Enhancing the expressivity of quantum neural networks with residual connections

• DOI: 10.1038/s42005-024-01719-1
• Publication Date: 2024-07-06T04:01:47Z
• Authors: Jingwei Wen; Zhiguo Huang; Dunbo Cai; Ling Qian
• Keywords: QB460-466; Quantum Physics; Physics; QC1-999; Astrophysics

Abstract In noisy intermediate-scale quantum era, the research on combination of artificial intelligence and computing has been greatly developed. Here we propose a circuit-based algorithm to implement residual neural networks, where connection channels are constructed by introducing auxiliary qubits data-encoding trainable blocks in networks. We prove that when this particular network architecture is applied l -layer data-encoding, number frequency generation forms extends from one, namely difference sum generator eigenvalues, $${{{{{{{\mathcal{O}}}}}}}}({l}^{2})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:msup> <mml:mi>l</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:math> , flexibility adjusting Fourier coefficients can also be improved. It indicates encoding achieve better spectral richness enhance expressivity various parameterized circuits. Extensive numerical demonstrations regression tasks image classification offered. Our work lays foundation for complete implementation classical networks offers feature map strategy machine learning.