Noise-tolerant parity learning with one quantum bit

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 new quantum parity learning algorithm with which the quantum advantage is retained as long as one qubit in the system has non-zero polarization. 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 non-local observables on the auxiliary result qubit having non-zero polarization and each data qubit. We also discuss the source of the quantum advantage in our algorithm from the resource-theoretic point of view.