Quantum Hamiltonian-Based Generative Modeling of Single-Cell Transcriptomics for Gene Regulatory Network Inference

Abstract:We introduce a novel quantum Hamiltonian-based gene expression model (QHGM), a generative framework for modeling pseudotime-ordered single-cell gene expression data. In QHGM, gene interactions are encoded via a parameterized Hamiltonian, and the outcomes of quantum measurements provide a discrete representation of the gene expression profile. To learn the Hamiltonian parameters and infer gene regulatory networks (GRNs), we develop a scalable variational quantum algorithm for network inference (VQ-Net) based on empirical risk minimization. We derive finite-sample recovery guarantees for accurate parameter estimation, demonstrating polynomial scaling with the number of genes. Experiments on synthetic data demonstrate accurate GRN recovery, with VQ-NET achieving over 25% improvement in edge recovery and over 50% improvement in parameter-sign recovery compared to state-of-the-art classical methods. We further apply the framework to glioblastoma scRNA-seq data, where it identifies biologically plausible regulatory interactions associated with cancer progression, highlighting the potential of quantum-like modeling beyond classical probabilistic frameworks.

Quantum Physics (quant-ph); Signal Processing (eess.SP)

arXiv:2602.19496 [quant-ph]

(or arXiv:2602.19496v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2602.19496 Focus to learn more arXiv-issued DOI via DataCite

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