As the next generation of advanced computing technology, quantum computers are on the brink of practical application. A landmark milestone was Google’s demonstration of quantum supremacy in 2019 using a 54-qubit superconducting quantum processor [1]. Since then, how to utilize quantum computing devices to solve real-world problems and achieve performance surpassing classical computers under existing hardware conditions has become one of the core issues in the field of quantum computing. To achieve this goal, variational quantum algorithms (VQAs) composed of quantum neural networks and classical optimizers have emerged. Although experimental researchers have demonstrated the feasibility of using VQAs to solve quantum chemistry and machine learning tasks, surpassing classical methods [2-4], the current capabilities of VQAs face two challenging problems: first, the optimization gradient information in VQAs disappears exponentially with the increase in the number of qubits and circuit depth [5]; furthermore, systematic errors in quantum computers accumulate with the increase in the number of qubits and circuit depth. These factors severely inhibit the performance of VQAs. Therefore, overcoming these challenges is of utmost importance for the large-scale and practical implementation of VQAs.
Figure 1 | Basic flowchart of QAS
To address the above issues, the quantum machine learning team at JD Explore Academy, in collaboration with the University of Sydney, Hon Hai Quantum Research Institute, and SenseTime, published a research article titled “Quantum circuit architecture search for variational quantum algorithms” in the Nature Portfolio journal npj Quantum Information. This research first proposed an efficient automated quantum neural network search scheme—quantum architecture search (QAS). As shown in Figure 1, QAS constructs all possible quantum neural network structures based on specified basic operational units within the quantum neural network and outputs superior quantum network neural structures and corresponding training parameters based on hardware topology, noise influence, and optimization performance. It is noteworthy that the number of structures of quantum neural networks often grows exponentially with the number of qubits and circuit depth, making it extremely challenging for QAS to search for superior quantum network neural structures among exponentially many possibilities. To this end, QAS significantly enhances learning performance by unifying the two independent issues of noise suppression and training performance, introducing weight sharing and a mixture of experts strategy, while maintaining computation time comparable to traditional VQAs.
Figure 2 | Performance comparison of QAS and traditional VQAs in classification tasks. (a) Visualization of classification data. (b) Traditional quantum classifier. (c) Quantum neural network structure output by QAS after training. (d) Performance of QAS under different iteration counts and number of experts. (e) Performance comparison of QAS under ideal and noisy environments. (f) Performance evaluation of QAS on the test set.
In experiments, QAS has achieved performance surpassing traditional VQAs in both machine learning and quantum chemistry tasks. As shown in Figure 2 (f), when using a noisy quantum device to solve a synthetic data binary classification task, the classification accuracy of the traditional quantum classifier is only 50%, while the quantum neural network output by QAS and its corresponding parameters can achieve 100% accuracy. Additionally, as shown in Figure 2 (d)–(e), by increasing the number of experts (W) and iteration counts (Epc), the performance of QAS can be continuously improved. When W=5 and Epc=400, a total of 151 quantum neural network structures and corresponding training parameters can achieve over 90% accuracy. For quantum chemistry tasks, we deployed both VQAs and QAS on the IBMQ quantum cloud’s 5-qubit quantum computer to approximate the ground state energy of the hydrogen atom. As shown in Figure 3, the relative errors of the quantum neural networks designed by conventional VQAs and QAS in this task are 36.1% and 6.8%, respectively. Furthermore, by increasing the number of experts (W), QAS can continuously improve its performance in the ground state energy estimation task. These experimental results provide evidence for the efficiency of QAS.
Figure 3 | Performance comparison of QAS and traditional VQAs in the ground state energy estimation task of the hydrogen atom. The left graph’s x-axis represents the number of iterative optimizations, and the y-axis represents the estimated ground state energy. The “cross” marks represent the estimated energy of VQAs and QAS on the IBMQ quantum computer. The right graph evaluates the performance of QAS under different numbers of experts in ideal and noisy environments.
The proposal of QAS opens up a new direction for integrating automated model design in deep learning with quantum computing, which not only allows VQAs to be compatible with various quantum hardware systems (such as superconducting quantum systems, ion trap systems, optical quantum systems, etc.), but also enables the efficient design of quantum neural networks tailored to specific problems, significantly enhancing the performance of VQAs. These features provide strong support for quantum computers to solve large-scale machine learning, quantum chemistry, and combinatorial optimization problems. The relevant code for this research has been open-sourced [6] to assist related researchers in further advancing the frontier exploration of quantum artificial intelligence.
References:
[1] Arute, Frank, et al. “Quantum supremacy using a programmable superconducting processor.” Nature574.7779 (2019): 505-510.
[2] Google AI Quantum. Hartree-Fock on a superconducting qubit quantum computer[J]. Science, 2020, 369(6507): 1084-1089.
[3] Havlíček, Vojtěch, et al. “Supervised learning with quantum-enhanced feature spaces.” Nature567.7747 (2019): 209-212.
[4] Huang, H. L., Du, Y., Gong, M., Zhao, Y., Wu, Y., Wang, C., … & Pan, J. W. (2021). Experimental quantum generative adversarial networks for image generation. Physical Review Applied,16(2), 024051.
[5] McClean, Jarrod R., et al. “Barren plateaus in quantum neural network training landscapes.” Nature communications9.1 (2018): 1-6.
[6] https://github.com/yuxuan-du/Quantum_architecture_search/.
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npj Quantum Information | doi: 10.1038/s41534-022-00570-y
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Quantum circuit architecture search for variational quantum algorithms
