Abstract We introduce a novel quantum Hamiltonian-based gene expression model (QHGM), a generative frame-work 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.
Abstract We introduce a novel quantum Hamiltonian-based gene expression model (QHGM), a generative frame-work 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.
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.
• Published on bioRxiv, proposing the 'Quantum Hamiltonian-based gene-expression model (QHGM)' for Gene Regulatory Network (GRN) inference. • Treats genes as 'qubits', interpreting gene interactions over pseudotime by encoding them into quantum entanglement and Hamiltonian matrices. • Applied to glioblastoma (GBM) single-cell RNA sequencing data, successfully elucidating complex cancer cell developmental networks by overcoming the limitations of classical machine learning models. [Quantum Biology Society] Gene Regulatory Networks (GRNs), which determine the cell fate and phenotype of living organisms, are highly dynamic systems where numerous genes and proteins intricately entangle and interact. Despite the massive influx of data from recent advancements in single-cell RNA sequencing (scRNA-seq) technology, existing classical machine learning models have faced limitations in perfectly capturing the delicate context of biological regulation and non-classical probabilistic features. A recent study has been published that dramatically solves this challenge in systems biology through the 'Quantum Hamiltonian Learning (QHL)' framework, which infers the parameters of a many-body quantum system. The paper, titled "Quantum Hamiltonian Learning using Time-Resolved Measurement Data and its Application to Gene Regulatory Network Inference," published on the preprint repository bioRxiv, showcases an unconventional approach of modeling gene networks as macroscopic quantum systems. A joint research team, including Mohammad Aamir Sohail and Professor Arvind Rao from the University of Michigan, USA, led this innovative study. ■ Genes as Qubits, Regulatory Networks as Hamiltonians The 'Quantum Hamiltonian-based gene-expression model (QHGM)' proposed by the research team treats individual genes as qubits. The unexpressed state of a gene is defined as the basis state |0>, and the expressed state as |1>. Regulatory interactions, such as activation or repression between genes, are encoded as weights within a parameterized Hamiltonian matrix constructed using tensor products. Gene qubits, which initially start in independent separable states, evolve according to the Schrödinger equation along pseudotime, an indicator of cell development that acts as physical time. During this evolution process, complex correlations akin to quantum entanglement are formed between genes according to the interaction rules inputted into the Hamiltonian. ■ Combination of IC-POVM Measurements and VQ-Net AI To extract gene expression data from these entangled quantum states, the researchers introduced single-qubit IC-POVM, an informationally complete quantum measurement technique. These measurement results are linked to the discretized gene expression profiles observed in actual scRNA-seq data. Subsequently, the team developed VQ-Net, a variational quantum network inference algorithm based on a mini-batch empirical risk minimization framework. Based on the scRNA-seq data collected over pseudotime, this algorithm minimizes the negative log-likelihood loss and learns by inversely tracing the weight parameters of the Hamiltonian. ■ Elucidating the Glioblastoma (GBM) Network… Outperforming Classical Models This quantum-biology hybrid model did not stop at mere theory but was deployed in actual cancer research. By analyzing scRNA-seq data from patients with IDH-wild-type glioblastoma (GBM), a malignant brain tumor, the researchers inferred the gene regulatory program governing the differentiation of OPC-like cells. The analysis revealed that the QHGM model accurately pinpointed how core genes such as ASCL1, CDK4, and STMN1 interact with cell-cycle proliferation and extracellular matrix (ECM) components, identifying dense feedback loops and directionality consistent with biological literature. Notably, this method scales polynomially with system size, and recorded overwhelmingly higher accuracy and F1 scores in network edge recovery and weight sign identification than representative classical inference algorithms such as ARACNE, GENIE3, and GeneNet. This study is a groundbreaking achievement demonstrating how powerfully "quantum-like" modeling, which interprets complex biological systems using the mathematical tools of quantum information theory, can be utilized in analyzing actual clinical and multi-omics data. The researchers emphasized that this framework will provide crucial insights for understanding the heterogeneity and plasticity of cancer cells and discovering new therapeutic targets in the future.
