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Credit: *Light: Science and Applications* (2024). DOI: 10.1038/s41377-024-01376-7

In recent years, artificial intelligence technologies, especially machine learning algorithms, have made great advances. These technologies have enabled unprecedented efficiency in tasks such as image recognition, natural language generation and processing, and object detection, but this exceptional functionality requires substantial computational power as a foundation.

Current computing resources are approaching their limit, therefore, effectively reducing the training cost of machine learning models and improving their training efficiency is an important issue in the field of research.

To solve the problem, great efforts have been made in two research directions: optical neural networks and quantum neural networks. Optical neural networks utilize advanced optical manipulation methods to execute machine learning algorithms in classical optical information processing. They have unique advantages such as low power consumption, low crosstalk, and low transmission latency. However, current optical neural networks do not feature algorithmic acceleration such as faster model convergence speed.

Quantum neural networks are neural network algorithms based on quantum computing theory. Recent research has shown that quantum neural networks can demonstrate algorithmic speedup due to quantum correlations. However, due to technical limitations, it is currently difficult to run such neural network algorithms on large-scale hardware, making them difficult to apply to practical problems faced by people today.

In a new article published in *Light: Science and Applications*, a team of scientists, led by Professor Xiangdong Zhang, from the Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements of the Ministry of Education; The Beijing Key Laboratory of Nanophotonics and Ultrathin Optoelectronic Systems, School of Physics, Beijing Institute of Technology, China, and coworkers have developed a new type of optical neural network that can exhibit acceleration analogous to a quantum neural network.

This interesting property arises due to the introduction of classical optical correlations as carriers of information. In fact, by using this type of carrier, one can imitate the way of processing information made possible by quantum computing, which has been proven by previous work by researchers.

Based on the property, researchers developed the convolutional and pooling operation on the correlated optical state and established a correlated optical convolutional neural network. This optical neural network has a one-to-one correspondence with the quantum convolutional neural network. It shows the acceleration of the training process in learning certain data sets and can be applied to identify the character of quantum states under a specific coding principle.

The reported method and technique will open new avenues for realizing algorithmically enhanced optical neural networks, which will benefit information processing in the era of big data.

The basic structure of a correlated optical convolutional neural network includes four parts: the correlated light source, the convolution, the clustering, and the detections. The core processing of the correlated optical state is done by the convolution and pooling part. Unlike classical convolutional neural networks, these two parts of the correlated convolutional optical neural network manipulate the correlation of optical states and generate the simplest correlated states by merging the beams.

“These two parts actually perform operations analogous to quantum gates in quantum convolutional neural networks,” the scientists said. “The convolution part of our network is composed of unitary operations on the correlated optical state.

“It is like the unitary operations in the Hilbert space of qubits. The grouping part we consider is equivalent to measuring partial qubits to obtain a sub-Hilbert space. Such a part leads to an exponential decrease in the dimension of the data. Therefore, the function of both parts contributes to faster convergence of the loss function when learning certain datasets.

“In addition, we also certified the similarity of our correlated optical convolutional neural network with the quantum convolutional neural network by performing topological phase identification of quantum states. The certification is supported by theoretical and experimental results.

“The results also indicate that the properties of the quantum neural network can be realized in a more accessible way,” they added.

“Despite the potential advantages of quantum neural networks, implementing them practically requires deep quantum circuits with many multi-qubit gates and complicated measurements. This requires significant resources to stabilize the circuits and correct errors, which is technically challenging due to the inevitable environmental disturbances .

“A potentially better alternative is to find a system described by the same mathematics as quantum theory and less disrupted by the environment. The proposed correlated optical neural networks serve as an example of such a system, as evidenced by the ease of element arrangements and low requirements on the circumstances in our experiments.

“Given the exponential growth of data and the scarcity of resources for high-quality computing, our approach presents a cost-effective, high-performance solution that could have widespread applications across multiple fields of data science research.”

**More information:**

Yifan Sun et al, Correlated optical convolutional neural network with “quantum acceleration”, *Light: Science and Applications* (2024). DOI: 10.1038/s41377-024-01376-7

**Diary information:**

Light: Science and Applications