Low-Overhead Error-Corrected QCNNs Using Bivariate Bicycle Codes

Quantum convolutional neural networks combine quantum computing speedups with classical neural network architectures for classification tasks. However, state-of-the-art noisy intermediate-scale quantum devices suffer from high physical error rates caused by decoherence and gate noise, which degrades the training loss landscape and causes unprotected QCNNs to fail to converge. While standard surface codes provide error protection, their prohibitive qubit cost makes them inefficient. This paper investigates whether recently introduced bivariate bicycle codes can provide low-overhead quantum error correction to enable practical QCNN execution.

To address hardware noise in quantum machine learning, the authors propose integrating a distance-4 bivariate bicycle quantum error correction technique into a 4-qubit quantum convolutional neural network. The bivariate bicycle code is a type of Calderbank-Shor-Steane stabilizer code constructed from bivariate polynomials over a quotient ring, offering a constant encoding rate and linear code distance. The architecture embeds the QCNN within the error-corrected code space using periodic syndrome measurement circuits. Syndrome extraction outputs are then processed using belief perception with an ordered statistics postprocessing decoder to estimate and correct Pauli errors on data qubits without collapsing the quantum state.

Through hardware-realistic noise simulations, the authors demonstrate that an unprotected 4-qubit QCNN fails to converge and exhibits a degraded learning rate. In contrast, incorporating the distance-4 bivariate bicycle code successfully stabilizes the network, sustaining error correction under low additional qubit overhead while reducing learning loss and improving convergence. This validates bivariate bicycle codes as a viable pathway for running deep quantum circuits like QCNNs on near-term hardware.