VQRC: Variational Quantum Residual Compensation for Deep Neural Network Compression

Abstract

The continuous scaling of neural networks improves representation capacity but imposes prohibitive storage, memory bandwidth, and energy costs during deployment. To address the accuracy degradation inherent in aggressive low-bit model compression, this paper proposes Variational Quantum Residual Compensation (VQRC), a novel hybrid quantum-classical post-quantization repair framework. VQRC structurally decouples primary weight storage from quantization error recovery. Specifically, pre-trained weight matrices are first partitioned into localized blocks and compressed via independent symmetric INT4 quantization, establishing a highly compact storage backbone. Subsequently, VQRC isolates the exact mathematical residual between the full-precision weights and the INT4 base, deploying Variational Quantum Singular Value Decomposition (VQSVD) to extract and repair the dominant low-rank error structures. Extensive experiments demonstrate that VQRC effectively reduces quantization error (-21.79% average MSE) and recovers classification accuracy (+0.56 percentage points), all while maintaining a robust 2.96× overall weight compression ratio. This establishes VQRC as an efficient, architecture-agnostic approach for mitigating low-bit quantization loss using near-term quantum algorithms.