Researchers from the University of Science and Technology of China, led by Academics Guoguangcan Guo, Chuanfeng Li, Xiaoye Xu, and Yongjian Han, in collaboration with Shaojun Dong from the Hefei Comprehensive National Science Center and Wenkang Wang from Southern University of Science and Technology, have harnessed artificial neural networks to effectively represent mixed quantum states in open systems. By innovating the natural gradient descent algorithm, they have significantly enhanced the training efficiency of neural networks, achieving a high-fidelity reconstruction of mixed quantum states in an open-system quantum walk with an intrinsically high-dimensional structure. Their findings were published in Science Advances on March 15.
Quantum walks have gained significant research interest in quantum simulation and quantum computing. Fully exploiting the computational and simulation capabilities of open quantum walks necessitates a comprehensive characterization of their evolutionary states. However, conventional state tomography methods are not applicable to open quantum systems of considerable scale. Therefore, efficiently characterizing mixed quantum states remains a significant challenge in various experimental systems.
Recent theoretical proposals have explored using artificial neural networks to learn open quantum systems. However, as the system scale expands, neural networks require increasingly complex structures to maintain their expressive power over mixed quantum states. Directly applying this method to reconstruct the evolutionary states of large-scale open quantum walks thus encounters intricate network training issues.
In this work, the research team constructed a novel interferometric setup to significantly increase the measurement basis and established a mapping between the open quantum walk system and a restricted Boltzmann machine network model. Simultaneously, they developed a novel gradient optimization algorithm to efficiently train the neural network, ultimately enabling the effective representation of mixed quantum states in an open quantum walk system of considerable scale. Compared to traditional state tomography methods, this efficient neural network state tomography utilizes only a fraction of the required measurements to reconstruct mixed quantum states with high fidelity.
To augment the neural network training data, the research team introduced an unequal-arm interferometer in the time domain on their previously constructed large-scale photonic quantum walk experimental system, realizing interference measurements between different lattice sites and considerably increasing the measurement basis.
Their results demonstrate that neural network techniques can achieve an average fidelity of 97.5% in fully characterizing the mixed quantum state of an open photonic quantum walk using only 50% of the measurement basis compared to conventional state tomography methods.
Furthermore, to enhance the training efficiency of complex neural networks, the research team devised a more effective generalized natural gradient descent algorithm by identifying a suitable new metric based on the natural gradient descent algorithm. Their findings indicate that neural networks trained with the new algorithm can reduce the number of training iterations by an order of magnitude compared to traditional gradient descent algorithms. Additionally, it effectively avoids the influence of local minima, allowing the loss function to reach lower values and significantly improving the reconstruction fidelity.
The researchers believe that this efficient neural network mixed quantum state tomography method unlocks new possibilities for the wider application of open quantum walks and lays the groundwork for further exploration of noise-assisted quantum computing and quantum simulation.
