Quantum error mitigation and correction mediated by Yang-Baxter equation and artificial neural network

Artificial error mitigation harmonizes classical and quantum computing, capitalizing on their individual strengths to offset weaknesses. Classical algorithms analyze and model errors in quantum computations, guiding corrective actions on quantum states to enhance reliability without the overhead of traditional error correction codes. This study demonstrates how machine learning and zero-noise extrapolation (ZNE) reduce quantum noise. ZNE faces challenges when generating noisy data for large quantum circuits and qubit systems. Focusing on quantum time dynamics (QTD) simulations, errors from unitary folding (a technique to generate noisy data in ZNE) can lead to undesired results. Also, implementing ZNE at each time step introduces significant overhead. Our solution uses artificial neural networks to master a subset of time steps and rectify the remaining dynamics. Leveraging the Yang-Baxter equation [1, 2, 3] for circuit compression provides control over depth and generates extra noise data without additional numerical errors.