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Unlocking the Secrets of Gene Regulatory Networks with 'Quantum Hamiltonian Learning (QHL)' AI

inquantio

Published Jul 13, 2026• 0 citations
Publisher

Abstract

• 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.

DOI
10.5281/zenodo.21329038

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• 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 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.
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.
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)\text{Ry}(\pi \mathrm{x})Ry(πx)rotations, and models directed regulation with controlled-Ry (θ−{i→j})\left.\theta _{-}\{\mathbf{i} \rightarrow \mathbf{j}\}\right)θ−​{i→j})gates. Circuit parameters are trained by a hybrid classical-quantum loop (SPSA/COBYLA on Aer), and the learnedθ\thetaθvalues yield a weighted, directed GRN. Experiments on synthetic and curated immune-pathway datasets (4−8\mathbf{4 - 8}4−8genes) show consistent gains over strong classical baselines. The PQC achieves 95.2% accuracy, 94.8% precision, 95.6 % recall,F1=95.2%\mathrm{F} 1=95.2 \%F1=95.2%, andAUC=0.98\text{AUC}=0.98AUC=0.98, improving performance by 5-6 percentage points while requiring fewer samples to reach a given accuracy (≈90%\approx 90 \%≈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.
A study published on bioRxiv presents the first proof-of-concept workflow that combines non-linear autoencoders (deep representation learning) with the Quantum Approximate Optimization Algorithm (QAOA) to detect functional modules within biological networks. By training on cardiac (left ventricle) and skeletal muscle transcriptomic data into a 10-dimensional latent space, the research converts the module search problem into a Quadratic Unconstrained Binary Optimization (QUBO) problem mapped onto quantum circuits, precisely capturing the heterogeneous shapes of real biological modules. It demonstrates the potential for quantum computing-based system biology module discovery by achieving high-quality approximations of irregular, dense latent-space networks that are difficult for classical methods to resolve. [Quantum Biology Society] Understanding biological systems, where genes, proteins, and metabolites are intertwined in a vast web, is akin to the "Holy Grail" of modern medicine and biotechnology. While identifying functional modules responsible for specific disease mechanisms or regulatory circuits within these complex networks is a core task of systems biology, existing classical computing methods have faced exponential computational bottlenecks as network scales increase. Recently, an innovative, data-driven workflow combining deep learning and quantum optimization has been unveiled, opening a new chapter in network biology. The paper titled "Quantum Deep Learning Pipeline for Next Generation Network Biology," published on the preprint repository bioRxiv, offers a practical path toward solving these complexity issues using quantum computing. This innovative research was led by a team from the Gisma University of Applied Sciences in Germany, including Milad Yazdi, Kushala Ralpati Srinivas, and Ajay Yadav. ■ A Powerful Combination of Autoencoders and QAOA The research team first input vast transcriptomic data obtained from GTEx Normal datasets (Heart Left Ventricle, Muscle Skeletal, UCSC Xena Toil, etc.) into a non-linear autoencoder—a deep representation learning model—to compress them into a 10-dimensional latent space. After constructing a correlation graph of the complex latent data obtained from this process, they transformed the module discovery problem into a Quadratic Unconstrained Binary Optimization (QUBO) form that quantum circuits can interpret. The key to this approach was solving this optimization problem using the Quantum Approximate Optimization Algorithm (QAOA, depth d=3). ■ The Power of Quantum Computation in Capturing Irregular Modules Experimental results demonstrate that this QAOA-based quantum deep learning pipeline precisely captured the highly heterogeneous and irregular shapes of biological modules that are difficult for classical algorithms to identify. In particular, it successfully achieved high-quality approximations of dense latent-space network structures that are easily overlooked by conventional methods. This serves as significant evidence that quantum computing can surpass the limitations of classical computing architectures in handling the inherent non-linearity and complexity of biological data. ■ A Robust Foundation for Next-Generation Network Biology This achievement goes beyond mere improvements in algorithmic performance. By successfully bridging the data processing power of deep learning with the computational efficiency of quantum optimization, the study proves that quantum computing can contribute as a practical driving force in identifying complex disease mechanisms and precise biological regulatory circuits at the large-scale genomic level. It is evaluated as having established the most robust and scalable technical framework for future next-generation network biology research. https://www.biorxiv.org/content/10.1101/2025.10.28.685074v1
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.