Noise-tolerant parity learning with one quantum bit

TL;DR

This paper introduces a noise-tolerant quantum parity learning algorithm that maintains quantum advantage with minimal quantum resources, specifically requiring only one qubit with nonzero polarization per query.

Contribution

The work presents a novel quantum parity learning method that remains effective under noise by leveraging a single polarized qubit, advancing practical quantum learning algorithms.

Findings

Quantum advantage persists with one polarized qubit per query.

The algorithm becomes deterministic quantum computation with one qubit.

Hidden parity functions can be efficiently revealed through nonlocal measurements.

Abstract

Demonstrating quantum advantage with less powerful but more realistic devices is of great importance in modern quantum information science. Recently, a significant quantum speedup was achieved in the problem of learning a hidden parity function with noise. However, if all data qubits at the query output are completely depolarized, the algorithm fails. In this work, we present a quantum parity learning algorithm that exhibits quantum advantage as long as one qubit is provided with nonzero polarization in each query. In this scenario, the quantum parity learning naturally becomes deterministic quantum computation with one qubit. Then the hidden parity function can be revealed by performing a set of operations that can be interpreted as measuring nonlocal observables on the auxiliary result qubit having nonzero polarization and each data qubit. We also discuss the source of the quantum advantage in our algorithm from the resource-theoretic point of view.