Abstract In this work, we present a quantum circuit model for inferring gene regulatory networks (GRNs) from single-cell transcriptomic data. The model employs qubit entanglement to simulate interactions between genes, resulting in competitive performance and promising potential for further exploration. We applied our quantum GRN modeling approach to single-cell transcriptomic data from human lymphoblastoid cells, focusing on a small set of genes involved in innate immunity regulation. Our quantum circuit model successfully predicted the presence and absence of regulatory interactions between genes, while also estimating the strength of these interactions. We argue that the application of quantum computing in biology has the potential to provide a better understanding of single-cell GRNs by more effectively approaching the relationship between fully interconnected genes compared to conventional statistical methods such as correlation and regression. Our results encourage further investigation into the creation of quantum algorithms that utilize single-cell data, paving the way for future research into the intersection of quantum computing and biology.
Machine learning is widely regarded as a promising application in which quantum computing could offer a computational advantage. However, general quantum machine learning models with provable guarantees on performance, trainability, and efficient inference remain limited. In this work, we introduce quantum Hamiltonian embeddings, a supervised learning framework in which a classical training dataset is encoded into a single effective, parameterized Hamiltonian. Training optimizes the parameters of this data-dependent Hamiltonian, whose approximate ground state defines the classification rule. Once the ground state has been approximated using a quantum algorithm, inference can be performed either classically using a classical representation of the learned state, or with a quantum representation of the state. We establish efficient methods for gradient estimation and prove favorable generalization guarantees. Furthermore, under standard cryptographic assumptions, we show that Hamiltonian embeddings can realize hypothesis functions beyond the reach of efficient classical algorithms. We then demonstrate the framework at scale on IBM Heron processors using a standard benchmark dataset. Together, these results establish Hamiltonian embeddings as a new framework for quantum machine learning, combining theoretical guarantees with a path for experimental investigations at scale on quantum hardware.
Abstract In this work, we present a quantum circuit model for inferring gene regulatory networks (GRNs). The model is based on the idea of using qubit-qubit entanglement to simulate interactions between genes. We provide preliminary results that suggest our quantum GRN modeling method is competitive and warrants further investigation. Specifically, we present the results derived from the single-cell transcriptomic data of human cell lines, focusing on genes in involving innate immunity regulation. We demonstrate that our quantum circuit model can be used to predict the presence or absence of regulatory interactions between genes and estimate the strength and direction of the interactions, setting the stage for further investigations on how quantum computing finds applications in data-driven life sciences and, more importantly, to invite exploration of quantum algorithm design that takes advantage of the single-cell data. The application of quantum computing on single-cell transcriptomic data likewise contributes to a novel understanding of GRNs, given that the relationship between fully interconnected genes can be approached more effectively by quantum modeling than by statistical correlations.
Gene regulatory networks (GRNs) encode the combinatorial dependencies that drive cellular programs but are difficult to learn from CRISPR perturbation data using classical models with pairwise features. We present a parameterized quantum circuit (PQC) implemented in Qiskit that represents each gene as a qubit, encodes expression with single-qubitRy(πx)rotations, and models directed regulation with controlled-Ry (θ−{i→j})gates. Circuit parameters are trained by a hybrid classical-quantum loop (SPSA/COBYLA on Aer), and the learnedθvalues yield a weighted, directed GRN. Experiments on synthetic and curated immune-pathway datasets (4−8genes) show consistent gains over strong classical baselines. The PQC achieves 95.2% accuracy, 94.8% precision, 95.6 % recall,F1=95.2%, andAUC=0.98, improving performance by 5-6 percentage points while requiring fewer samples to reach a given accuracy (≈90%using only 50 % of the training set). Graph analysis of the inferred network ranks TP53, NFKB1, IL6, MAPK1, and VEGFA as top regulators, aligning with biological priors. We also evaluate sparse interaction topologies that reduce two-qubit depth while retaining accuracy, underscoring near-term hardware viability using Ry and CNOT-based decompositions. Our results provide an interpretable and data-efficient quantum blueprint for CRISPR-guided network inference and motivate larger-scale tests on real quantum devices. Code and circuits are available for reproducibility.