statistical) variations in the composition of the training set, provided it is large enough. This machine can be used an arbitrary number of times without retraining. Its required classical memory grows only logarithmically with the number of training qubits, while its excess risk decreases as the inverse of this number, and twice as fast as the excess risk of an estimate-and-discriminate machine, which estimates the states of the training qubits and classifies the data qubit with a discrimination protocol tailored to the obtained estimates.