New directions in quantum neural networks research

Wei CUI, Shilu YAN

School of Automation Science and Engineering,South China University of Technology,Guangzhou Guangdong 510640,China

With the development of quantum information technology,the performance highlighted by quantum computing represents the unparalleled superiority over the classical computing.As a new computing paradigm,it has attracted more and more attentions.Quantum theory and artificial neural networks have many essential intercommunication in solving problems.The fusion of these two fields forms the discipline of quantum neural networks[1,2],meanwhile,provides many research opportunities. Firstly, a number of recent works have used neural networks to study properties of quantum systems. Secondly, redefining and reconstructing more efficient neural networks based on quantum information theory have gradually aroused people’s interest.

In the former aspect,there are many complicated problems in quantum many-body systems[3].These problems often transcend the processing power of traditional exhaustive methods and logical programming methods. For example,simulating waves functions of quantum systems,identifying different quantum phases of matter,classifying different quantum states, and so on. In the general quantum many-body system, the Hilbert space dimension will increase exponentially to the system scale[3],which bring essential difficulties to the description and calculation of many-body wave functions of the quantum correlated systems,especially the strongly correlated system[1].As the neural network models show the ability to represent complex multivariable functions, it can be used to represent the association and entanglement of quantum many-body wave functions, and then calculate the wave functions generated by ground state[4,5]or quantum dynamics evolution[6-8].

The latest research shows that a new deep learning architecture,the Fermion neural network,can correctly solve the Schr¨odinger equation[9],which demonstrates that deep neural networks can outperform existing ab-initio methods,opening the possibility of accurate direct optimization of wave functions for previously intractable molecules and solids. For the classification problem, physicists have found that the neural network models can be trained to spontaneously discover and learn the concept of sequence parameters, and thus to identify the phases and phase transitions in condensed matter systems[10].Even if non-trivial topological quantum states cannot be characterized by local order parameters,physicists also have made a lot of attempts to learn these non-local topological information by training neural networks,including topological quantum numbers[11].In addition,neural networks can effectively learn and classify quantum states in the absence of complete information on quantum states[12],and accelerate the design and discovery of new materials[13,14].

However, the direct application of these classical neural networks algorithms is also challenging for some intrinsically quantum problems. Considering that the quantum neural networks have the advantages of exponential memory capacity and recall speed, as well as smaller network size and simple network topology, which provide tremendous opportunities for people to create extraordinary information processing systems,the quantum version of neural network is expected to propose a new learning model from the perspective of quantum physics and solves some key problems of classical neural networks,including a large amount of training data,a slow training process,and a gradient disappearance or explosion.

Reference [15] demonstrates that a quantum neural network model based on periodic activation functions only requires a quantum gate of complexity to simulate a classical neural network containing neurons. Reference [16]reveals that by encoding the network into the amplitudes of quantum states, an exponentially large network can be stored in a polynomial number of quantum bits, which may achieve exponential acceleration for the neural network of a particular model. Recently, a quantum convolutional neural network uses only O(log(N)) variational parameters for input sizes of n qubits, allowing for its efficient training and implementation on realistic, near-term quantum devices,which has been explicitly proved to recognize quantum states associated with a one-dimensional symmetry-protected topological phase,with performance surpassing existing approaches[1].And Google’s research shows that the unique characteristics of quantum geometry can clearly prevent the gradient problem from becoming a hindrance in the process of neural network training. This research on geometric state may provide a reliable strategy for the initialization and training of quantum neural networks in the future [17]. Moreover, if the training data consist of samples of measurements made on high-dimensional spaces, quantum adversarial networks may exhibit an exponential advantage over classical adversarial networks[18,19].

We list some of the recent research on quantum neural networks above and we are so glad to see that more and more researchers are working on these areas to contribute to the development of quantum technology and neural networks. We expect the convergence of these two areas will not only greatly accelerate the progress of quantum theory,but also deepen people’s understanding of many basic problems in the field of neural networks.