Quantum Latent Semantic Analysis

Bas C. van Fraassen

Marco Aurelio De Cunha

S. Kozhisseri, Илья Алексеевич Суров

The paper reports a method for compressed representation of matrix data on the principles of quantum theory. The method is formalized as complex-valued matrix factorization based on standard singular value decomposition. The developed approach establishes a bridge between standard methods of semantic data analysis and quantum models of cognition and decision. According to the quantum theory, real-valued observable quantities are generated by wavefunctions being complex-valued vectors in multidimensional Hilbert-space. Wavefunctions are defined as superpositions of basis vectors encoding composition of semantic factors. Basis vectors are found by singular value decomposition of the initial data matrix transformed to a real-valued amplitude form. Phase-dependent superposition amplitudes are found to optimize approximation of the source data. The resulting model represents the observed real-valued data as generated from a small number of basis wavefunctions superposed with complex-valued coefficients. The method is tested for random matrices of sizes from 3 × 3 to 12 × 12 and dimensionality of latent Hilbert-space from 2 to 4. The best approximation is achieved by encoding latent factors in normalized complex-valued amplitude vectors interpreted as wavefunctions generating the data. In terms of approximation fitness, the developed method surpasses standard truncated SVD of the same dimensionality. The mean advantage over the considered range of parameters is 22 %. The method permits cognitive interpretation in accord with the existing quantum models of cognition and decision. The method can be integrated in the algorithms of semantic data analysis including natural language processing. In these tasks, the obtained improvement of approximation translates to the increased precision of similarity measures, principal component analysis, advantage in classification, and document ranking methods. Integration with quantum models of cognition and decision is expected to boost methods of artificial intelligence and machine learning improving imitation of natural thinking.

Christopher J. Agostino, Q. Le Thien, Molly Apsel +3 more

Peiyuan Si, Liangxin Qian, Renyang Liu +2 more

Semantic communication (SemCom) has recently gained attention for its ability to achieve high transmission efficiency with minimal data distortion under limited communication resources. However, the strong correlation between source data and channel input leaves SemCom schemes vulnerable to eavesdropping. Additionally, advances in quantum computing threaten traditional cryptographic methods such as RSA due to Shor’s algorithm. To address these risks, a secure SemCom framework with post-quantum protection is essential. This paper presents a post-quantum secure semantic communication (PQSC) framework by integrating learning with errors (LWE) encryption (widely regarded as quantum-resistant) into a VQ-VAE-based SemCom system. The proposed PQSC framework not only resists quantum attacks but also defends against chosen-plaintext attacks. Experiments show that PQSC consistently outperforms baseline methods across various datasets, channel conditions, and SNR levels. To simulate practical wireless environments, we implement channel coding and modulation using Nvidia Sionna, a GPU-accelerated library for physical layer research. We further examine the trade-off between compression efficiency and computational cost. A downlink use case is modeled to analyze recovery quality, energy consumption, and latency. Our mathematical analysis offers insights into system design and parameter selection for real-world deployment.

Alеxander Raikov