Boolean networks are commonly used in systems biology to dynamically model gene regulatory interactions. Here, we present a protocol for implementing Boolean network dynamics as quantum circuits. We describe steps for accessing cloud-based quantum processing units offered by IBM and IonQ and downloading and parsing logic for gene regulatory networks. We then detail procedures for performing simulations of quantum circuits on local devices and visualizing measurement results. For complete details on the use and execution of this protocol, please refer to Weidner et al.1
Boolean networks are commonly used in systems biology to dynamically model gene regulatory interactions. Here, we present a protocol for implementing Boolean network dynamics as quantum circuits. We describe steps for accessing cloud-based quantum processing units offered by IBM and IonQ and downloading and parsing logic for gene regulatory networks. We then detail procedures for performing simulations of quantum circuits on local devices and visualizing measurement results. For complete details on the use and execution of this protocol, please refer to Weidner et al.1
• Published in the international journal Patterns, successfully implementing the dynamics of biological Boolean networks (BNs) on a real quantum processing unit (QPU). • Demonstrated the efficiency of utilizing quantum superposition states to compute gene knockout and overexpression perturbation experiments in a single ensemble operation. • Traced back the predecessors of an attractor using Grover's search algorithm and successfully estimated the basin size through quantum counting techniques. [Quantum Biology Society] When analyzing complex biological mechanisms such as intracellular gene expression or metabolic pathways, classical computers face the limitation of exponentially expanding state spaces to compute as the number of components (nodes) increases. Recently, an empirical study that groundbreakingly resolved this fundamental computational bottleneck in systems biology through quantum computing has been published, drawing significant attention. A paper titled "Leveraging quantum computing for dynamic analyses of logical networks in systems biology" was published in Patterns, a data science journal published by Cell Press. A joint research team, including Felix M. Weidner and Professor Hans A. Kestler from Ulm University in Germany, presented a groundbreaking proof of principle for implementing the dynamics of biological logical networks using qubits. ■ 'Quantum Superposition' Taming Exponential Expansion In biological Boolean networks (BNs), when there are n components, the number of states the entire system can have increases exponentially to 2ⁿ. Focusing on the fact that the dimension of the computational space of an entangled system of qubits also expands exponentially, the research team successfully matched the exponential growth of network states to a system of multiple qubits. In a 5-gene network experiment (Emx2, Pax6, Coup-tfi, Sp8, Fgf8) modeling the development of the mammalian cerebral cortex, the research team created a uniform superposition of all possible initial states using Hadamard gates. With just a single run of the quantum state transition circuit, they were able to simultaneously evaluate multiple classical state transitions and ultimately converge the system into an attractor state, which signifies a stable phenotype. ■ 'Quantum Perturbation' Experiments Instead of Genetic Scissors In traditional biological research, an enormous number of classical simulations are required to understand the impact of specific gene knockouts or overexpression. However, in a quantum network model, biologically meaningful stable state information can be efficiently extracted through algorithms that utilize quantum properties such as superposition. The research team processed combinations of perturbations of multiple genes in a single ensemble operation using superposition states, and successfully derived a more realistic basin size by weighting specific genes to reflect prior biological knowledge. ■ Tracing the Origins of Disease with Grover's Algorithm What is particularly notable is that by combining the characteristics of quantum circuits with Grover's search algorithm, they traced back the initial predecessors that caused a specific final phenotype (attractor). Furthermore, they successfully estimated the total number of states leading to that attractor using quantum counting techniques. Such quantum backtracking techniques can serve as highly powerful and practical analytical tools for inversely identifying the pathogenic pathways of complex metabolic diseases at the molecular network level and selecting key target proteins. ■ Going Beyond Simulators to Successfully Run on Real Quantum Hardware (QPU) This research did not stop at a simple theoretical proposal. The research team directly ran and demonstrated this biological quantum circuit while comparing the performance of two real quantum computers with classical simulators. This is evaluated as a major breakthrough proving that algorithms impossible to implement on classical hardware can be introduced to real quantum computers for the dynamic analysis of biological systems.
The dynamics of cellular mechanisms can be investigated through the analysis of networks. One of the simplest but most popular modeling strategies involves logic-based models. However, these models still face exponential growth in simulation complexity compared with a linear increase in nodes. We transfer this modeling approach to quantum computing and use the upcoming technique in the field to simulate the resulting networks. Leveraging logic modeling in quantum computing has many benefits, including complexity reduction and quantum algorithms for systems biology tasks. To showcase the applicability of our approach to systems biology tasks, we implemented a model of mammalian cortical development. Here, we applied a quantum algorithm to estimate the tendency of the model to reach particular stable conditions and further revert dynamics. Results from two actual quantum processing units and a noisy simulator are presented, and current technical challenges are discussed.
Describing gene interactions in cells is challenging due to their complexity and the limited microscopic detail available. Boolean networks offer a powerful, coarse-grained approach to modeling these dynamics using binary agents and their interactions. In this context, attractors-stable states of the system-are associated with biological phenotypes, making their identification biologically important. However, traditional computing struggles with the exponential growth of the state space in such models. Here, we present a novel quantum search algorithm for identifying attractors in synchronous Boolean networks, specifically designed for use on quantum computers. The algorithm iteratively suppresses known attractor basins, increasing the probability of detecting new ones. Unlike classical methods, it guarantees the discovery of a new attractor in each run. Early tests demonstrate strong resilience to noise on current NISQ (noisy intermediate-scale quantum) devices, marking a promising advance toward practical quantum-enhanced biological modeling.
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.
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.