Variational Quantum Machine Learning with Quantum Error Detection

Quantum machine learning (QML) is an emerging field that promises advantages such as faster training, improved reliability and superior feature extraction over classical counterparts. However, its implementation on quantum hardware is challenging due to the noise inherent in these systems, necessitating the use of quantum error correction (QEC) codes. Current QML research remains primarily theoretical, often assuming noise-free environments and offering little insight into the integration of QEC with QML implementations. To address this, we investigate the performance of a simple, parity-classifying Variational Quantum Classifier (VQC) implemented with the [[4,2,2]] error-detecting stabiliser code in a simulated noisy environment, marking the first study into the implementation of a QML algorithm with a QEC code. We invoke ancilla qubits to logically encode rotation gates, and classically simulate the logically-encoded VQC under two simple noise models representing gate noise and environmental noise. We demonstrate that the stabiliser code improves the training accuracy at convergence compared to noisy implementations without QEC. However, we find that the effectiveness and reliability of error detection is contingent upon keeping the ancilla qubit error rates below a specific threshold, due to the propagation of ancilla errors to the physical qubits. Our results provide an important insight: for QML implementations with QEC codes that both require ancilla qubits for logical rotations and cannot fully correct errors propagated between ancilla and physical qubits, the maximum achievable accuracy of the QML model is limited. This highlights the need for additional error correction or mitigation strategies to support the practical implementation of QML algorithms with QEC on quantum devices.