With the emergence of quantum computers, many different architectures have been proposed, which can provide advantages over classical architectures. Quantum Neural Network (QNN) is one of the most promising architectures, and its applications include physical simulation, optimization and more general machine learning tasks. Although QNN has great potential, it has been proved that it presents a "barren plateau", and the gradient of cost function disappears exponentially with the scale of the system, making it impossible for the architecture to train for large-scale problems.
Here, the Los Alamos National Laboratory (LANL) cooperated with researchers from the University of London to show that there is no barren plateau in a specific QNN building.
Researchers analyzed an architecture called Quantum Convolutional Neural Network (QCNN), which was recently proposed to solve the problem of quantum data classification. For example, QCNN can be trained to classify according to the relative quantum state of the substance. Moreover, researchers have proved that QCNN will not be affected by barren plateau, so they are highlighted as potential candidate architectures to achieve quantum superiority in the short term.
This research is called "There is no barren platform in quantum convection neural network" and published in Physical Review X of 202 1, 10, 15.
QNN has aroused people's interest around the possibility of effectively analyzing quantum data. However, this excitement is relieved by the existence of exponential disappearance gradients of many QNN structures (called barren plateau landscapes). Recently, QCNN is proposed, which involves a series of convolution layers and pool layers, and reduces the number of qubits while retaining the characteristic information of data.
QCNN schematic diagram
In this work, the researchers strictly analyzed the gradient scale of parameters in the QCNN architecture. It is found that the variance of gradient disappears faster than polynomial, which means that QCNN does not show barren plateau. This result provides an analytical guarantee for the trainability of QNN random initialization, and highlights the trainability of QNN random initialization. This is different from many other QNN buildings.
In order to get the results, the researchers introduced a new graph-based method to analyze the unitary expected value of Haar distribution; This may be useful in other situations; In addition, the researchers conducted a numerical simulation to verify the analysis results.
Tensor network representation of quantum cellular neural network.
As an artificial intelligence method, QCNN is inspired by the visual cortex. Therefore, they involve a series of convolution layers or filters, which are interleaved with aggregation layers to reduce the dimension of data while maintaining the important features of data sets. These neural networks can be used to solve a series of problems from image recognition to material discovery. Overcoming the barren plateau is the key to tap the full potential of quantum computer in artificial intelligence applications and show its superiority over classical computers.
Marco Cerezo (one of the co-authors of the paper) said that so far, researchers of quantum machine learning have analyzed how to reduce the impact of barren plateau, but they lack the theoretical basis to completely avoid this impact. LANL's work shows that some quantum neural networks are actually unaffected by the barren plateau.
"With this guarantee, researchers will now be able to screen quantum computer data about quantum systems and use this information to study material properties or discover new materials. Patrick Coles, a quantum physicist at LANL, said.
Coles believes that as researchers use the recent quantum computers more frequently and generate more and more data, the application of quantum artificial intelligence algorithms will be more-all machine learning programs need a lot of data.
GRIM module of QCNN architecture.
For more than 40 years, physicists have always believed that quantum computers will be proved to be able to simulate and understand the quantum system of particles, which will stifle the traditional classical computers. LANL's research proves that the robust quantum convolutional neural network type is expected to be applied to the analysis of quantum simulation data.
"The field of quantum machine learning started late. Coles said, "There is a famous saying about lasers. When it was first discovered, people said they were looking for a solution to the problem. Now lasers are used everywhere. Similarly, many of us doubt whether quantum data can become highly available, which may mean that quantum machine learning will also take off. 」
For example, Coles said that the research focus is on ceramic materials as high-temperature superconductors, which can improve frictionless transportation, such as maglev trains. However, it is an arduous task to analyze and classify a large number of phase data affected by temperature, pressure and impurities in materials. Using scalable quantum neural network, quantum computer can screen a large number of data sets about various states of a given material, and associate these states with them to determine the best state of high temperature superconductivity.
Arthur Pesah, the author of the paper, said: "With the vigorous development of QNN, we think it is very important to conduct similar analysis on other candidate architectures, and the technology developed in our work can be used as a blueprint for this analysis. 」
Paper link: https://journals.aps.org/prx/abstract/10.1103/physrevx.11.04164.
Related reports: https://phys.org/news/2021-kloc-0/0-breakthrough-proof-path-quantum-ai.html.